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[SOURCE: https://en.wikipedia.org/wiki/Texels] | [TOKENS: 446] |
Contents Texel (graphics) In computer graphics, a texel, texture element, or texture pixel is the fundamental unit of a texture map. Textures are represented by arrays of texels representing the texture space, just as other images are represented by arrays of pixels. Texels can also be described by image regions that are obtained through simple procedures such as thresholding. Voronoi tesselation can be used to define their spatial relationships—divisions are made at the midpoints between the centroids of each texel and the centroids of every surrounding texel for the entire texture. This results in each texel centroid having a Voronoi polygon surrounding it, which consists of all points that are closer to its own texel centroid than any other centroid. Rendering When texturing a 3D surface or surfaces (a process known as texture mapping), the renderer maps texels to appropriate pixels in the geometric fragment (typically a triangle) in the output picture. On modern computers, this operation is accomplished on the graphics processing unit. The texturing process starts with a location in space. The location can be in world space, but typically it is local to a model space so that the texture moves with the model. A projector function is applied to the location to change the location from a three-element vector ( ( x , y , z ) {\displaystyle \left(x,y,z\right)} ) to a two-element ( ( u , v ) {\displaystyle \left(u,v\right)} ) vector with values ranging from zero to one (uv). These values are multiplied by the resolution of the texture to obtain the location of the texel. When a texel is requested that is not on an integer position, texture filtering is applied. When a texel is requested that is outside of the texture, one of two techniques is used: clamping or wrapping. Clamping limits the texel to the texture size, moving it to the nearest edge if it is more than the texture size. Wrapping moves the texel in increments of the texture's size to bring it back into the texture. Wrapping causes a texture to be repeated; clamping causes it to be in one spot only. See also References |
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[SOURCE: https://en.wikipedia.org/wiki/Fixed_function_unit] | [TOKENS: 61] |
Glossary of computer graphics This is a glossary of terms relating to computer graphics. For more general computer hardware terms, see glossary of computer hardware terms. 0–9 A B C D E F G H I K L M N O P Q R S T U V W Z References |
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[SOURCE: https://en.wikipedia.org/wiki/Tile-based_deferred_rendering] | [TOKENS: 1086] |
Contents Tiled rendering Tiled rendering is the process of subdividing a computer graphics image by a regular grid in optical space and rendering each section of the grid, or tile, separately. The advantage to this design is that the amount of memory and bandwidth is reduced compared to immediate mode rendering systems that draw the entire frame at once. This has made tile rendering systems particularly common for low-power handheld device use. Tiled rendering is sometimes known as a "sort middle" architecture, because it performs the sorting of the geometry in the middle of the graphics pipeline instead of near the end. Basic concept Creating a 3D image for display consists of a series of steps. First, the objects to be displayed are loaded into memory from individual models. The system then applies mathematical functions to transform the models into a common coordinate system, the world view. From this world view, a series of polygons (typically triangles) is created that approximates the original models as seen from a particular viewpoint, the camera. Next, a compositing system produces an image by rendering the triangles and applying textures to the outside. Textures are small images that are painted onto the triangles to produce realism. The resulting image is then combined with various special effects, and moved into a frame buffer, which video hardware then scans to produce the displayed image. This basic conceptual layout is known as the display pipeline. Each of these steps increases the amount of memory needed to hold the resulting image. By the time it reaches the end of the pipeline the images are so large that typical graphics card designs often use specialized high-speed memory and a very fast computer bus to provide the required bandwidth to move the image in and out of the various sub-components of the pipeline. This sort of support is possible on dedicated graphics cards, but as power and size budgets become more limited, providing enough bandwidth becomes expensive in design terms. Tiled renderers address this concern by breaking down the image into sections known as tiles, and rendering each one separately. This reduces the amount of memory needed during the intermediate steps, and the amount of data being moved about at any given time. To do this, the system sorts the triangles making up the geometry by location, allowing to quickly find which triangles overlap the tile boundaries. It then loads just those triangles into the rendering pipeline, performs the various rendering operations in the GPU, and sends the result to the frame buffer. Very small tiles can be used, 16×16 and 32×32 pixels are popular tile sizes, which makes the amount of memory and bandwidth required in the internal stages small as well. And because each tile is independent, it naturally lends itself to simple parallelization. In a typical tiled renderer, geometry must first be transformed into screen space and assigned to screen-space tiles. This requires some storage for the lists of geometry for each tile. In early tiled systems, this was performed by the CPU, but all modern hardware contains hardware to accelerate this step. The list of geometry can also be sorted front to back, allowing the GPU to use hidden surface removal to avoid processing pixels that are hidden behind others, saving on memory bandwidth for unnecessary texture lookups. There are two main disadvantages of the tiled approach. One is that some triangles may be drawn several times if they overlap several tiles. This means the total rendering time would be higher than an immediate-mode rendering system. There are also possible issues when the tiles have to be stitched together to make a complete image, but this problem was solved long ago[citation needed]. More difficult to solve is that some image techniques are applied to the frame as a whole, and these are difficult to implement in a tiled render where the idea is to not have to work with the entire frame. These tradeoffs are well known, and of minor consequence for systems where the advantages are useful; tiled rendering systems are widely found in handheld computing devices. Tiled rendering should not be confused with tiled/nonlinear framebuffer addressing schemes, which make adjacent pixels also adjacent in memory. These addressing schemes are used by a wide variety of architectures, not just tiled renderers. Early work Much of the early work on tiled rendering was done as part of the Pixel Planes 5 architecture (1989). The Pixel Planes 5 project validated the tiled approach and invented a lot of the techniques now viewed as standard for tiled renderers. It is the work most widely cited by other papers in the field. The tiled approach was also known early in the history of software rendering. Implementations of Reyes rendering often divide the image into "tile buckets". Commercial products – Desktop and console Early in the development of desktop GPUs, several companies developed tiled architectures. Over time, these were largely supplanted by immediate-mode GPUs with fast custom external memory systems. Major examples of this are: Examples of non-tiled architectures that use large on-chip buffers are: Commercial products – Embedded Due to the relatively low external memory bandwidth, and the modest amount of on-chip memory required, tiled rendering is a popular technology for embedded GPUs. Current examples include: Tile-based immediate mode rendering (TBIM): Tile-based deferred rendering (TBDR): Vivante produces mobile GPUs which have tightly coupled frame buffer memory (similar to the Xbox 360 GPU described above). Although this can be used to render parts of the screen, the large size of the rendered regions means that they are not usually described as using a tile-based architecture. See also References |
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[SOURCE: https://en.wikipedia.org/wiki/Flight_simulation] | [TOKENS: 4578] |
Contents Flight simulator A flight simulator is a device that artificially re-creates aircraft flight and the environment in which it flies, for pilot training, design, or other purposes. It includes replicating the equations that govern how aircraft fly, how they react to applications of flight controls, the effects of other aircraft systems, and how the aircraft reacts to external factors such as air density, turbulence, wind shear, cloud, precipitation, etc. Flight simulation is used for a variety of reasons, including flight training (mainly of pilots), the design and development of the aircraft itself, and research into aircraft characteristics and control handling qualities. The term "flight simulator" may carry slightly different meaning in general language and technical documents. In past regulations, it referred specifically to devices which can closely mimic the behavior of aircraft throughout various procedures and flight conditions. In more recent definitions, this has been named "full flight simulator". The more generic term "flight simulation training device" (FSTD) is used to refer to different kinds of flight training devices, and that corresponds more closely to meaning of the phrase "flight simulator" in general English. History of flight simulation In 1910, on the initiative of the French commanders Clolus and Laffont and Lieutenant Clavenad, the first ground training aircraft for military aircraft were built. The "Tonneau Antoinette" (Antoinette barrel), created by the Antoinette company, seems to be the precursor of flight simulators. An area of training was for air gunnery handled by the pilot or a specialist air gunner. Firing at a moving target requires aiming ahead of the target (which involves the so-called lead angle) to allow for the time the bullets require to reach the vicinity of the target. This is sometimes also called "deflection shooting" and requires skill and practice. During World War I, some ground-based simulators were developed to teach this skill to new pilots. The Flying Scooters originated in the 1920s and 1930s as a flight training device, later became an amusement ride was developed by Alvin Bisch and his partner, Ralph Rocco. They applied for a patent for a “Device to train aviators or for amusement purposes” in 1929.. When in operation, a motor causes the arms to spin, with centrifugal forces causing the ride vehicles to fly outwards. Each ride vehicle is equipped with a large rudder, allowing riders to control the motion of their vehicle. The best-known early flight simulation device was the Link Trainer, produced by Edwin Link in Binghamton, New York, United States, which he started building in 1927. He later patented his design, which was first available for sale in 1929. The Link Trainer was a basic metal frame flight simulator usually painted in its well-known blue color. Some of these early war era flight simulators still exist, but it is becoming increasingly difficult to find working examples. The Link family firm in Binghamton manufactured player pianos and organs, and Ed Link was therefore familiar with such components as leather bellows and reed switches. He was also a pilot, but dissatisfied with the amount of real flight training that was available, he decided to build a ground-based device to provide such training without the restrictions of weather and the availability of aircraft and flight instructors. His design had a pneumatic motion platform driven by inflatable bellows which provided pitch and roll cues. A vacuum motor similar to those used in player pianos rotated the platform, providing yaw cues. A generic replica cockpit with working instruments was mounted on the motion platform. When the cockpit was covered, pilots could practice flying by instruments in a safe environment. The motion platform gave the pilot cues as to real angular motion in pitch (nose up and down), roll (wing up or down) and yaw (nose left and right). Initially, aviation flight schools showed little interest in the "Link Trainer". Link also demonstrated his trainer to the U.S. Army Air Force (USAAF), but with no result. However, the situation changed in 1934 when the Army Air Force was given a government contract to fly the postal mail. This included having to fly in bad weather as well as good, for which the USAAF had not previously carried out much training. During the first weeks of the mail service, nearly a dozen Army pilots were killed. The Army Air Force hierarchy remembered Ed Link and his trainer. Link flew in to meet them at Newark Field in New Jersey, and they were impressed by his ability to arrive on a day with poor visibility, due to practice on his training device. The result was that the USAAF purchased six Link Trainers, and this can be said to mark the start of the world flight simulation industry. The principal pilot trainer used during World War II was the Link Trainer. Some 10,000 were produced to train 500,000 new pilots from allied nations, many in the US and Canada because many pilots were trained in those countries before returning to Europe or the Pacific to fly combat missions. Almost all US Army Air Force pilots were trained in a Link Trainer. A different type of World War II trainer was used for navigating at night by the stars. The Celestial Navigation Trainer of 1941 was 13.7 m (45 ft) high and capable of accommodating the navigation team of a bomber crew. It enabled sextants to be used for taking "star shots" from a projected display of the night sky. In 1954 United Airlines bought four flight simulators at a cost of $3 million from Curtiss-Wright that were similar to the earlier models, with the addition of visuals, sound and movement. This was the first of today's modern flight simulators for commercial aircraft. A simulator for helicopters existed as the Jacobs Jaycopter as means of “Cutting helicopter training cost.”. The simulator was later sold as a funfair ride in the 1964-65 New York World's Fair. The simulator manufacturers are consolidating and integrate vertically as training offers double-digit growth: CAE forecast 255,000 new airline pilots from 2017 to 2027 (70 a day), and 180,000 first officers evolving to captains. The largest manufacturer is Canadian CAE Inc. with a 70% market share and $2.8 billion annual revenues, manufacturing training devices for 70 years but moved into training in 2000 with multiple acquisitions. Now CAE makes more from training than from producing the simulators. Crawley-based L3 CTS entered the market in 2012 by acquiring Thales Training & Simulation's manufacturing plant near Gatwick Airport where it assembles up to 30 devices a year, then UK CTC training school in 2015, Aerosim in Sanford, Florida in 2016, and Portuguese academy G Air in October 2017. Global Training Schools like Aerosim also offer aircraft-specific simulators, such as for the Airbus A320. With a 20% market share, equipment still accounts for more than half of L3 CTS turnover but that could soon be reversed as it educates 1,600 commercial pilots each year, 7% of the 22,000 entering the profession annually, and aims for 10% in a fragmented market. The third largest is TRU Simulation + Training, created in 2014 when parent Textron Aviation merged its simulators with Mechtronix, OPINICUS and ProFlight, focusing on simulators and developing the first full-flight simulators for the 737 MAX and the 777X. The fourth is FlightSafety International, focused on general, business and regional aircraft. Airbus and Boeing have invested in their own training centres, aiming for higher margins than aircraft manufacturing like MRO, competing with their suppliers CAE and L3. In June 2018, there were 1,270 commercial airline simulators in service, up by 50 over a year: 85% FFSs and 15% FTDs. CAE supplied 56% of this installed base, L3 CTS 20% and FlightSafety International 10%, while CAE's training centres are the largest operator, with a 13% share. North America has 38% of the world's training devices, Asia-Pacific 25% and Europe 24%. Boeing types represent 45% of all simulated aircraft, followed by Airbus with 35%, then Embraer at 7%, Bombardier at 6% and ATR at 3%. Applications Most flight simulators are used primarily for flight training. The simplest simulators are used to practice basic cockpit procedures, such as processing emergency checklists, and for cockpit familiarization. They are also used for instrument flight training, for which the outside view is less important. Certain aircraft systems may or may not be simulated, and the aerodynamic model is usually extremely generic if present at all. Depending on the level of certification, instruments that would have moving indicators in a real aircraft may be implemented with a display. With more advanced displays, cockpit representation and motion systems, flight simulators can be used to credit different amount of flight hours towards a pilot license. Specific classes of simulators are also used for training other than obtaining initial license such as instrument rating revalidation, or most commonly obtaining type rating for specific kind of aircraft. During the aircraft design process, flight simulators can be used instead of performing actual flight tests. Such "engineering flight simulators" can provide a fast way to find errors, reducing both the risks and the cost of development significantly. Additionally, this allows use of extra measurement equipment that might be too large or otherwise impractical to include during onboard a real aircraft. Throughout different phases of the design process, different engineering simulators with various level of complexity are used.: 13 Flight simulators may include training tasks for crew other than pilots. Examples include gunners on a military aircraft or hoist operators. Separate simulators have also been used for tasks related to flight, like evacuating the aircraft in case of a crash in water. With high complexity of many systems composing contemporary aircraft, aircraft maintenance simulators are increasingly popular. Qualification and approval Before September 2018, when a manufacturer wished to have an ATD model approved, a document that contains the specifications for the model line and that proves compliance with the appropriate regulations is submitted to the FAA. Once this document, called a Qualification Approval Guide (QAG), has been approved, all future devices conforming to the QAG are automatically approved and individual evaluation is neither required nor available. The actual procedure accepted by all CAAs (Civil Aviation Authorities) around the world is to propose 30 days prior qualification date (40 days for CAAC) a MQTG document (Master Qualification Test Guide), which is proper to a unique simulator device and will live along the device itself, containing objective, and functional and subjective tests to demonstrate the representativeness of the simulator compare to the airplane. The results will be compared to Flight Test Data provided by aircraft OEMs or from test campaign ordered by simulator OEMs or also can be compared by POM (Proof Of Match) data provided by aircraft OEMs development simulators. Some of the QTGs will be rerun during the year to prove during continuous qualification that the simulator is still in the tolerances approved by the CAA. These definitions apply to both airplanes and helicopters unless specified otherwise. Training devices briefly compared below are all different subclasses of Flight simulation training device (FSTD). Basic instrument training device (BITD) airplanes only : A basic student station for instrument flight procedures; can use spring loaded flight controls, and instruments displayed on a screen Flight Navigation and Procedures Trainer (FNPT) : Representation of cockpit with all equipment and software to replicate function of aircraft systems Flight Training Devices (FTD) Full Flight Simulators (FFS) Technology Flight simulators are an example of a human-in-the-loop system, in which interaction with a human user is constantly happening. From perspective of the device, the inputs are primary flight controls, instrument panel buttons and switches and the instructor's station, if present. Based on these, the internal state is updated, and equations of motion solved for the new time step. The new state of the simulated aircraft is shown to the user through visual, auditory, motion and touch channels. To simulate cooperative tasks, the simulator can be suited for multiple users, as is the case with multi-crew cooperation simulators. Alternatively, more simulators can be connected, what is known as "parallel simulation" or "distributed simulation". As military aircraft often need to cooperate with other craft or military personnel, wargames are a common use for distributed simulation. Because of that, numerous standards for distributed simulation including aircraft have been developed with military organisations. Some examples include SIMNET, DIS and HLA . The central element of a simulation model are the equations of motion for the aircraft. As the aircraft moves through atmosphere it can exhibit both translational and rotational degrees of freedom. To achieve perception of fluent movement, these equations are solved 50 or 60 times per second.: 16 The forces for motion are calculated from aerodynamical models, which in turn depend on state of control surfaces, driven by specific systems, with their avionics, etc. As is the case with modelling, depending on the required level of realism, there are different levels of detail, with some sub-models omitted in simpler simulators. If a human user is part of the simulator, which might not be the case for some engineering simulators, there is a need to perform the simulation in real-time. Low refresh rates not only reduce realism of simulation, but they have also been linked with increase in simulator sickness. The regulations place a limit on maximum latency between pilot input and aircraft reaction. Because of that, tradeoffs are made to reach the required level of realism with a lower computational cost. Flight simulators typically don't include full computational fluid dynamics models for forces or weather, but use databases of prepared results from calculations and data acquired in real flights. As an example, instead of simulating flow over the wings, lift coefficient may be defined in terms of motion parameters like angle of attack.: 17 While different models need to exchange data, most often they can be separated into a modular architecture, for better organisation and ease of development. Typically, gear model for ground handling would be separate input to the main equations of motion. Each engine and avionics instrument is also a self-contained system with well-defined inputs and outputs. All classes of FSTD require some form of replicating the cockpit. As they are the primary means of interaction between the pilot and the aircraft special importance is assigned to cockpit controls. To achieve good transfer of skills, there are very specific requirements in the flight simulator regulations that determine how closely they must match the real aircraft. These requirements in case of full flight simulators are so detailed, that it may be cost-effective to use the real part certified to fly, rather than manufacture a dedicated replica.: 18 Lower classes of simulators may use springs to mimic forces felt when moving the controls. When there is a need to better replicate the control forces or dynamic response, many simulators are equipped with actively driven force feedback systems. Vibration actuators may also be included, either due to helicopter simulation requirements, or for aircraft equipped with a stick shaker. Another form of tactile input from the pilot are instruments located on the panels in the cockpit. As they are used to interact with various aircraft systems, just that may be sufficient for some forms of procedure training. Displaying them on a screen is sufficient for the most basic BITD simulators and amateur flight simulation, however most classes of certified simulators need all buttons, switches and other inputs to be operated in the same way as in the aircraft cockpit. The necessity for a physical copy of a cockpit contributes to the cost of simulator construction, and ties the hardware to a specific aircraft type. Because of these reasons, there is ongoing research on interactions in virtual reality, however lack of tactile feedback negatively affects users' performance when using this technology. Outside view from the aircraft is an important cue for flying the aircraft, and is the primary means of navigation for visual flight rules operation. One of the primary characteristics of a visual system is the field of view. Depending on the simulator type it may be sufficient to provide only a view forward using a flat display. However, some types of craft, e.g. fighter aircraft, require a very large field of view, preferably almost full sphere, due to the manoeuvres that are performed during air combat. Similarly, since helicopters can perform hover flight in any direction, some classes of helicopter flight simulators require even 180 degrees of horizontal field of view. There are many parameters in visual system design. For a narrow field of view, a single display may be sufficient, however typically multiple projectors are required. This arrangement needs additional calibration, both in terms of distortion from not projecting on a flat surface, as well as brightness in regions with overlapping projections. There are also different shapes of screens used, including cylindrical, spherical or ellipsoidal. The image can be projected on the viewing side of the projection screen, or alternatively "back-projection" onto a translucent screen. Because the screen is much closer than objects outside aircraft, the most advanced flight simulators employ cross-cockpit collimated displays that eliminate the parallax effect between the pilots' point of view, and provide a more realistic view of distant objects. An alternative to large-scale displays are virtual reality simulators using a head-mounted display. This approach allows for a complete field of view, and makes the simulator size considerably smaller. There are examples of use in research, as well as certified FSTD. Visual simulation science applied from the visual systems developed in flight simulators were also an important precursor to three dimensional computer graphics and Computer Generated Imagery (CGI) systems today. Namely because the object of flight simulation is to reproduce on the ground the behavior of an aircraft in flight. Much of this reproduction had to do with believable visual synthesis that mimicked reality. Combined with the need to pair virtual synthesis with military level training requirements, graphics technologies applied in flight simulation were often years ahead of what would have been available in commercial products. When CGI was first used to train pilots, early systems proved effective for certain simple training missions but needed further development for sophisticated training tasks as terrain following and other tactical maneuvers. Early CGI systems could depict only objects consisting of planar polygons. Advances in algorithms and electronics in flight simulator visual systems and CGI in the 1970s and 1980s influenced many technologies still used in modern graphics. Over time CGI systems were able to superimpose texture over the surfaces and transition from one level of image detail to the next one in a smooth manner. Real-time computer graphics visualization of virtual worlds makes some aspects of flight simulator visual systems very similar to game engines, sharing some techniques like different levels of details or libraries like OpenGL.: 343 Many computer graphics visionaries began their careers at Evans & Sutherland and Link Flight Simulation, Division of Singer Company, two leading companies in flight simulation before today's modern computing era. For example, the Singer Link Digital Image Generator (DIG) created in 1978 was considered one of the worlds first CGI system. Initially, the motion systems used separate axes of movement, similar to a gimbal. After the invention of Stewart platform simultaneous operation of all actuators became the preferred choice, with some FFS regulations specifically requiring "synergistic" 6 degrees of freedom motion. In contrast to real aircraft, the simulated motion system has a limited range in which it is able to move. That especially affects the ability to simulate sustained accelerations, and requires a separate model to approximate the cues to the human vestibular system within the given constraints.: 451 Motion system is a major contributor to overall simulator cost,: 423 but assessments of skill transfer based on training on a simulator and leading to handling an actual aircraft are difficult to make, particularly where motion cues are concerned. Large samples of pilot opinion are required and many subjective opinions tend to be aired, particularly by pilots not used to making objective assessments and responding to a structured test schedule. For many years, it was believed that 6 DOF motion-based simulation gave the pilot closer fidelity to flight control operations and aircraft responses to control inputs and external forces and gave a better training outcome for students than non-motion-based simulation. This is described as "handling fidelity", which can be assessed by test flight standards such as the numerical Cooper-Harper rating scale for handling qualities. Recent scientific studies have shown that the use of technology such as vibration or dynamic seats within flight simulators can be equally effective in the delivery of training as large and expensive 6-DOF FFS devices. Modern high-end flight simulators The largest flight simulator in the world is the Vertical Motion Simulator (VMS) at NASA Ames Research Center, in Mountain View, California. This has a very large-throw motion system with 60 feet (+/- 30 ft) of vertical movement (heave). The heave system supports a horizontal beam on which are mounted 40 ft rails, allowing lateral movement of a simulator cab of +/- 20 feet. A conventional 6-degree of freedom hexapod platform is mounted on the 40 ft beam, and an interchangeable cabin is mounted on the platform. This design permits quick switching of different aircraft cabins. Simulations have ranged from blimps, commercial and military aircraft to the Space Shuttle. In the case of the Space Shuttle, the large Vertical Motion Simulator was used to investigate a longitudinal pilot-induced oscillation (PIO) that occurred on an early Shuttle flight just before landing. After identification of the problem on the VMS, it was used to try different longitudinal control algorithms and recommend the best for use in the Shuttle program. AMST Systemtechnik GmbH (AMST) of Austria and Environmental Tectonics Corporation (ETC) of Philadelphia, US, manufacture a range of simulators for disorientation training, that have full freedom in yaw. The most complex of these devices is the Desdemona simulator at the TNO Research Institute in The Netherlands, manufactured by AMST. This large simulator has a gimballed cockpit mounted on a framework which adds vertical motion. The framework is mounted on rails attached to a rotating platform. The rails allow the simulator cab to be positioned at different radii from the centre of rotation and this gives a sustained G capability up to about 3.5. See also References External links |
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[SOURCE: https://en.wikipedia.org/wiki/Video_card] | [TOKENS: 4416] |
Contents Graphics card A graphics card, also known as a video card, display card, graphics accelerator, graphics adapter, VGA card/VGA, video adapter, or display adapter GPU, is a computer expansion card that generates a feed of graphics output to a display device such as a monitor. Graphics cards are sometimes called discrete or dedicated graphics cards to emphasize their distinction to an integrated graphics processor on the motherboard or the central processing unit (CPU). A graphics processing unit (GPU) that performs the necessary computations is the main component in a graphics card, but the acronym "GPU" is sometimes also used to refer to the graphics card as a whole erroneously. Most graphics cards are not limited to simple display output. The graphics processing unit can be used for additional processing, which reduces the load from the CPU. Additionally, computing platforms such as OpenCL and CUDA allow using graphics cards for general-purpose computing. Applications of general-purpose computing on graphics cards include AI training, cryptocurrency mining, and molecular simulation. Usually, a graphics card comes in the form of a printed circuit board (expansion board) which is to be inserted into an expansion slot. Others may have dedicated enclosures, and they are connected to the computer via a docking station or a cable. These are known as external GPUs (eGPUs). Graphics cards are often preferred over integrated graphics for increased performance. A more powerful graphics card will be able to render more frames per second. History Graphics cards, also known as video cards or graphics processing units (GPUs), have historically evolved alongside computer display standards to accommodate advancing technologies and user demands. In the realm of IBM PC compatibles, the early standards included Monochrome Display Adapter (MDA), Color Graphics Adapter (CGA), Hercules Graphics Card, Enhanced Graphics Adapter (EGA), and Video Graphics Array (VGA). Each of these standards represented a step forward in the ability of computers to display more colors, higher resolutions, and richer graphical interfaces, laying the foundation for the development of modern graphical capabilities. In the late 1980s, advancements in personal computing led companies like Radius to develop specialized graphics cards for the Apple Macintosh II. These cards were unique in that they incorporated discrete 2D QuickDraw capabilities, enhancing the graphical output of Macintosh computers by accelerating 2D graphics rendering. QuickDraw, a core part of the Macintosh graphical user interface, allowed for the rapid rendering of bitmapped graphics, fonts, and shapes, and the introduction of such hardware-based enhancements signaled an era of specialized graphics processing in consumer machines. The evolution of graphics processing took a major leap forward in the mid-1990s with 3dfx Interactive's introduction of the Voodoo series, one of the earliest consumer-facing GPUs that supported 3D acceleration. The Voodoo's architecture marked a major shift in graphical computing by offloading the demanding task of 3D rendering from the CPU to the GPU, significantly improving gaming performance and graphical realism. The development of fully integrated GPUs that could handle both 2D and 3D rendering came with the introduction of the NVIDIA RIVA 128. Released in 1997, the RIVA 128 was one of the first consumer-facing GPUs to integrate both 3D and 2D processing units on a single chip. This innovation simplified the hardware requirements for end-users, as they no longer needed separate cards for 2D and 3D rendering, thus paving the way for the widespread adoption of more powerful and versatile GPUs in personal computers. In contemporary times, the majority of graphics cards are built using chips sourced from two dominant manufacturers: AMD and Nvidia. These modern graphics cards are multifunctional and support various tasks beyond rendering 3D images for gaming. They also provide 2D graphics processing, video decoding, TV output, and multi-monitor setups. Additionally, many graphics cards now have integrated sound capabilities, allowing them to transmit audio alongside video output to connected TVs or monitors with built-in speakers, further enhancing the multimedia experience. Within the graphics industry, these products are often referred to as graphics add-in boards (AIBs). The term "AIB" emphasizes the modular nature of these components, as they are typically added to a computer's motherboard to enhance its graphical capabilities. The evolution from the early days of separate 2D and 3D cards to today's integrated and multifunctional GPUs reflects the ongoing technological advancements and the increasing demand for high-quality visual and multimedia experiences in computing. Discrete vs integrated graphics As an alternative to the use of a graphics card, video hardware can be integrated into the motherboard, CPU, or a system-on-chip as integrated graphics. Motherboard-based implementations are sometimes called "on-board video". Some motherboards support using both integrated graphics and a graphics card simultaneously to feed separate displays. The main advantages of integrated graphics are: low cost, compactness, simplicity, and low energy consumption. Integrated graphics often have less performance than a graphics card because the graphics processing unit inside integrated graphics needs to share system resources with the CPU. On the other hand, a graphics card has a separate random access memory (RAM), cooling system, and dedicated power regulators. A graphics card can offload work and reduce memory-bus-contention from the CPU and system RAM, therefore, the overall performance for a computer could improve, in addition to increased performance in graphics processing. Such improvements to performance can be seen in video gaming, 3D animation, and video editing. Both AMD and Intel have introduced CPUs and motherboard chipsets that support the integration of a GPU into the same die as the CPU. AMD advertises CPUs with integrated graphics under the trademark Accelerated Processing Unit (APU), while Intel brands similar technology under "Intel Graphics Technology". Power demand As the processing power of graphics cards increased, so did their demand for electrical power. Current high-performance graphics cards tend to consume large amounts of power. For example, the thermal design power (TDP) for the GeForce Titan RTX is 280 watts. When tested with video games, the GeForce RTX 2080 Ti Founder's Edition averaged 300 watts of power consumption. While CPU and power supply manufacturers have recently aimed toward higher efficiency, power demands of graphics cards continued to rise, with the largest power consumption of any individual part in a computer. Although power supplies have also increased their power output, the bottleneck occurs in the PCI-Express connection, which is limited to supplying 75 watts. Modern graphics cards with a power consumption of over 75 watts usually include a combination of six-pin (75 W) or eight-pin (150 W) sockets that connect directly to the power supply. Providing adequate cooling becomes a challenge in such computers. Computers with multiple graphics cards may require power supplies over 750 watts. Heat extraction becomes a major design consideration for computers with two or more high-end graphics cards.[citation needed] As of the Nvidia GeForce RTX 30 series, Ampere architecture, a custom flashed RTX 3090 named "Hall of Fame" has been recorded to reach a peak power draw as high as 630 watts. A standard RTX 3090 can peak at up to 450 watts. The RTX 3080 can reach up to 350 watts, while a 3070 can reach a similar, if not slightly lower, peak power draw. Ampere cards of the Founders Edition variant feature a "dual axial flow through" cooler design, which includes fans above and below the card to dissipate as much heat as possible towards the rear of the computer case. A similar design was used by the Sapphire Radeon RX Vega 56 Pulse graphics card. Size Graphics cards for desktop computers have different size profiles, which allows graphics cards to be added to smaller-sized computers. Some graphics cards are not of the usual size, and are named as "low profile". Graphics card profiles are based on height only, with low-profile cards taking up less than the height of a PCIe slot. Length and thickness can vary greatly, with high-end cards usually occupying two or three expansion slots, and with modern high-end graphics cards such as the RTX 4090 exceeding 300mm in length. A lower profile card is preferred when trying to fit multiple cards or if graphics cards run into clearance issues with other motherboard components like the DIMM or PCIE slots. This can be fixed with a larger computer case such as mid-tower or full tower. Full towers are usually able to fit larger motherboards in sizes like ATX and micro ATX.[citation needed] In the late 2010s and early 2020s, some high-end graphics card models have become so heavy that it is possible for them to sag downwards after installing without proper support, which is why many manufacturers provide additional support brackets. GPU sag can damage a GPU in the long term. Multicard scaling Some graphics cards can be linked together to allow scaling graphics processing across multiple cards. This is done using either the PCIe bus on the motherboard or, more commonly, a data bridge. Usually, the cards must be of the same model to be linked, and most low end cards are not able to be linked in this way. AMD and Nvidia both have proprietary scaling methods, CrossFireX for AMD, and SLI (since the Turing generation, superseded by NVLink) for Nvidia. Cards from different chip-set manufacturers or architectures cannot be used together for multi-card scaling. If graphics cards have different sizes of memory, the lowest value will be used, with the higher values disregarded. Currently, scaling on consumer-grade cards can be done using up to four cards. The use of four cards requires a large motherboard with a proper configuration. Nvidia's GeForce GTX 590 graphics card can be configured in a four-card configuration. As stated above, users will want to stick to cards with the same performances for optimal use. Motherboards including ASUS Maximus 3 Extreme and Gigabyte GA EX58 Extreme are certified to work with this configuration. A large power supply is necessary to run the cards in SLI or CrossFireX. Power demands must be known before a proper supply is installed. For the four card configuration, a 1000+ watt supply is needed. With any relatively powerful graphics card, thermal management cannot be ignored. Graphics cards require well-vented chassis and good thermal solutions. Air or water cooling are usually required, though low end GPUs can use passive cooling. Larger configurations use water solutions or immersion cooling to achieve proper performance without thermal throttling. SLI and Crossfire have become increasingly uncommon as most games do not fully utilize multiple GPUs, due to the fact that most users cannot afford them. Multiple GPUs are still used on supercomputers (like in Summit), on workstations to accelerate video and 3D rendering, visual effects, for simulations, and for training artificial intelligence. 3D graphics APIs A graphics driver usually supports one or multiple cards by the same vendor and has to be written for a specific operating system. Additionally, the operating system or an extra software package may provide certain programming APIs for applications to perform 3D rendering. GPUs are designed with specific usages in mind, such product lines are categorized here : Industry As of 2025, the primary suppliers of the GPUs (graphics chips or chipsets) used in graphics cards are AMD and Nvidia. In the third quarter of 2013, AMD had a 35.5% market share while Nvidia had 64.5%, according to Jon Peddie Research. In economics, this industry structure is termed a duopoly. AMD and Nvidia also build and sell graphics cards, which are termed graphics add-in-boards (AIBs) in the industry. (See Comparison of Nvidia graphics processing units and Comparison of AMD graphics processing units.) In addition to marketing their own graphics cards, AMD and Nvidia sell their GPUs to authorized AIB suppliers, which AMD and Nvidia refer to as "partners". The fact that Nvidia and AMD compete directly with their customer/partners complicates relationships in the industry. AMD and Intel being direct competitors in the CPU industry is also noteworthy, since AMD-based graphics cards may be used in computers with Intel CPUs. Intel's integrated graphics may weaken AMD, in which the latter derives a significant portion of its revenue from its APUs. As of the second quarter of 2013, there were 52 AIB suppliers. These AIB suppliers may market graphics cards under their own brands, produce graphics cards for private label brands, or produce graphics cards for computer manufacturers. Some AIB suppliers such as MSI build both AMD-based and Nvidia-based graphics cards. Others, such as EVGA, build only Nvidia-based graphics cards, while XFX, now builds only AMD-based graphics cards. Several AIB suppliers are also motherboard suppliers. Most of the largest AIB suppliers are based in Taiwan and they include ASUS, MSI, GIGABYTE, and Palit. Hong Kong–based AIB manufacturers include Sapphire and Zotac. Sapphire and Zotac also sell graphics cards exclusively for AMD and Nvidia GPUs respectively. Market Graphics card shipments peaked at a total of 114 million in 1999. By contrast, they totaled 14.5 million units in the third quarter of 2013, a 17% fall from Q3 2012 levels. Shipments reached an annual total of 44 million in 2015.[citation needed] The sales of graphics cards have trended downward due to improvements in integrated graphics technologies; high-end, CPU-integrated graphics can provide competitive performance with low-end graphics cards. At the same time, graphics card sales have grown within the high-end segment, as manufacturers have shifted their focus to prioritize the gaming and enthusiast market. Beyond the gaming and multimedia segments, graphics cards have been increasingly used for general-purpose computing, such as big data processing. The growth of cryptocurrency has placed a severely high demand on high-end graphics cards, especially in large quantities, due to their advantages in the process of cryptocurrency mining. In January 2018, mid- to high-end graphics cards experienced a major surge in price, with many retailers having stock shortages due to the significant demand among this market. Graphics card companies released mining-specific cards designed to run 24 hours a day, seven days a week, and without video output ports. The graphics card industry took a setback due to the 2020–21 chip shortage. Parts A modern graphics card consists of a printed circuit board on which the components are mounted. These include: A graphics processing unit (GPU), also occasionally called visual processing unit (VPU), is a specialized electronic circuit designed to rapidly manipulate and alter memory to accelerate the building of images in a frame buffer intended for output to a display. Because of the large degree of programmable computational complexity for such a task, a modern graphics card is also a computer unto itself. A heat sink is mounted on most modern graphics cards. A heat sink spreads out the heat produced by the graphics processing unit evenly throughout the heat sink and unit itself. The heat sink commonly has a fan mounted to cool the heat sink and the graphics processing unit. Not all cards have heat sinks, for example, some cards are liquid-cooled and instead have a water block; additionally, cards from the 1980s and early 1990s did not produce much heat, and did not require heat sinks. Most modern graphics cards need proper thermal solutions. They can be water-cooled or through heat sinks with additional connected heat pipes usually made of copper for the best thermal transfer.[citation needed] The video BIOS or firmware contains a minimal program for the initial set up and control of the graphics card. It may contain information on the memory and memory timing, operating speeds and voltages of the graphics processor, and other details which can sometimes be changed.[citation needed] Modern Video BIOSes do not support full functionalities of graphics cards; they are only sufficient to identify and initialize the card to display one of a few frame buffer or text display modes. It does not support YUV to RGB translation, video scaling, pixel copying, compositing or any of the multitude of other 2D and 3D features of the graphics card, which must be accessed by software drivers.[citation needed] The memory capacity of most modern graphics cards ranges from 2 to 24 GB. But with up to 32 GB as of the late 2010s, the applications for graphics use are becoming more powerful and widespread. Since video memory needs to be accessed by the GPU and the display circuitry, it often uses special high-speed or multi-port memory, such as VRAM, WRAM, SGRAM, etc. Around 2003, the video memory was typically based on DDR technology. During and after that year, manufacturers moved towards DDR2, GDDR3, GDDR4, GDDR5, GDDR5X, and GDDR6. The effective memory clock rate in modern cards is generally between 2 and 15 GHz.[citation needed] Video memory may be used for storing other data as well as the screen image, such as the Z-buffer, which manages the depth coordinates in 3D graphics, as well as textures, vertex buffers, and compiled shader programs. The RAMDAC, or random-access-memory digital-to-analog converter, converts digital signals to analog signals for use by a computer display that uses analog inputs such as cathode-ray tube (CRT) displays. The RAMDAC is a kind of RAM chip that regulates the functioning of the graphics card. Depending on the number of bits used and the RAMDAC-data-transfer rate, the converter will be able to support different computer-display refresh rates. With CRT displays, it is best to work over 75 Hz and never under 60 Hz, to minimize flicker. (This is not a problem with liquid-crystal displays, as they have little to no flicker.[citation needed]) Due to the growing popularity of digital computer displays and the integration of the RAMDAC onto the GPU die, it has mostly disappeared as a discrete component. All current LCD/plasma monitors and TVs and projectors with only digital connections work in the digital domain and do not require a RAMDAC for those connections. There are displays that feature analog inputs (VGA, component, SCART, etc.) only. These require a RAMDAC, but they reconvert the analog signal back to digital before they can display it, with the unavoidable loss of quality stemming from this digital-to-analog-to-digital conversion.[citation needed] With the VGA standard being phased out in favor of digital formats, RAMDACs have started to disappear from graphics cards.[citation needed] The most common connection systems between the graphics card and the computer display are: Also known as D-sub, VGA is an analog-based standard adopted in the late 1980s designed for CRT displays, also called VGA connector. Today, the VGA analog interface is used for high definition video resolutions including 1080p and higher. Some problems of this standard are electrical noise, image distortion and sampling error in evaluating pixels. While the VGA transmission bandwidth is high enough to support even higher resolution playback, the picture quality can degrade depending on cable quality and length. The extent of quality difference depends on the individual's eyesight and the display; when using a DVI or HDMI connection, especially on larger sized LCD/LED monitors or TVs, quality degradation, if present, is prominently visible. Blu-ray playback at 1080p is possible via the VGA analog interface, if Image Constraint Token (ICT) is not enabled on the Blu-ray disc. Digital Visual Interface is a digital-based standard designed for displays such as flat-panel displays (LCDs, plasma screens, wide high-definition television displays) and video projectors. There were also some rare high-end CRT monitors that use DVI. It avoids image distortion and electrical noise, corresponding each pixel from the computer to a display pixel, using its native resolution. Most manufacturers include a DVI-I connector, allowing (via simple adapter) standard RGB signal output to an old CRT or LCD monitor with VGA input. These connectors are included to allow connection with televisions, DVD players, video recorders and video game consoles. They often come in two 10-pin mini-DIN connector variations, and the VIVO splitter cable generally comes with either 4 connectors (S-Video in and out plus composite video in and out), or 6 connectors (S-Video in and out, component YPBPR out and composite in and out). HDMI is a compact audio/video interface for transferring uncompressed video data and compressed/uncompressed digital audio data from an HDMI-compliant device ("the source device") to a compatible digital audio device, computer monitor, video projector, or digital television. HDMI is a digital replacement for existing analog video standards. HDMI supports copy protection through HDCP. DisplayPort is a digital display interface developed by the Video Electronics Standards Association (VESA). The interface is primarily used to connect a video source to a display device such as a computer monitor, though it can also be used to transmit audio, USB, and other forms of data. The VESA specification is royalty-free. VESA designed it to replace VGA, DVI, and LVDS. Backward compatibility to VGA and DVI by using adapter dongles enables consumers to use DisplayPort fitted video sources without replacing existing display devices. Although DisplayPort has a greater throughput of the same functionality as HDMI, it is expected to complement the interface, not replace it. USB-C is an extensible connector used for USB, display port, thunderbolt, power delivery. The USB-C is a 24 pin reversible connector that supersedes previous USB connectors. Some newer graphics cards use USB-C ports for versatility. Chronologically, connection systems between graphics card and motherboard were, mainly: The following table is a comparison between features of some interfaces listed above. See also References Sources External links |
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[SOURCE: https://en.wikipedia.org/wiki/Clipping_(computer_graphics)] | [TOKENS: 983] |
Contents Clipping (computer graphics) Clipping, in the context of computer graphics, is a method to selectively enable or disable rendering operations within a defined region of interest. Mathematically, clipping can be described using the terminology of constructive geometry. A rendering algorithm only draws pixels in the intersection between the clip region and the scene model. Lines and surfaces outside the view volume (aka. frustum) are removed. Clip regions are commonly specified to improve render performance. A well-chosen clip[clarification needed] allows the renderer to save time and energy by skipping calculations related to pixels that the user cannot see. Pixels that will be drawn are said to be within the clip region. Pixels that will not be drawn are outside the clip region. More informally, pixels that will not be drawn are said to be "clipped." In 2D graphics In two-dimensional graphics, a clip region may be defined so that pixels are only drawn within the boundaries of a window or frame. Clip regions can also be used to selectively control pixel rendering for aesthetic or artistic purposes. In many implementations, the final clip region is the composite (or intersection) of one or more application-defined shapes, as well as any system hardware constraints In one example application, consider an image editing program. A user application may render the image into a viewport. As the user zooms and scrolls to view a smaller portion of the image, the application can set a clip boundary so that pixels outside the viewport are not rendered. In addition, GUI widgets, overlays, and other windows or frames may obscure some pixels from the original image. In this sense, the clip region is the composite of the application-defined "user clip" and the "device clip" enforced by the system's software and hardware implementation. Application software can take advantage of this clip information to save computation time, energy, and memory, avoiding work related to pixels that aren't visible. In 3D graphics In three-dimensional graphics, the terminology of clipping can be used to describe many related features. Typically, "clipping" refers to operations in the plane that work with rectangular shapes, and "culling" refers to more general methods to selectively process scene model elements. This terminology is not rigid, and exact usage varies among many sources. Scene model elements include geometric primitives: points or vertices; line segments or edges; polygons or faces; and more abstract model objects such as curves, splines, surfaces, and even text. In complicated scene models, individual elements may be selectively disabled (clipped) for reasons including visibility within the viewport (frustum culling); orientation (backface culling), obscuration by other scene or model elements (occlusion culling, depth- or "z" clipping). Sophisticated algorithms exist to efficiently detect and perform such clipping. Many optimized clipping methods rely on specific hardware acceleration logic provided by a graphics processing unit (GPU). The concept of clipping can be extended to higher dimensionality using methods of abstract algebraic geometry. Beyond projection of vertices & 2D clipping, near clipping is required to correctly rasterise 3D primitives; this is because vertices may have been projected behind the eye. Near clipping ensures that all the vertices used have valid 2D coordinates. Together with far-clipping it also helps prevent overflow of depth-buffer values. Some early texture mapping hardware (using forward texture mapping) in video games suffered from complications associated with near clipping and UV coordinates. In 3D computer graphics, "Z" often refers to the depth axis in the system of coordinates centered at the viewport origin: "Z" is used interchangeably with "depth", and conceptually corresponds to the distance "into the virtual screen." In this coordinate system, "X" and "Y" therefore refer to a conventional cartesian coordinate system laid out on the user's screen or viewport. This viewport is defined by the geometry of the viewing frustum, and parameterizes the field of view. Z-clipping, or depth clipping, refers to techniques that selectively render certain scene objects based on their depth relative to the screen. Most graphics toolkits allow the programmer to specify a "near" and "far" clip depth, and only portions of objects between those two planes are displayed. A creative application programmer can use this method to render visualizations of the interior of a 3D object in the scene. For example, a medical imaging application could use this technique to render the organs inside a human body. A video game programmer can use clipping information to accelerate game logic. For example, a tall wall or building that occludes other game entities can save GPU time that would otherwise be spent transforming and texturing items in the rear areas of the scene; and a tightly integrated software program can use this same information to save CPU time by optimizing out game logic for objects that aren't seen by the player. Algorithms See also Further reading References |
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[SOURCE: https://en.wikipedia.org/wiki/Rendering_primitive] | [TOKENS: 61] |
Glossary of computer graphics This is a glossary of terms relating to computer graphics. For more general computer hardware terms, see glossary of computer hardware terms. 0–9 A B C D E F G H I K L M N O P Q R S T U V W Z References |
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[SOURCE: https://en.wikipedia.org/wiki/Tomographic_reconstruction] | [TOKENS: 1965] |
Contents Tomographic reconstruction Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann Radon. A notable example of applications is the reconstruction of computed tomography (CT) where cross-sectional images of patients are obtained in non-invasive manner. Recent developments have seen the Radon transform and its inverse used for tasks related to realistic object insertion required for testing and evaluating computed tomography use in airport security. This article applies in general to reconstruction methods for all kinds of tomography, but some of the terms and physical descriptions refer directly to the reconstruction of X-ray computed tomography. Introducing formula The projection of an object, resulting from the tomographic measurement process at a given angle θ {\displaystyle \theta } , is made up of a set of line integrals (see Fig. 1). A set of many such projections under different angles organized in 2D is called a sinogram (see Fig. 3). In X-ray CT, the line integral represents the total attenuation of the beam of X-rays as it travels in a straight line through the object. As mentioned above, the resulting image is a 2D (or 3D) model of the attenuation coefficient. That is, we wish to find the image μ ( x , y ) {\displaystyle \mu (x,y)} . The simplest and easiest way to visualise the method of scanning is the system of parallel projection, as used in the first scanners. For this discussion we consider the data to be collected as a series of parallel rays, at position r {\displaystyle r} , across a projection at angle θ {\displaystyle \theta } . This is repeated for various angles. Attenuation occurs exponentially in tissue: where μ ( x , y ) {\displaystyle \mu (x,y)} is the attenuation coefficient as a function of position. Therefore, generally the total attenuation p {\displaystyle p} of a ray at position r {\displaystyle r} , on the projection at angle θ {\displaystyle \theta } , is given by the line integral: Using the coordinate system of Figure 1, the value of r {\displaystyle r} onto which the point ( x , y ) {\displaystyle (x,y)} will be projected at angle θ {\displaystyle \theta } is given by: So the equation above can be rewritten as where f ( x , y ) {\displaystyle f(x,y)} represents μ ( x , y ) {\displaystyle \mu (x,y)} and δ ( ) {\displaystyle \delta ()} is the Dirac delta function. This function is known as the Radon transform (or sinogram) of the 2D object. The Fourier Transform of the projection can be written as where g θ ( x cos θ + y sin θ ) {\displaystyle g_{\theta }(x\cos \theta +y\sin \theta )} is the derivative of the Hilbert transform of p θ ( r ) {\displaystyle p_{\theta }(r)} In theory, the inverse Radon transformation would yield the original image. The projection-slice theorem tells us that if we had an infinite number of one-dimensional projections of an object taken at an infinite number of angles, we could perfectly reconstruct the original object, f ( x , y ) {\displaystyle f(x,y)} . However, there will only be a finite number of projections available in practice. Assuming f ( x , y ) {\displaystyle f(x,y)} has effective diameter d {\displaystyle d} and desired resolution is R s {\displaystyle R_{s}} , a rule of thumb for the number of projections needed for reconstruction is N > π d / R s {\displaystyle N>\pi d/R_{s}} Reconstruction algorithms Practical reconstruction algorithms have been developed to implement the process of reconstruction of a three-dimensional object from its projections. These algorithms are designed largely based on the mathematics of the X-ray transform, statistical knowledge of the data acquisition process and geometry of the data imaging system. Reconstruction can be made using interpolation. Assume N {\displaystyle N} projections of f ( x , y ) {\displaystyle f(x,y)} are generated at equally spaced angles, each sampled at the same rate. The discrete Fourier transform (DFT) on each projection yields sampling in the frequency domain. Combining all the frequency-sampled projections generates a polar raster in the frequency domain. The polar raster is sparse, so interpolation is used to fill the unknown DFT points, and reconstruction can be done through the inverse discrete Fourier transform. Reconstruction performance may improve by designing methods to change the sparsity of the polar raster, facilitating the effectiveness of interpolation. For instance, a concentric square raster in the frequency domain can be obtained by changing the angle between each projection as follow: where R 0 {\displaystyle R_{0}} is highest frequency to be evaluated. The concentric square raster improves computational efficiency by allowing all the interpolation positions to be on rectangular DFT lattice. Furthermore, it reduces the interpolation error. Yet, the Fourier-Transform algorithm has a disadvantage of producing inherently noisy output. In practice of tomographic image reconstruction, often a stabilized and discretized version of the inverse Radon transform is used, known as the filtered back projection algorithm. With a sampled discrete system, the inverse Radon transform is where Δ θ {\displaystyle \Delta \theta } is the angular spacing between the projections and k ( t ) {\displaystyle k(t)} is a Radon kernel with frequency response | ω | {\displaystyle |\omega |} . The name back-projection comes from the fact that a one-dimensional projection needs to be filtered by a one-dimensional Radon kernel (back-projected) in order to obtain a two-dimensional signal. The filter used does not contain DC gain, so adding DC bias may be desirable. Reconstruction using back-projection allows better resolution than interpolation method described above. However, it induces greater noise because the filter is prone to amplify high-frequency content. The iterative algorithm is computationally intensive but it allows the inclusion of a priori information about the system f ( x , y ) {\displaystyle f(x,y)} . Let N {\displaystyle N} be the number of projections and D i {\displaystyle D_{i}} be the distortion operator for the i {\displaystyle i} th projection taken at an angle θ i {\displaystyle \theta _{i}} . { λ i } {\displaystyle \{\lambda _{i}\}} are a set of parameters to optimize the conversion of iterations. An alternative family of recursive tomographic reconstruction algorithms are the algebraic reconstruction techniques and iterative sparse asymptotic minimum variance. Use of a noncollimated fan beam is common since a collimated beam of radiation is difficult to obtain. Fan beams will generate series of line integrals, not parallel to each other, as projections. The fan-beam system requires a 360-degree range of angles, which imposes mechanical constraints, but it allows faster signal acquisition time, which may be advantageous in certain settings such as in the field of medicine. Back projection follows a similar two-step procedure that yields reconstruction by computing weighted sum back-projections obtained from filtered projections. Deep learning methods are widely applied to image reconstruction nowadays and have achieved impressive results in various image reconstruction tasks, including low-dose denoising, sparse-view reconstruction, limited angle tomography and metal artifact reduction. An excellent overview can be found in the special issue of IEEE Transaction on Medical Imaging. One group of deep learning reconstruction algorithms apply post-processing neural networks to achieve image-to-image reconstruction, where input images are reconstructed by conventional reconstruction methods. Artifact reduction using the U-Net in limited angle tomography is such an example application. However, incorrect structures may occur in an image reconstructed by such a completely data-driven method, as displayed in the figure. Therefore, integration of known operators into the architecture design of neural networks appears beneficial, as described in the concept of precision learning. For example, direct image reconstruction from projection data can be learnt from the framework of filtered back-projection. Another example is to build neural networks by unrolling iterative reconstruction algorithms. Except for precision learning, using conventional reconstruction methods with deep learning reconstruction prior is also an alternative approach to improve the image quality of deep learning reconstruction. Tomographic reconstruction software Tomographic systems have significant variability in their applications and geometries (locations of sources and detectors). This variability creates the need for very specific, tailored implementations of the processing and reconstruction algorithms. Thus, most CT manufacturers provide their own custom proprietary software. This is done not only to protect intellectual property, but may also be enforced by a government regulatory agency. Regardless, there are a number of general purpose tomographic reconstruction software packages that have been developed over the last couple decades, both commercial and open-source. Most of the commercial software packages that are available for purchase focus on processing data for benchtop cone-beam CT systems. A few of these software packages include Volume Graphics, InstaRecon, iTomography, Livermore Tomography Tools (LTT), Cone Beam Software Tools (CST), and Bronnikov Algorithms Library. Some noteworthy examples of open-source reconstruction software include: Reconstruction Toolkit (RTK), CONRAD, TomoPy, the ASTRA toolbox, PYRO-NN, ODL, TIGRE, and LEAP. Gallery Shown in the gallery is the complete process for a simple object tomography and the following tomographic reconstruction based on ART. See also References Further reading External links |
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[SOURCE: https://en.wikipedia.org/wiki/Texture_mapping#cite_note-17] | [TOKENS: 4408] |
Contents Texture mapping Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV space). Semantic Texture mapping can multiply refer to (1) the task of unwrapping a 3D model (converting the surface of a 3D model into a 2D texture map), (2) applying a 2D texture map onto the surface of a 3D model, and (3) the 3D software algorithm that performs both tasks. A texture map refers to a 2D image ("texture") that adds visual detail to a 3D model. The image can be stored as a raster graphic. A texture that stores a specific property—such as bumpiness, reflectivity, or transparency—is also referred to as a color map or roughness map. The coordinate space that converts from a 3D model's 3D space into a 2D space for sampling from the texture map is variously called UV space, UV coordinates, or texture space. Algorithm The following is a simplified explanation of how an algorithm could work to render an image: History The original technique was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. Texture maps A texture map is an image applied ("mapped") to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3D model formats or material definitions, and assembled into resource bundles. They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources (which may be located in device memory) as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping. Texture maps usually contain RGB color data (either stored as direct color, compressed formats, or indexed color), and sometimes an additional channel for alpha blending (RGBA) especially for billboards and decal overlay textures. It is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity. Multiple texture maps (or channels) may be combined for control over specularity, normals, displacement, or subsurface scattering, e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered a modern evolution of tile map graphics). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning or digital photography, designed in image manipulation software such as GIMP or Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush. This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2D case is also known as UV coordinates). This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3D space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface (which is important for render mapping and light mapping, also known as baking). Texture mapping maps the model surface (or screen space during rasterization) into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on the screen) are calculated from the texels (texture pixels) is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination) into a surface texture (possibly on a low-resolution model). This technique is called baking (or render mapping) and is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games (e.g. Messiah) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps in a process called surface caching. Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Rasterisation algorithms Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility, and performance. Affine texture mapping linearly interpolates texture coordinates across a surface, making it the fastest form of texture mapping. Some software and hardware (such as the original PlayStation) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed-point UV coordinates or by an incremental error algorithm akin to Bresenham's line algorithm. In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (as shown in the figure: the checker box texture appears bent), especially as primitives near the camera. This distortion can be reduced by subdividing polygons into smaller polygons. Using quad primitives for rectangular objects can look less incorrect than if those rectangles were split into triangles. However, since interpolating four points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the forward texture mapping used by the Nvidia NV1, offered efficient quad primitives. With perspective correction, triangles become equivalent to quad primitives and this advantage disappears. For rectangular objects that are at right angles to the viewer (like floors and walls), the perspective only needs to be corrected in one direction across the screen rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor. Affine linear interpolation across that horizontal span will look correct because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space rather than simply interpolating coordinates in 2D screen space. While achieving the correct visual effect, perspective correct texturing is more expensive to calculate. To perform perspective correction of the texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, it is possible to take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across the surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} , and v {\displaystyle v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to produce a perspective correct texture mapping. To do this, the reciprocals at each vertex of the geometry (three points for a triangle) are calculated. Vertex n {\displaystyle n} has reciprocals u n z n {\displaystyle {\frac {u_{n}}{z_{n}}}} , v n z n {\displaystyle {\frac {v_{n}}{z_{n}}}} , and 1 z n {\displaystyle {\frac {1}{z_{n}}}} . Then, linear interpolation can be done on these reciprocals between the n {\displaystyle n} vertices (e.g., using barycentric coordinates), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} and 1 z i {\displaystyle {\frac {1}{z_{i}}}} (reciprocal z i {\displaystyle z_{i}} ). However, as our division by z {\displaystyle z} altered their coordinate system, this u i , v i {\displaystyle u_{i},v_{i}} cannot be used as texture coordinates. To correct back to the u , v {\displaystyle u,v} space, the corrected z {\displaystyle z} is calculated by taking the reciprocal once again: z c o r r e c t = 1 1 z i {\displaystyle z_{correct}={\frac {1}{\frac {1}{z_{i}}}}} . This is then used to correct the u i , v i {\displaystyle u_{i},v_{i}} coordinates: u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that the difference from pixel to pixel between texture coordinates is smaller in parts of the polygon that are closer to the viewer (stretching the texture wider) and is larger in parts that are farther away (compressing the texture). Affine texture mapping directly interpolates a texture coordinate u α {\displaystyle u_{\alpha }} between two endpoints u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} : u α = ( 1 − α ) u 0 + α u 1 {\displaystyle u_{\alpha }=(1-\alpha )u_{0}+\alpha u_{1}} where 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1} . Perspective correct mapping interpolates after dividing by depth z {\displaystyle z} , then uses its interpolated reciprocal to recover the correct coordinate: u α = ( 1 − α ) u 0 z 0 + α u 1 z 1 ( 1 − α ) 1 z 0 + α 1 z 1 {\displaystyle u_{\alpha }={\frac {(1-\alpha ){\frac {u_{0}}{z_{0}}}+\alpha {\frac {u_{1}}{z_{1}}}}{(1-\alpha ){\frac {1}{z_{0}}}+\alpha {\frac {1}{z_{1}}}}}} 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality and precision trade-offs, which can be applied to both software and hardware. Classic software texture mappers generally only performed simple texture mapping with one lighting effect at most (typically applied through a lookup table), and the perspective correctness was about 16 times more expensive.[compared to?] The Doom engine restricted the world to vertical walls and horizontal floors and ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors and ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom while using the same rendering technique. Some engines were able to render texture mapped heightmaps (e.g. Nova Logic's Voxel Space, and the engine for Outcast) via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals: keeping the arithmetic mill busy at all times and producing faster arithmetic results.[vague] For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware and had a relatively high triangle throughput compared to its peers. Software renderers generally prefer screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2D affine interpolation), thus lessening the overhead further. Another reason is that affine texture mapping does not fit into the low number of CPU registers of the x86 CPU; the 68000 and RISC processors are much more suited for that approach. A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. As the polygons are rendered independently, it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z, but the effort seems not to be worth it.[original research?] One other technique is to approximate the perspective with a faster calculation, such as a polynomial. A second uses the 1 z i {\textstyle {\frac {1}{z_{i}}}} value of the last two drawn pixels to linearly extrapolate the next value. For the latter, the division is then done starting from those values so that all that has to be divided is a small remainder. However, the amount of bookkeeping needed makes this technique too slow on most systems.[citation needed] A third technique, used by the Build Engine (used, most notably, in Duke Nukem 3D), builds on the constant distance trick used by the Doom engine by finding and rendering along the line of constant distance for arbitrary polygons. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG) and professional graphics workstations (such as Silicon Graphics) and broadcast digital video effects machines such as the Ampex ADO. Texture mapping hardware later appeared in arcade cabinets, consumer video game consoles, and PC video cards in the mid-1990s. In flight simulations, texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. Additionally, texture mapping was implemented so that real-time processing of prefiltered texture patterns stored in memory could be accessed by the video processor in real-time. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU. Some hardware implementations combine texture mapping with hidden-surface determination in tile-based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting. On earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen: Of these methods, inverse texture mapping has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive. The primary advantage of this method is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage is that the memory access pattern in the texture space will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness. Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer. This was used by some hardware, such as the 3DO, the Sega Saturn and the NV1. The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see the § Affine texture mapping section above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness. UV mapping became an important technique for 3D modelling and assisted in clipping the texture correctly when the primitive went past the edge of the screen, but existing hardware did not provide effective implementations of this. These shortcomings could have been addressed with further development, but GPU design has mostly shifted toward using the inverse mapping technique. Applications Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks: It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results. Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Exposé in Mac OS X. See also References Software External links |
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Editing Texture mapping (section) Copy and paste: – — ° ′ ″ ≈ ≠ ≤ ≥ ± − × ÷ ← → · § Cite your sources: <ref></ref> {{}} {{{}}} | [] [[]] [[Category:]] #REDIRECT [[]] <s></s> <sup></sup> <sub></sub> <code></code> <pre></pre> <blockquote></blockquote> <ref></ref> <ref name="" /> {{Reflist}} <references /> <includeonly></includeonly> <noinclude></noinclude> {{DEFAULTSORT:}} <nowiki></nowiki> <!-- --> <span class="plainlinks"></span> Symbols: ~ | ¡ ¿ † ‡ ↔ ↑ ↓ • ¶ # ∞ ‹› «» ¤ ₳ ฿ ₵ ¢ ₡ ₢ $ ₫ ₯ € ₠ ₣ ƒ ₴ ₭ ₤ ℳ ₥ ₦ ₧ ₰ £ ៛ ₨ ₪ ৳ ₮ ₩ ¥ ♠ ♣ ♥ ♦ 𝄫 ♭ ♮ ♯ 𝄪 © ¼ ½ ¾ Latin: A a Á á À à  â Ä ä Ǎ ǎ Ă ă Ā ā à ã Å å Ą ą Æ æ Ǣ ǣ B b C c Ć ć Ċ ċ Ĉ ĉ Č č Ç ç D d Ď ď Đ đ Ḍ ḍ Ð ð E e É é È è Ė ė Ê ê Ë ë Ě ě Ĕ ĕ Ē ē Ẽ ẽ Ę ę Ẹ ẹ Ɛ ɛ Ǝ ǝ Ə ə F f G g Ġ ġ Ĝ ĝ Ğ ğ Ģ ģ H h Ĥ ĥ Ħ ħ Ḥ ḥ I i İ ı Í í Ì ì Î î Ï ï Ǐ ǐ Ĭ ĭ Ī ī Ĩ ĩ Į į Ị ị J j Ĵ ĵ K k Ķ ķ L l Ĺ ĺ Ŀ ŀ Ľ ľ Ļ ļ Ł ł Ḷ ḷ Ḹ ḹ M m Ṃ ṃ N n Ń ń Ň ň Ñ ñ Ņ ņ Ṇ ṇ Ŋ ŋ O o Ó ó Ò ò Ô ô Ö ö Ǒ ǒ Ŏ ŏ Ō ō Õ õ Ǫ ǫ Ọ ọ Ő ő Ø ø Œ œ Ɔ ɔ P p Q q R r Ŕ ŕ Ř ř Ŗ ŗ Ṛ ṛ Ṝ ṝ S s Ś ś Ŝ ŝ Š š Ş ş Ș ș Ṣ ṣ ß T t Ť ť Ţ ţ Ț ț Ṭ ṭ Þ þ U u Ú ú Ù ù Û û Ü ü Ǔ ǔ Ŭ ŭ Ū ū Ũ ũ Ů ů Ų ų Ụ ụ Ű ű Ǘ ǘ Ǜ ǜ Ǚ ǚ Ǖ ǖ V v W w Ŵ ŵ X x Y y Ý ý Ŷ ŷ Ÿ ÿ Ỹ ỹ Ȳ ȳ Z z Ź ź Ż ż Ž ž ß Ð ð Þ þ Ŋ ŋ Ə ə Greek: Ά ά Έ έ Ή ή Ί ί Ό ό Ύ ύ Ώ ώ Α α Β β Γ γ Δ δ Ε ε Ζ ζ Η η Θ θ Ι ι Κ κ Λ λ Μ μ Ν ν Ξ ξ Ο ο Π π Ρ ρ Σ σ ς Τ τ Υ υ Φ φ Χ χ Ψ ψ Ω ω {{Polytonic|}} Cyrillic: А а Б б В в Г г Ґ ґ Ѓ ѓ Д д Ђ ђ Е е Ё ё Є є Ж ж З з Ѕ ѕ И и І і Ї ї Й й Ј ј К к Ќ ќ Л л Љ љ М м Н н Њ њ О о П п Р р С с Т т Ћ ћ У у Ў ў Ф ф Х х Ц ц Ч ч Џ џ Ш ш Щ щ Ъ ъ Ы ы Ь ь Э э Ю ю Я я ́ IPA: t̪ d̪ ʈ ɖ ɟ ɡ ɢ ʡ ʔ ɸ β θ ð ʃ ʒ ɕ ʑ ʂ ʐ ç ʝ ɣ χ ʁ ħ ʕ ʜ ʢ ɦ ɱ ɳ ɲ ŋ ɴ ʋ ɹ ɻ ɰ ʙ ⱱ ʀ ɾ ɽ ɫ ɬ ɮ ɺ ɭ ʎ ʟ ɥ ʍ ɧ ʼ ɓ ɗ ʄ ɠ ʛ ʘ ǀ ǃ ǂ ǁ ɨ ʉ ɯ ɪ ʏ ʊ ø ɘ ɵ ɤ ə ɚ ɛ œ ɜ ɝ ɞ ʌ ɔ æ ɐ ɶ ɑ ɒ ʰ ʱ ʷ ʲ ˠ ˤ ⁿ ˡ ˈ ˌ ː ˑ ̪ {{IPA|}} This page is a member of 12 hidden categories (help): |
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[SOURCE: https://en.wikipedia.org/w/index.php?title=Texture_mapping&action=edit§ion=23] | [TOKENS: 1430] |
Editing Texture mapping (section) Copy and paste: – — ° ′ ″ ≈ ≠ ≤ ≥ ± − × ÷ ← → · § Cite your sources: <ref></ref> {{}} {{{}}} | [] [[]] [[Category:]] #REDIRECT [[]] <s></s> <sup></sup> <sub></sub> <code></code> <pre></pre> <blockquote></blockquote> <ref></ref> <ref name="" /> {{Reflist}} <references /> <includeonly></includeonly> <noinclude></noinclude> {{DEFAULTSORT:}} <nowiki></nowiki> <!-- --> <span class="plainlinks"></span> Symbols: ~ | ¡ ¿ † ‡ ↔ ↑ ↓ • ¶ # ∞ ‹› «» ¤ ₳ ฿ ₵ ¢ ₡ ₢ $ ₫ ₯ € ₠ ₣ ƒ ₴ ₭ ₤ ℳ ₥ ₦ ₧ ₰ £ ៛ ₨ ₪ ৳ ₮ ₩ ¥ ♠ ♣ ♥ ♦ 𝄫 ♭ ♮ ♯ 𝄪 © ¼ ½ ¾ Latin: A a Á á À à  â Ä ä Ǎ ǎ Ă ă Ā ā à ã Å å Ą ą Æ æ Ǣ ǣ B b C c Ć ć Ċ ċ Ĉ ĉ Č č Ç ç D d Ď ď Đ đ Ḍ ḍ Ð ð E e É é È è Ė ė Ê ê Ë ë Ě ě Ĕ ĕ Ē ē Ẽ ẽ Ę ę Ẹ ẹ Ɛ ɛ Ǝ ǝ Ə ə F f G g Ġ ġ Ĝ ĝ Ğ ğ Ģ ģ H h Ĥ ĥ Ħ ħ Ḥ ḥ I i İ ı Í í Ì ì Î î Ï ï Ǐ ǐ Ĭ ĭ Ī ī Ĩ ĩ Į į Ị ị J j Ĵ ĵ K k Ķ ķ L l Ĺ ĺ Ŀ ŀ Ľ ľ Ļ ļ Ł ł Ḷ ḷ Ḹ ḹ M m Ṃ ṃ N n Ń ń Ň ň Ñ ñ Ņ ņ Ṇ ṇ Ŋ ŋ O o Ó ó Ò ò Ô ô Ö ö Ǒ ǒ Ŏ ŏ Ō ō Õ õ Ǫ ǫ Ọ ọ Ő ő Ø ø Œ œ Ɔ ɔ P p Q q R r Ŕ ŕ Ř ř Ŗ ŗ Ṛ ṛ Ṝ ṝ S s Ś ś Ŝ ŝ Š š Ş ş Ș ș Ṣ ṣ ß T t Ť ť Ţ ţ Ț ț Ṭ ṭ Þ þ U u Ú ú Ù ù Û û Ü ü Ǔ ǔ Ŭ ŭ Ū ū Ũ ũ Ů ů Ų ų Ụ ụ Ű ű Ǘ ǘ Ǜ ǜ Ǚ ǚ Ǖ ǖ V v W w Ŵ ŵ X x Y y Ý ý Ŷ ŷ Ÿ ÿ Ỹ ỹ Ȳ ȳ Z z Ź ź Ż ż Ž ž ß Ð ð Þ þ Ŋ ŋ Ə ə Greek: Ά ά Έ έ Ή ή Ί ί Ό ό Ύ ύ Ώ ώ Α α Β β Γ γ Δ δ Ε ε Ζ ζ Η η Θ θ Ι ι Κ κ Λ λ Μ μ Ν ν Ξ ξ Ο ο Π π Ρ ρ Σ σ ς Τ τ Υ υ Φ φ Χ χ Ψ ψ Ω ω {{Polytonic|}} Cyrillic: А а Б б В в Г г Ґ ґ Ѓ ѓ Д д Ђ ђ Е е Ё ё Є є Ж ж З з Ѕ ѕ И и І і Ї ї Й й Ј ј К к Ќ ќ Л л Љ љ М м Н н Њ њ О о П п Р р С с Т т Ћ ћ У у Ў ў Ф ф Х х Ц ц Ч ч Џ џ Ш ш Щ щ Ъ ъ Ы ы Ь ь Э э Ю ю Я я ́ IPA: t̪ d̪ ʈ ɖ ɟ ɡ ɢ ʡ ʔ ɸ β θ ð ʃ ʒ ɕ ʑ ʂ ʐ ç ʝ ɣ χ ʁ ħ ʕ ʜ ʢ ɦ ɱ ɳ ɲ ŋ ɴ ʋ ɹ ɻ ɰ ʙ ⱱ ʀ ɾ ɽ ɫ ɬ ɮ ɺ ɭ ʎ ʟ ɥ ʍ ɧ ʼ ɓ ɗ ʄ ɠ ʛ ʘ ǀ ǃ ǂ ǁ ɨ ʉ ɯ ɪ ʏ ʊ ø ɘ ɵ ɤ ə ɚ ɛ œ ɜ ɝ ɞ ʌ ɔ æ ɐ ɶ ɑ ɒ ʰ ʱ ʷ ʲ ˠ ˤ ⁿ ˡ ˈ ˌ ː ˑ ̪ {{IPA|}} This page is a member of 12 hidden categories (help): |
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[SOURCE: https://en.wikipedia.org/wiki/2.5D] | [TOKENS: 5012] |
Contents 2.5D 2.5D (basic pronunciation two-and-a-half dimensional, two-point-five-d) perspective refers to gameplay or movement in a video game or virtual reality environment that is restricted to a two-dimensional (2D) plane with little to no access to a third dimension in a space that otherwise appears to be three-dimensional and is often simulated and rendered in a 3D digital environment. This is related to but separate from pseudo-3D perspective (sometimes called three-quarter view when the environment is portrayed from an angled top-down perspective), which refers to 2D graphical projections and similar techniques used to cause images or scenes to simulate the appearance of being three-dimensional (3D) when in fact they are not. By contrast, games, spaces or perspectives that are simulated and rendered in 3D and used in 3D level design are said to be true 3D, and 2D rendered games made to appear as 2D without approximating a 3D image are said to be true 2D. Common in video games, 2.5D projections have also been useful in geographic visualization (GVIS) to help understand visual-cognitive spatial representations or 3D visualization. The terms three-quarter perspective and three-quarter view trace their origins to the three-quarter profile in portraiture and facial recognition, which depicts a person's face that is partway between a frontal view and a side view. Computer graphics In axonometric projection and oblique projection, two forms of parallel projection, the viewpoint is rotated slightly to reveal other facets of the environment than what are visible in a top-down perspective or side view, thereby producing a three-dimensional effect. An object is "considered to be in an inclined position resulting in foreshortening of all three axes", and the image is a "representation on a single plane (as a drawing surface) of a three-dimensional object placed at an angle to the plane of projection." Lines perpendicular to the plane become points, lines parallel to the plane have true length, and lines inclined to the plane are foreshortened. They are popular camera perspectives among 2D video games, most commonly those released for 16-bit or earlier and handheld consoles, as well as in later strategy and role-playing video games. The advantage of these perspectives is that they combine the visibility and mobility of a top-down game with the character recognizability of a side-scrolling game. Thus the player can be presented an overview of the game world in the ability to see it from above, more or less, and with additional details in artwork made possible by using an angle: Instead of showing a humanoid in top-down perspective, as a head and shoulders seen from above, the entire body can be drawn when using a slanted angle; turning a character around would reveal how it looks from the sides, the front and the back, while the top-down perspective will display the same head and shoulders regardless. There are three main divisions of axonometric projection: isometric (equal measure), dimetric (symmetrical and unsymmetrical), and trimetric (single-view or only two sides). The most common of these drawing types in engineering drawing is isometric projection. This projection is tilted so that all three axes create equal angles at intervals of 120 degrees. The result is that all three axes are equally foreshortened. In video games, a form of dimetric projection with a 2:1 pixel ratio is more common due to the problems of anti-aliasing and square pixels found on most computer monitors. In oblique projection typically all three axes are shown without foreshortening. All lines parallel to the axes are drawn to scale, and diagonals and curved lines are distorted. One tell-tale sign of oblique projection is that the face pointed toward the camera retains its right angles with respect to the image plane.[clarification needed] Two examples of oblique projection are Ultima VII: The Black Gate and Paperboy. Examples of axonometric projection include SimCity 2000, and the role-playing games Diablo and Baldur's Gate. In three-dimensional scenes, the term billboarding is applied to a technique in which objects are sometimes represented by two-dimensional images applied to a single polygon which is typically kept perpendicular to the line of sight. The name refers to the fact that objects are seen as if drawn on a billboard. This technique was commonly used in early 1990s video games when consoles did not have the hardware power to render fully 3D objects. This is also known as a backdrop. This can be used to good effect for a significant performance boost when the geometry is sufficiently distant that it can be seamlessly replaced with a 2D sprite. In games, this technique is most frequently applied to objects such as particles (smoke, sparks, rain) and low-detail vegetation. It has since become mainstream, and is found in many games such as Rome: Total War, where it is exploited to simultaneously display thousands of individual soldiers on a battlefield. Early examples include early first-person shooters like Marathon Trilogy, Wolfenstein 3D, Doom, Hexen and Duke Nukem 3D as well as racing games like Carmageddon and Super Mario Kart and platformers like Super Mario 64. Skyboxes and skydomes are methods used to easily create a background to make a game level look bigger than it really is. If the level is enclosed in a cube, the sky, distant mountains, distant buildings, and other unreachable objects are rendered onto the cube's faces using a technique called cube mapping, thus creating the illusion of distant three-dimensional surroundings. A skydome employs the same concept but uses a sphere or hemisphere instead of a cube. As a viewer moves through a 3D scene, it is common for the skybox or skydome to remain stationary with respect to the viewer. This technique gives the skybox the illusion of being very far away since other objects in the scene appear to move, while the skybox does not. This imitates real life, where distant objects such as clouds, stars and even mountains appear to be stationary when the viewpoint is displaced by relatively small distances. Effectively, everything in a skybox will always appear to be infinitely distant from the viewer. This consequence of skyboxes dictates that designers should be careful not to carelessly include images of discrete objects in the textures of a skybox since the viewer may be able to perceive the inconsistencies of those objects' sizes as the scene is traversed. In some games, sprites are scaled larger or smaller depending on its distance to the player, producing the illusion of motion along the Z (forward) axis. Sega's 1986 video game Out Run, which runs on the Sega OutRun arcade system board, is a good example of this technique. In Out Run, the player drives a Ferrari into depth of the game window. The palms on the left and right side of the street are the same bitmap, but have been scaled to different sizes, creating the illusion that some are closer than others. The angles of movement are "left and right" and "into the depth" (while still capable of doing so technically, this game did not allow making a U-turn or going into reverse, therefore moving "out of the depth", as this did not make sense to the high-speed game play and tense time limit). Notice the view is comparable to that which a driver would have in reality when driving a car. The position and size of any billboard is generated by a (complete 3D) perspective transformation as are the vertices of the poly-line representing the center of the street. Often the center of the street is stored as a spline and sampled in a way that on straight streets every sampling point corresponds to one scan-line on the screen. Hills and curves lead to multiple points on one line and one has to be chosen. Or one line is without any point and has to be interpolated lineary from the adjacent lines. Very memory intensive billboards are used in Out Run to draw corn-fields and water waves which are wider than the screen even at the largest viewing distance and also in Test Drive to draw trees and cliffs. Drakkhen was notable for being among the first role-playing video games to feature a three-dimensional playing field. However, it did not employ a conventional 3D game engine, instead emulating one using character-scaling algorithms. The player's party travels overland on a flat terrain made up of vectors, on which 2D objects are zoomed. Drakkhen features an animated day-night cycle, and the ability to wander freely about the game world, both rarities for a game of its era. This type of engine was later used in the game Eternam. Some mobile games that were released on the Java ME platform, such as the mobile version of Asphalt: Urban GT and Driver: L.A. Undercover, used this method for rendering the scenery. While the technique is similar to some of Sega's arcade games, such as Thunder Blade and Cool Riders and the 32-bit version of Road Rash, it uses polygons instead of sprite scaling for buildings and certain objects though it looks flat shaded. Later mobile games (mainly from Gameloft), such as Asphalt 4: Elite Racing and the mobile version of Iron Man 2, uses a mix of sprite scaling and texture mapping for some buildings and objects. Parallaxing refers to when a collection of 2D sprites or layers of sprites are made to move independently of each other and/or the background to create a sense of added depth.: 103 This depth cue is created by relative motion of layers. The technique grew out of the multiplane camera technique used in traditional animation since the 1940s. This type of graphical effect was first used in the 1982 arcade game Moon Patrol. Examples include the skies in Rise of the Triad, the arcade version of Rygar, Sonic the Hedgehog, Street Fighter II, Shadow of the Beast and Dracula X Chronicles, as well as Super Mario World. Mode 7, a display system effect that included rotation and scaling, allowed for a 3D effect while moving in any direction without any actual 3D models, and was used to simulate 3D graphics on the SNES. Ray casting is a first person pseudo-3D technique in which a ray for every vertical slice of the screen is sent from the position of the camera. These rays shoot out until they hit an object or wall, and that part of the wall is rendered in that vertical screen slice. Due to the limited camera movement and internally 2D playing field, this is often considered 2.5D. Bump mapping, normal mapping and parallax mapping are techniques applied to textures in 3D rendering applications such as video games to simulate bumps and wrinkles on the surface of an object without using more polygons. To the end user, this means that textures such as stone walls will have more apparent depth and thus greater realism with less of an influence on the performance of the simulation. Bump mapping is achieved by perturbing the surface normals of an object and using a grayscale image and the perturbed normal during illumination calculations. The result is an apparently bumpy surface rather than a perfectly smooth surface although the surface of the underlying object is not actually changed. Bump mapping was introduced by Blinn in 1978. In normal mapping, the unit vector from the shading point to the light source is dotted with the unit vector normal to that surface, and the dot product is the intensity of the light on that surface. Imagine a polygonal model of a sphere—you can only approximate the shape of the surface. By using a 3-channel bitmapped image textured across the model, more detailed normal vector information can be encoded. Each channel in the bitmap corresponds to a spatial dimension (x, y and z). These spatial dimensions are relative to a constant coordinate system for object-space normal maps, or to a smoothly varying coordinate system (based on the derivatives of position with respect to texture coordinates) in the case of tangent-space normal maps. This adds much more detail to the surface of a model, especially in conjunction with advanced lighting techniques. Parallax mapping (also called offset mapping or virtual displacement mapping) is an enhancement of the bump mapping and normal mapping techniques implemented by displacing the texture coordinates at a point on the rendered polygon by a function of the view angle in tangent space (the angle relative to the surface normal) and the value of the height map at that point. At steeper view-angles, the texture coordinates are displaced more, giving the illusion of depth due to parallax effects as the view changes. Film and animation techniques The term is also used to describe an animation effect commonly used in music videos and, more frequently, title sequences. Brought to wide attention by the motion picture The Kid Stays in the Picture, an adaptation of film producer Robert Evans's memoir, it involves the layering and animating of two-dimensional pictures in three-dimensional space. Earlier examples of this technique include Liz Phair's music video "Down" (directed by Rodney Ascher) and "A Special Tree" (directed by musician Giorgio Moroder). On a larger scale, the 2018 movie In Saturn's Rings used over 7.5 million separate two-dimensional images, captured in space or by telescopes, which were composited and moved using multi-plane animation techniques. Graphic design The term also refers to an often-used effect in the design of icons and graphical user interfaces (GUIs), where a slight 3D illusion is created by the presence of a virtual light source to the left (or in some cases right) side, and above a person's computer monitor. The light source itself is always invisible, but its effects are seen in the lighter colors for the top and left side, simulating reflection, and the darker colours to the right and below of such objects, simulating shadow. An advanced version of this technique can be found in some specialised graphic design software, such as Pixologic's ZBrush. The idea is that the program's canvas represents a normal 2D painting surface, but that the data structure that holds the pixel information is also able to store information with respect to a z-index, as well material settings, specularity, etc. Again, with this data it is thus possible to simulate lighting, shadows, and so forth. History The first video games that used pseudo-3D were primarily arcade games, the earliest known examples dating back to the mid-1970s, when they began using microprocessors. In 1975, Taito released Interceptor, an early first-person shooter and combat flight simulator that involved piloting a jet fighter, using an eight-way joystick to aim with a crosshair and shoot at enemy aircraft that move in formations of two and increase/decrease in size depending on their distance to the player. In 1976, Sega released Moto-Cross, an early black-and-white motorbike racing video game, based on the motocross competition, that was most notable for introducing an early three-dimensional third-person perspective. Later that year, Sega-Gremlin re-branded the game as Fonz, as a tie-in for the popular sitcom Happy Days. Both versions of the game displayed a constantly changing forward-scrolling road and the player's bike in a third-person perspective where objects nearer to the player are larger than those nearer to the horizon, and the aim was to steer the vehicle across the road, racing against the clock, while avoiding any on-coming motorcycles or driving off the road. That same year also saw the release of two arcade games that extended the car driving subgenre into three dimensions with a first-person perspective: Sega's Road Race, which displayed a constantly changing forward-scrolling S-shaped road with two obstacle race cars moving along the road that the player must avoid crashing while racing against the clock, and Atari's Night Driver, which presented a series of posts by the edge of the road though there was no view of the road or the player's car. Games using vector graphics had an advantage in creating pseudo-3D effects. 1979's Speed Freak recreated the perspective of Night Driver in greater detail. In 1979, Nintendo debuted Radar Scope, a shoot 'em up that introduced a three-dimensional third-person perspective to the genre, imitated years later by shooters such as Konami's Juno First and Activision's Beamrider. In 1980, Atari's Battlezone was a breakthrough for pseudo-3D gaming, recreating a 3D perspective with unprecedented realism, though the gameplay was still planar. It was followed up that same year by Red Baron, which used scaling vector images to create a forward scrolling rail shooter. Sega's arcade shooter Space Tactics, released in 1980, allowed players to take aim using crosshairs and shoot lasers into the screen at enemies coming towards them, creating an early 3D effect. It was followed by other arcade shooters with a first-person perspective during the early 1980s, including Taito's 1981 release Space Seeker, and Sega's Star Trek in 1982. Sega's SubRoc-3D in 1982 also featured a first-person perspective and introduced the use of stereoscopic 3-D through a special eyepiece. Sega's Astron Belt in 1983 was the first laserdisc video game, using full-motion video to display the graphics from a first-person perspective. Third-person rail shooters were also released in arcades at the time, including Sega's Tac/Scan in 1982, Nippon's Ambush in 1983, Nichibutsu's Tube Panic in 1983, and Sega's 1982 release Buck Rogers: Planet of Zoom, notable for its fast pseudo-3D scaling and detailed sprites. In 1981, Sega's Turbo was the first racing game to use sprite scaling with full-colour graphics. Pole Position by Namco is one of the first racing games to use the trailing camera effect that is now so familiar [citation needed]. In this particular example, the effect was produced by linescroll—the practice of scrolling each line independently in order to warp an image. In this case, the warping would simulate curves and steering. To make the road appear to move towards the player, per-line color changes were used, though many console versions opted for palette animation instead. Zaxxon, a shooter introduced by Sega in 1982, was the first game to use isometric axonometric projection, from which its name is derived. Though Zaxxon's playing field is semantically 3D, the game has many constraints which classify it as 2.5D: a fixed point of view, scene composition from sprites, and movements such as bullet shots restricted to straight lines along the axes. It was also one of the first video games to display shadows. The following year, Sega released the first pseudo-3D isometric platformer, Congo Bongo. Another early pseudo-3D platform game released that year was Konami's Antarctic Adventure, where the player controls a penguin in a forward-scrolling third-person perspective while having to jump over pits and obstacles. It was one of the earliest pseudo-3D games available on a computer, released for the MSX in 1983. That same year, Irem's Moon Patrol was a side-scrolling run & gun platform-shooter that introduced the use of layered parallax scrolling to give a pseudo-3D effect. In 1985, Space Harrier introduced Sega's "Super Scaler" technology that allowed pseudo-3D sprite-scaling at high frame rates, with the ability to scale 32,000 sprites and fill a moving landscape with them. The first original home console game to use pseudo-3D, and also the first to use multiple camera angles mirrored on television sports broadcasts, was Intellivision World Series Baseball (1983) by Don Daglow and Eddie Dombrower, published by Mattel. Its television sports style of display was later adopted by 3D sports games and is now used by virtually all major team sports titles. In 1984, Sega ported several pseudo-3D arcade games to the Sega SG-1000 console, including a smooth conversion of the third-person pseudo-3D rail shooter Buck Rogers: Planet of Zoom. By 1989, 2.5D representations were surfaces drawn with depth cues and a part of graphic libraries like GINO. 2.5D was also used in terrain modeling with software packages such as ISM from Dynamic Graphics, GEOPAK from Uniras and the Intergraph DTM system. 2.5D surface techniques gained popularity within the geography community because of its ability to visualize the normal thickness to area ratio used in many geographic models; this ratio was very small and reflected the thinness of the object in relation to its width, which made it the object realistic in a specific plane. These representations were axiomatic in that the entire subsurface domain was not used or the entire domain could not be reconstructed; therefore, it used only a surface and a surface is one aspect not the full 3D identity. The specific term "two-and-a-half-D" was used as early as 1994 by Warren Spector in an interview in the North American premiere issue of PC Gamer magazine. At the time, the term was understood to refer specifically to first-person shooters like Wolfenstein 3D and Doom, to distinguish them from System Shock's "true" 3D engine. With the advent of consoles and computer systems that were able to handle several thousand polygons (the most basic element of 3D computer graphics) per second and the usage of 3D specialized graphics processing units, pseudo-3D became obsolete. But even today, there are computer systems in production, such as cellphones, which are often not powerful enough to display true 3D graphics, and therefore use pseudo-3D for that purpose. Many games from the 1980s' pseudo-3D arcade era and 16-bit console era are ported to these systems, giving the manufacturers the possibility to earn revenues from games that are several decades old. The resurgence of 2.5D or visual analysis, in natural and earth science, has increased the role of computer systems in the creation of spatial information in mapping. GVIS has made real the search for unknowns, real-time interaction with spatial data, and control over map display and has paid particular attention to three-dimensional representations. Efforts in GVIS have attempted to expand higher dimensions and make them more visible; most efforts have focused on "tricking" vision into seeing three dimensions in a 2D plane. Much like 2.5D displays where the surface of a three-dimensional object is represented but locations within the solid are distorted or not accessible. Technical aspects and generalizations The reason for using pseudo-3D instead of "real" 3D computer graphics is that the system that has to simulate a 3D-looking graphic is not powerful enough to handle the calculation-intensive routines of 3D computer graphics, yet is capable of using tricks of modifying 2D graphics like bitmaps. One of these tricks is to stretch a bitmap more and more, therefore making it larger with each step, as to give the effect of an object coming closer and closer towards the player. Even simple shading and size of an image could be considered pseudo-3D, as shading makes it look more realistic. If the light in a 2D game were 2D, it would only be visible on the outline, and because outlines are often dark, they would not be very clearly visible. However, any visible shading would indicate the usage of pseudo-3D lighting and that the image uses pseudo-3D graphics. Changing the size of an image can cause the image to appear to be moving closer or further away, which could be considered simulating a third dimension. Dimensions are the variables of the data and can be mapped to specific locations in space; 2D data can be given 3D volume by adding a value to the x, y, or z plane. "Assigning height to 2D regions of a topographic map" associating every 2D location with a height/elevation value creates a 2.5D projection; this is not considered a "true 3D representation", however is used like 3D visual representation to "simplify visual processing of imagery and the resulting spatial cognition". See also References |
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[SOURCE: https://en.wikipedia.org/wiki/Texture_mapping#cite_ref-Catmull_thesis_4-0] | [TOKENS: 4408] |
Contents Texture mapping Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV space). Semantic Texture mapping can multiply refer to (1) the task of unwrapping a 3D model (converting the surface of a 3D model into a 2D texture map), (2) applying a 2D texture map onto the surface of a 3D model, and (3) the 3D software algorithm that performs both tasks. A texture map refers to a 2D image ("texture") that adds visual detail to a 3D model. The image can be stored as a raster graphic. A texture that stores a specific property—such as bumpiness, reflectivity, or transparency—is also referred to as a color map or roughness map. The coordinate space that converts from a 3D model's 3D space into a 2D space for sampling from the texture map is variously called UV space, UV coordinates, or texture space. Algorithm The following is a simplified explanation of how an algorithm could work to render an image: History The original technique was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. Texture maps A texture map is an image applied ("mapped") to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3D model formats or material definitions, and assembled into resource bundles. They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources (which may be located in device memory) as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping. Texture maps usually contain RGB color data (either stored as direct color, compressed formats, or indexed color), and sometimes an additional channel for alpha blending (RGBA) especially for billboards and decal overlay textures. It is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity. Multiple texture maps (or channels) may be combined for control over specularity, normals, displacement, or subsurface scattering, e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered a modern evolution of tile map graphics). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning or digital photography, designed in image manipulation software such as GIMP or Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush. This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2D case is also known as UV coordinates). This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3D space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface (which is important for render mapping and light mapping, also known as baking). Texture mapping maps the model surface (or screen space during rasterization) into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on the screen) are calculated from the texels (texture pixels) is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination) into a surface texture (possibly on a low-resolution model). This technique is called baking (or render mapping) and is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games (e.g. Messiah) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps in a process called surface caching. Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Rasterisation algorithms Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility, and performance. Affine texture mapping linearly interpolates texture coordinates across a surface, making it the fastest form of texture mapping. Some software and hardware (such as the original PlayStation) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed-point UV coordinates or by an incremental error algorithm akin to Bresenham's line algorithm. In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (as shown in the figure: the checker box texture appears bent), especially as primitives near the camera. This distortion can be reduced by subdividing polygons into smaller polygons. Using quad primitives for rectangular objects can look less incorrect than if those rectangles were split into triangles. However, since interpolating four points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the forward texture mapping used by the Nvidia NV1, offered efficient quad primitives. With perspective correction, triangles become equivalent to quad primitives and this advantage disappears. For rectangular objects that are at right angles to the viewer (like floors and walls), the perspective only needs to be corrected in one direction across the screen rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor. Affine linear interpolation across that horizontal span will look correct because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space rather than simply interpolating coordinates in 2D screen space. While achieving the correct visual effect, perspective correct texturing is more expensive to calculate. To perform perspective correction of the texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, it is possible to take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across the surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} , and v {\displaystyle v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to produce a perspective correct texture mapping. To do this, the reciprocals at each vertex of the geometry (three points for a triangle) are calculated. Vertex n {\displaystyle n} has reciprocals u n z n {\displaystyle {\frac {u_{n}}{z_{n}}}} , v n z n {\displaystyle {\frac {v_{n}}{z_{n}}}} , and 1 z n {\displaystyle {\frac {1}{z_{n}}}} . Then, linear interpolation can be done on these reciprocals between the n {\displaystyle n} vertices (e.g., using barycentric coordinates), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} and 1 z i {\displaystyle {\frac {1}{z_{i}}}} (reciprocal z i {\displaystyle z_{i}} ). However, as our division by z {\displaystyle z} altered their coordinate system, this u i , v i {\displaystyle u_{i},v_{i}} cannot be used as texture coordinates. To correct back to the u , v {\displaystyle u,v} space, the corrected z {\displaystyle z} is calculated by taking the reciprocal once again: z c o r r e c t = 1 1 z i {\displaystyle z_{correct}={\frac {1}{\frac {1}{z_{i}}}}} . This is then used to correct the u i , v i {\displaystyle u_{i},v_{i}} coordinates: u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that the difference from pixel to pixel between texture coordinates is smaller in parts of the polygon that are closer to the viewer (stretching the texture wider) and is larger in parts that are farther away (compressing the texture). Affine texture mapping directly interpolates a texture coordinate u α {\displaystyle u_{\alpha }} between two endpoints u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} : u α = ( 1 − α ) u 0 + α u 1 {\displaystyle u_{\alpha }=(1-\alpha )u_{0}+\alpha u_{1}} where 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1} . Perspective correct mapping interpolates after dividing by depth z {\displaystyle z} , then uses its interpolated reciprocal to recover the correct coordinate: u α = ( 1 − α ) u 0 z 0 + α u 1 z 1 ( 1 − α ) 1 z 0 + α 1 z 1 {\displaystyle u_{\alpha }={\frac {(1-\alpha ){\frac {u_{0}}{z_{0}}}+\alpha {\frac {u_{1}}{z_{1}}}}{(1-\alpha ){\frac {1}{z_{0}}}+\alpha {\frac {1}{z_{1}}}}}} 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality and precision trade-offs, which can be applied to both software and hardware. Classic software texture mappers generally only performed simple texture mapping with one lighting effect at most (typically applied through a lookup table), and the perspective correctness was about 16 times more expensive.[compared to?] The Doom engine restricted the world to vertical walls and horizontal floors and ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors and ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom while using the same rendering technique. Some engines were able to render texture mapped heightmaps (e.g. Nova Logic's Voxel Space, and the engine for Outcast) via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals: keeping the arithmetic mill busy at all times and producing faster arithmetic results.[vague] For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware and had a relatively high triangle throughput compared to its peers. Software renderers generally prefer screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2D affine interpolation), thus lessening the overhead further. Another reason is that affine texture mapping does not fit into the low number of CPU registers of the x86 CPU; the 68000 and RISC processors are much more suited for that approach. A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. As the polygons are rendered independently, it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z, but the effort seems not to be worth it.[original research?] One other technique is to approximate the perspective with a faster calculation, such as a polynomial. A second uses the 1 z i {\textstyle {\frac {1}{z_{i}}}} value of the last two drawn pixels to linearly extrapolate the next value. For the latter, the division is then done starting from those values so that all that has to be divided is a small remainder. However, the amount of bookkeeping needed makes this technique too slow on most systems.[citation needed] A third technique, used by the Build Engine (used, most notably, in Duke Nukem 3D), builds on the constant distance trick used by the Doom engine by finding and rendering along the line of constant distance for arbitrary polygons. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG) and professional graphics workstations (such as Silicon Graphics) and broadcast digital video effects machines such as the Ampex ADO. Texture mapping hardware later appeared in arcade cabinets, consumer video game consoles, and PC video cards in the mid-1990s. In flight simulations, texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. Additionally, texture mapping was implemented so that real-time processing of prefiltered texture patterns stored in memory could be accessed by the video processor in real-time. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU. Some hardware implementations combine texture mapping with hidden-surface determination in tile-based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting. On earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen: Of these methods, inverse texture mapping has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive. The primary advantage of this method is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage is that the memory access pattern in the texture space will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness. Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer. This was used by some hardware, such as the 3DO, the Sega Saturn and the NV1. The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see the § Affine texture mapping section above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness. UV mapping became an important technique for 3D modelling and assisted in clipping the texture correctly when the primitive went past the edge of the screen, but existing hardware did not provide effective implementations of this. These shortcomings could have been addressed with further development, but GPU design has mostly shifted toward using the inverse mapping technique. Applications Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks: It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results. Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Exposé in Mac OS X. See also References Software External links |
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[SOURCE: https://en.wikipedia.org/wiki/Texture_mapping#cite_ref-3] | [TOKENS: 4408] |
Contents Texture mapping Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV space). Semantic Texture mapping can multiply refer to (1) the task of unwrapping a 3D model (converting the surface of a 3D model into a 2D texture map), (2) applying a 2D texture map onto the surface of a 3D model, and (3) the 3D software algorithm that performs both tasks. A texture map refers to a 2D image ("texture") that adds visual detail to a 3D model. The image can be stored as a raster graphic. A texture that stores a specific property—such as bumpiness, reflectivity, or transparency—is also referred to as a color map or roughness map. The coordinate space that converts from a 3D model's 3D space into a 2D space for sampling from the texture map is variously called UV space, UV coordinates, or texture space. Algorithm The following is a simplified explanation of how an algorithm could work to render an image: History The original technique was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. Texture maps A texture map is an image applied ("mapped") to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3D model formats or material definitions, and assembled into resource bundles. They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources (which may be located in device memory) as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping. Texture maps usually contain RGB color data (either stored as direct color, compressed formats, or indexed color), and sometimes an additional channel for alpha blending (RGBA) especially for billboards and decal overlay textures. It is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity. Multiple texture maps (or channels) may be combined for control over specularity, normals, displacement, or subsurface scattering, e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered a modern evolution of tile map graphics). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning or digital photography, designed in image manipulation software such as GIMP or Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush. This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2D case is also known as UV coordinates). This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3D space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface (which is important for render mapping and light mapping, also known as baking). Texture mapping maps the model surface (or screen space during rasterization) into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on the screen) are calculated from the texels (texture pixels) is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination) into a surface texture (possibly on a low-resolution model). This technique is called baking (or render mapping) and is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games (e.g. Messiah) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps in a process called surface caching. Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Rasterisation algorithms Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility, and performance. Affine texture mapping linearly interpolates texture coordinates across a surface, making it the fastest form of texture mapping. Some software and hardware (such as the original PlayStation) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed-point UV coordinates or by an incremental error algorithm akin to Bresenham's line algorithm. In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (as shown in the figure: the checker box texture appears bent), especially as primitives near the camera. This distortion can be reduced by subdividing polygons into smaller polygons. Using quad primitives for rectangular objects can look less incorrect than if those rectangles were split into triangles. However, since interpolating four points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the forward texture mapping used by the Nvidia NV1, offered efficient quad primitives. With perspective correction, triangles become equivalent to quad primitives and this advantage disappears. For rectangular objects that are at right angles to the viewer (like floors and walls), the perspective only needs to be corrected in one direction across the screen rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor. Affine linear interpolation across that horizontal span will look correct because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space rather than simply interpolating coordinates in 2D screen space. While achieving the correct visual effect, perspective correct texturing is more expensive to calculate. To perform perspective correction of the texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, it is possible to take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across the surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} , and v {\displaystyle v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to produce a perspective correct texture mapping. To do this, the reciprocals at each vertex of the geometry (three points for a triangle) are calculated. Vertex n {\displaystyle n} has reciprocals u n z n {\displaystyle {\frac {u_{n}}{z_{n}}}} , v n z n {\displaystyle {\frac {v_{n}}{z_{n}}}} , and 1 z n {\displaystyle {\frac {1}{z_{n}}}} . Then, linear interpolation can be done on these reciprocals between the n {\displaystyle n} vertices (e.g., using barycentric coordinates), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} and 1 z i {\displaystyle {\frac {1}{z_{i}}}} (reciprocal z i {\displaystyle z_{i}} ). However, as our division by z {\displaystyle z} altered their coordinate system, this u i , v i {\displaystyle u_{i},v_{i}} cannot be used as texture coordinates. To correct back to the u , v {\displaystyle u,v} space, the corrected z {\displaystyle z} is calculated by taking the reciprocal once again: z c o r r e c t = 1 1 z i {\displaystyle z_{correct}={\frac {1}{\frac {1}{z_{i}}}}} . This is then used to correct the u i , v i {\displaystyle u_{i},v_{i}} coordinates: u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that the difference from pixel to pixel between texture coordinates is smaller in parts of the polygon that are closer to the viewer (stretching the texture wider) and is larger in parts that are farther away (compressing the texture). Affine texture mapping directly interpolates a texture coordinate u α {\displaystyle u_{\alpha }} between two endpoints u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} : u α = ( 1 − α ) u 0 + α u 1 {\displaystyle u_{\alpha }=(1-\alpha )u_{0}+\alpha u_{1}} where 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1} . Perspective correct mapping interpolates after dividing by depth z {\displaystyle z} , then uses its interpolated reciprocal to recover the correct coordinate: u α = ( 1 − α ) u 0 z 0 + α u 1 z 1 ( 1 − α ) 1 z 0 + α 1 z 1 {\displaystyle u_{\alpha }={\frac {(1-\alpha ){\frac {u_{0}}{z_{0}}}+\alpha {\frac {u_{1}}{z_{1}}}}{(1-\alpha ){\frac {1}{z_{0}}}+\alpha {\frac {1}{z_{1}}}}}} 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality and precision trade-offs, which can be applied to both software and hardware. Classic software texture mappers generally only performed simple texture mapping with one lighting effect at most (typically applied through a lookup table), and the perspective correctness was about 16 times more expensive.[compared to?] The Doom engine restricted the world to vertical walls and horizontal floors and ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors and ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom while using the same rendering technique. Some engines were able to render texture mapped heightmaps (e.g. Nova Logic's Voxel Space, and the engine for Outcast) via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals: keeping the arithmetic mill busy at all times and producing faster arithmetic results.[vague] For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware and had a relatively high triangle throughput compared to its peers. Software renderers generally prefer screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2D affine interpolation), thus lessening the overhead further. Another reason is that affine texture mapping does not fit into the low number of CPU registers of the x86 CPU; the 68000 and RISC processors are much more suited for that approach. A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. As the polygons are rendered independently, it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z, but the effort seems not to be worth it.[original research?] One other technique is to approximate the perspective with a faster calculation, such as a polynomial. A second uses the 1 z i {\textstyle {\frac {1}{z_{i}}}} value of the last two drawn pixels to linearly extrapolate the next value. For the latter, the division is then done starting from those values so that all that has to be divided is a small remainder. However, the amount of bookkeeping needed makes this technique too slow on most systems.[citation needed] A third technique, used by the Build Engine (used, most notably, in Duke Nukem 3D), builds on the constant distance trick used by the Doom engine by finding and rendering along the line of constant distance for arbitrary polygons. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG) and professional graphics workstations (such as Silicon Graphics) and broadcast digital video effects machines such as the Ampex ADO. Texture mapping hardware later appeared in arcade cabinets, consumer video game consoles, and PC video cards in the mid-1990s. In flight simulations, texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. Additionally, texture mapping was implemented so that real-time processing of prefiltered texture patterns stored in memory could be accessed by the video processor in real-time. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU. Some hardware implementations combine texture mapping with hidden-surface determination in tile-based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting. On earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen: Of these methods, inverse texture mapping has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive. The primary advantage of this method is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage is that the memory access pattern in the texture space will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness. Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer. This was used by some hardware, such as the 3DO, the Sega Saturn and the NV1. The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see the § Affine texture mapping section above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness. UV mapping became an important technique for 3D modelling and assisted in clipping the texture correctly when the primitive went past the edge of the screen, but existing hardware did not provide effective implementations of this. These shortcomings could have been addressed with further development, but GPU design has mostly shifted toward using the inverse mapping technique. Applications Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks: It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results. Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Exposé in Mac OS X. See also References Software External links |
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[SOURCE: https://en.wikipedia.org/wiki/Texture_mapping#cite_ref-8] | [TOKENS: 4408] |
Contents Texture mapping Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV space). Semantic Texture mapping can multiply refer to (1) the task of unwrapping a 3D model (converting the surface of a 3D model into a 2D texture map), (2) applying a 2D texture map onto the surface of a 3D model, and (3) the 3D software algorithm that performs both tasks. A texture map refers to a 2D image ("texture") that adds visual detail to a 3D model. The image can be stored as a raster graphic. A texture that stores a specific property—such as bumpiness, reflectivity, or transparency—is also referred to as a color map or roughness map. The coordinate space that converts from a 3D model's 3D space into a 2D space for sampling from the texture map is variously called UV space, UV coordinates, or texture space. Algorithm The following is a simplified explanation of how an algorithm could work to render an image: History The original technique was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. Texture maps A texture map is an image applied ("mapped") to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3D model formats or material definitions, and assembled into resource bundles. They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources (which may be located in device memory) as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping. Texture maps usually contain RGB color data (either stored as direct color, compressed formats, or indexed color), and sometimes an additional channel for alpha blending (RGBA) especially for billboards and decal overlay textures. It is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity. Multiple texture maps (or channels) may be combined for control over specularity, normals, displacement, or subsurface scattering, e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered a modern evolution of tile map graphics). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning or digital photography, designed in image manipulation software such as GIMP or Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush. This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2D case is also known as UV coordinates). This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3D space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface (which is important for render mapping and light mapping, also known as baking). Texture mapping maps the model surface (or screen space during rasterization) into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on the screen) are calculated from the texels (texture pixels) is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination) into a surface texture (possibly on a low-resolution model). This technique is called baking (or render mapping) and is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games (e.g. Messiah) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps in a process called surface caching. Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Rasterisation algorithms Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility, and performance. Affine texture mapping linearly interpolates texture coordinates across a surface, making it the fastest form of texture mapping. Some software and hardware (such as the original PlayStation) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed-point UV coordinates or by an incremental error algorithm akin to Bresenham's line algorithm. In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (as shown in the figure: the checker box texture appears bent), especially as primitives near the camera. This distortion can be reduced by subdividing polygons into smaller polygons. Using quad primitives for rectangular objects can look less incorrect than if those rectangles were split into triangles. However, since interpolating four points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the forward texture mapping used by the Nvidia NV1, offered efficient quad primitives. With perspective correction, triangles become equivalent to quad primitives and this advantage disappears. For rectangular objects that are at right angles to the viewer (like floors and walls), the perspective only needs to be corrected in one direction across the screen rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor. Affine linear interpolation across that horizontal span will look correct because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space rather than simply interpolating coordinates in 2D screen space. While achieving the correct visual effect, perspective correct texturing is more expensive to calculate. To perform perspective correction of the texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, it is possible to take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across the surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} , and v {\displaystyle v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to produce a perspective correct texture mapping. To do this, the reciprocals at each vertex of the geometry (three points for a triangle) are calculated. Vertex n {\displaystyle n} has reciprocals u n z n {\displaystyle {\frac {u_{n}}{z_{n}}}} , v n z n {\displaystyle {\frac {v_{n}}{z_{n}}}} , and 1 z n {\displaystyle {\frac {1}{z_{n}}}} . Then, linear interpolation can be done on these reciprocals between the n {\displaystyle n} vertices (e.g., using barycentric coordinates), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} and 1 z i {\displaystyle {\frac {1}{z_{i}}}} (reciprocal z i {\displaystyle z_{i}} ). However, as our division by z {\displaystyle z} altered their coordinate system, this u i , v i {\displaystyle u_{i},v_{i}} cannot be used as texture coordinates. To correct back to the u , v {\displaystyle u,v} space, the corrected z {\displaystyle z} is calculated by taking the reciprocal once again: z c o r r e c t = 1 1 z i {\displaystyle z_{correct}={\frac {1}{\frac {1}{z_{i}}}}} . This is then used to correct the u i , v i {\displaystyle u_{i},v_{i}} coordinates: u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that the difference from pixel to pixel between texture coordinates is smaller in parts of the polygon that are closer to the viewer (stretching the texture wider) and is larger in parts that are farther away (compressing the texture). Affine texture mapping directly interpolates a texture coordinate u α {\displaystyle u_{\alpha }} between two endpoints u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} : u α = ( 1 − α ) u 0 + α u 1 {\displaystyle u_{\alpha }=(1-\alpha )u_{0}+\alpha u_{1}} where 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1} . Perspective correct mapping interpolates after dividing by depth z {\displaystyle z} , then uses its interpolated reciprocal to recover the correct coordinate: u α = ( 1 − α ) u 0 z 0 + α u 1 z 1 ( 1 − α ) 1 z 0 + α 1 z 1 {\displaystyle u_{\alpha }={\frac {(1-\alpha ){\frac {u_{0}}{z_{0}}}+\alpha {\frac {u_{1}}{z_{1}}}}{(1-\alpha ){\frac {1}{z_{0}}}+\alpha {\frac {1}{z_{1}}}}}} 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality and precision trade-offs, which can be applied to both software and hardware. Classic software texture mappers generally only performed simple texture mapping with one lighting effect at most (typically applied through a lookup table), and the perspective correctness was about 16 times more expensive.[compared to?] The Doom engine restricted the world to vertical walls and horizontal floors and ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors and ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom while using the same rendering technique. Some engines were able to render texture mapped heightmaps (e.g. Nova Logic's Voxel Space, and the engine for Outcast) via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals: keeping the arithmetic mill busy at all times and producing faster arithmetic results.[vague] For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware and had a relatively high triangle throughput compared to its peers. Software renderers generally prefer screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2D affine interpolation), thus lessening the overhead further. Another reason is that affine texture mapping does not fit into the low number of CPU registers of the x86 CPU; the 68000 and RISC processors are much more suited for that approach. A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. As the polygons are rendered independently, it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z, but the effort seems not to be worth it.[original research?] One other technique is to approximate the perspective with a faster calculation, such as a polynomial. A second uses the 1 z i {\textstyle {\frac {1}{z_{i}}}} value of the last two drawn pixels to linearly extrapolate the next value. For the latter, the division is then done starting from those values so that all that has to be divided is a small remainder. However, the amount of bookkeeping needed makes this technique too slow on most systems.[citation needed] A third technique, used by the Build Engine (used, most notably, in Duke Nukem 3D), builds on the constant distance trick used by the Doom engine by finding and rendering along the line of constant distance for arbitrary polygons. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG) and professional graphics workstations (such as Silicon Graphics) and broadcast digital video effects machines such as the Ampex ADO. Texture mapping hardware later appeared in arcade cabinets, consumer video game consoles, and PC video cards in the mid-1990s. In flight simulations, texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. Additionally, texture mapping was implemented so that real-time processing of prefiltered texture patterns stored in memory could be accessed by the video processor in real-time. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU. Some hardware implementations combine texture mapping with hidden-surface determination in tile-based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting. On earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen: Of these methods, inverse texture mapping has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive. The primary advantage of this method is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage is that the memory access pattern in the texture space will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness. Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer. This was used by some hardware, such as the 3DO, the Sega Saturn and the NV1. The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see the § Affine texture mapping section above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness. UV mapping became an important technique for 3D modelling and assisted in clipping the texture correctly when the primitive went past the edge of the screen, but existing hardware did not provide effective implementations of this. These shortcomings could have been addressed with further development, but GPU design has mostly shifted toward using the inverse mapping technique. Applications Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks: It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results. Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Exposé in Mac OS X. See also References Software External links |
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[SOURCE: https://en.wikipedia.org/wiki/Texture_mapping#cite_ref-6] | [TOKENS: 4408] |
Contents Texture mapping Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV space). Semantic Texture mapping can multiply refer to (1) the task of unwrapping a 3D model (converting the surface of a 3D model into a 2D texture map), (2) applying a 2D texture map onto the surface of a 3D model, and (3) the 3D software algorithm that performs both tasks. A texture map refers to a 2D image ("texture") that adds visual detail to a 3D model. The image can be stored as a raster graphic. A texture that stores a specific property—such as bumpiness, reflectivity, or transparency—is also referred to as a color map or roughness map. The coordinate space that converts from a 3D model's 3D space into a 2D space for sampling from the texture map is variously called UV space, UV coordinates, or texture space. Algorithm The following is a simplified explanation of how an algorithm could work to render an image: History The original technique was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. Texture maps A texture map is an image applied ("mapped") to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3D model formats or material definitions, and assembled into resource bundles. They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources (which may be located in device memory) as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping. Texture maps usually contain RGB color data (either stored as direct color, compressed formats, or indexed color), and sometimes an additional channel for alpha blending (RGBA) especially for billboards and decal overlay textures. It is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity. Multiple texture maps (or channels) may be combined for control over specularity, normals, displacement, or subsurface scattering, e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered a modern evolution of tile map graphics). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning or digital photography, designed in image manipulation software such as GIMP or Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush. This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2D case is also known as UV coordinates). This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3D space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface (which is important for render mapping and light mapping, also known as baking). Texture mapping maps the model surface (or screen space during rasterization) into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on the screen) are calculated from the texels (texture pixels) is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination) into a surface texture (possibly on a low-resolution model). This technique is called baking (or render mapping) and is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games (e.g. Messiah) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps in a process called surface caching. Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Rasterisation algorithms Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility, and performance. Affine texture mapping linearly interpolates texture coordinates across a surface, making it the fastest form of texture mapping. Some software and hardware (such as the original PlayStation) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed-point UV coordinates or by an incremental error algorithm akin to Bresenham's line algorithm. In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (as shown in the figure: the checker box texture appears bent), especially as primitives near the camera. This distortion can be reduced by subdividing polygons into smaller polygons. Using quad primitives for rectangular objects can look less incorrect than if those rectangles were split into triangles. However, since interpolating four points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the forward texture mapping used by the Nvidia NV1, offered efficient quad primitives. With perspective correction, triangles become equivalent to quad primitives and this advantage disappears. For rectangular objects that are at right angles to the viewer (like floors and walls), the perspective only needs to be corrected in one direction across the screen rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor. Affine linear interpolation across that horizontal span will look correct because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space rather than simply interpolating coordinates in 2D screen space. While achieving the correct visual effect, perspective correct texturing is more expensive to calculate. To perform perspective correction of the texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, it is possible to take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across the surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} , and v {\displaystyle v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to produce a perspective correct texture mapping. To do this, the reciprocals at each vertex of the geometry (three points for a triangle) are calculated. Vertex n {\displaystyle n} has reciprocals u n z n {\displaystyle {\frac {u_{n}}{z_{n}}}} , v n z n {\displaystyle {\frac {v_{n}}{z_{n}}}} , and 1 z n {\displaystyle {\frac {1}{z_{n}}}} . Then, linear interpolation can be done on these reciprocals between the n {\displaystyle n} vertices (e.g., using barycentric coordinates), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} and 1 z i {\displaystyle {\frac {1}{z_{i}}}} (reciprocal z i {\displaystyle z_{i}} ). However, as our division by z {\displaystyle z} altered their coordinate system, this u i , v i {\displaystyle u_{i},v_{i}} cannot be used as texture coordinates. To correct back to the u , v {\displaystyle u,v} space, the corrected z {\displaystyle z} is calculated by taking the reciprocal once again: z c o r r e c t = 1 1 z i {\displaystyle z_{correct}={\frac {1}{\frac {1}{z_{i}}}}} . This is then used to correct the u i , v i {\displaystyle u_{i},v_{i}} coordinates: u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that the difference from pixel to pixel between texture coordinates is smaller in parts of the polygon that are closer to the viewer (stretching the texture wider) and is larger in parts that are farther away (compressing the texture). Affine texture mapping directly interpolates a texture coordinate u α {\displaystyle u_{\alpha }} between two endpoints u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} : u α = ( 1 − α ) u 0 + α u 1 {\displaystyle u_{\alpha }=(1-\alpha )u_{0}+\alpha u_{1}} where 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1} . Perspective correct mapping interpolates after dividing by depth z {\displaystyle z} , then uses its interpolated reciprocal to recover the correct coordinate: u α = ( 1 − α ) u 0 z 0 + α u 1 z 1 ( 1 − α ) 1 z 0 + α 1 z 1 {\displaystyle u_{\alpha }={\frac {(1-\alpha ){\frac {u_{0}}{z_{0}}}+\alpha {\frac {u_{1}}{z_{1}}}}{(1-\alpha ){\frac {1}{z_{0}}}+\alpha {\frac {1}{z_{1}}}}}} 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality and precision trade-offs, which can be applied to both software and hardware. Classic software texture mappers generally only performed simple texture mapping with one lighting effect at most (typically applied through a lookup table), and the perspective correctness was about 16 times more expensive.[compared to?] The Doom engine restricted the world to vertical walls and horizontal floors and ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors and ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom while using the same rendering technique. Some engines were able to render texture mapped heightmaps (e.g. Nova Logic's Voxel Space, and the engine for Outcast) via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals: keeping the arithmetic mill busy at all times and producing faster arithmetic results.[vague] For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware and had a relatively high triangle throughput compared to its peers. Software renderers generally prefer screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2D affine interpolation), thus lessening the overhead further. Another reason is that affine texture mapping does not fit into the low number of CPU registers of the x86 CPU; the 68000 and RISC processors are much more suited for that approach. A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. As the polygons are rendered independently, it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z, but the effort seems not to be worth it.[original research?] One other technique is to approximate the perspective with a faster calculation, such as a polynomial. A second uses the 1 z i {\textstyle {\frac {1}{z_{i}}}} value of the last two drawn pixels to linearly extrapolate the next value. For the latter, the division is then done starting from those values so that all that has to be divided is a small remainder. However, the amount of bookkeeping needed makes this technique too slow on most systems.[citation needed] A third technique, used by the Build Engine (used, most notably, in Duke Nukem 3D), builds on the constant distance trick used by the Doom engine by finding and rendering along the line of constant distance for arbitrary polygons. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG) and professional graphics workstations (such as Silicon Graphics) and broadcast digital video effects machines such as the Ampex ADO. Texture mapping hardware later appeared in arcade cabinets, consumer video game consoles, and PC video cards in the mid-1990s. In flight simulations, texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. Additionally, texture mapping was implemented so that real-time processing of prefiltered texture patterns stored in memory could be accessed by the video processor in real-time. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU. Some hardware implementations combine texture mapping with hidden-surface determination in tile-based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting. On earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen: Of these methods, inverse texture mapping has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive. The primary advantage of this method is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage is that the memory access pattern in the texture space will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness. Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer. This was used by some hardware, such as the 3DO, the Sega Saturn and the NV1. The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see the § Affine texture mapping section above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness. UV mapping became an important technique for 3D modelling and assisted in clipping the texture correctly when the primitive went past the edge of the screen, but existing hardware did not provide effective implementations of this. These shortcomings could have been addressed with further development, but GPU design has mostly shifted toward using the inverse mapping technique. Applications Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks: It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results. Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Exposé in Mac OS X. See also References Software External links |
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[SOURCE: https://en.wikipedia.org/wiki/Texture_mapping#cite_ref-NGen15_11-1] | [TOKENS: 4408] |
Contents Texture mapping Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV space). Semantic Texture mapping can multiply refer to (1) the task of unwrapping a 3D model (converting the surface of a 3D model into a 2D texture map), (2) applying a 2D texture map onto the surface of a 3D model, and (3) the 3D software algorithm that performs both tasks. A texture map refers to a 2D image ("texture") that adds visual detail to a 3D model. The image can be stored as a raster graphic. A texture that stores a specific property—such as bumpiness, reflectivity, or transparency—is also referred to as a color map or roughness map. The coordinate space that converts from a 3D model's 3D space into a 2D space for sampling from the texture map is variously called UV space, UV coordinates, or texture space. Algorithm The following is a simplified explanation of how an algorithm could work to render an image: History The original technique was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. Texture maps A texture map is an image applied ("mapped") to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3D model formats or material definitions, and assembled into resource bundles. They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources (which may be located in device memory) as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping. Texture maps usually contain RGB color data (either stored as direct color, compressed formats, or indexed color), and sometimes an additional channel for alpha blending (RGBA) especially for billboards and decal overlay textures. It is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity. Multiple texture maps (or channels) may be combined for control over specularity, normals, displacement, or subsurface scattering, e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered a modern evolution of tile map graphics). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning or digital photography, designed in image manipulation software such as GIMP or Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush. This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2D case is also known as UV coordinates). This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3D space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface (which is important for render mapping and light mapping, also known as baking). Texture mapping maps the model surface (or screen space during rasterization) into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on the screen) are calculated from the texels (texture pixels) is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination) into a surface texture (possibly on a low-resolution model). This technique is called baking (or render mapping) and is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games (e.g. Messiah) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps in a process called surface caching. Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Rasterisation algorithms Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility, and performance. Affine texture mapping linearly interpolates texture coordinates across a surface, making it the fastest form of texture mapping. Some software and hardware (such as the original PlayStation) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed-point UV coordinates or by an incremental error algorithm akin to Bresenham's line algorithm. In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (as shown in the figure: the checker box texture appears bent), especially as primitives near the camera. This distortion can be reduced by subdividing polygons into smaller polygons. Using quad primitives for rectangular objects can look less incorrect than if those rectangles were split into triangles. However, since interpolating four points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the forward texture mapping used by the Nvidia NV1, offered efficient quad primitives. With perspective correction, triangles become equivalent to quad primitives and this advantage disappears. For rectangular objects that are at right angles to the viewer (like floors and walls), the perspective only needs to be corrected in one direction across the screen rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor. Affine linear interpolation across that horizontal span will look correct because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space rather than simply interpolating coordinates in 2D screen space. While achieving the correct visual effect, perspective correct texturing is more expensive to calculate. To perform perspective correction of the texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, it is possible to take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across the surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} , and v {\displaystyle v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to produce a perspective correct texture mapping. To do this, the reciprocals at each vertex of the geometry (three points for a triangle) are calculated. Vertex n {\displaystyle n} has reciprocals u n z n {\displaystyle {\frac {u_{n}}{z_{n}}}} , v n z n {\displaystyle {\frac {v_{n}}{z_{n}}}} , and 1 z n {\displaystyle {\frac {1}{z_{n}}}} . Then, linear interpolation can be done on these reciprocals between the n {\displaystyle n} vertices (e.g., using barycentric coordinates), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} and 1 z i {\displaystyle {\frac {1}{z_{i}}}} (reciprocal z i {\displaystyle z_{i}} ). However, as our division by z {\displaystyle z} altered their coordinate system, this u i , v i {\displaystyle u_{i},v_{i}} cannot be used as texture coordinates. To correct back to the u , v {\displaystyle u,v} space, the corrected z {\displaystyle z} is calculated by taking the reciprocal once again: z c o r r e c t = 1 1 z i {\displaystyle z_{correct}={\frac {1}{\frac {1}{z_{i}}}}} . This is then used to correct the u i , v i {\displaystyle u_{i},v_{i}} coordinates: u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that the difference from pixel to pixel between texture coordinates is smaller in parts of the polygon that are closer to the viewer (stretching the texture wider) and is larger in parts that are farther away (compressing the texture). Affine texture mapping directly interpolates a texture coordinate u α {\displaystyle u_{\alpha }} between two endpoints u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} : u α = ( 1 − α ) u 0 + α u 1 {\displaystyle u_{\alpha }=(1-\alpha )u_{0}+\alpha u_{1}} where 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1} . Perspective correct mapping interpolates after dividing by depth z {\displaystyle z} , then uses its interpolated reciprocal to recover the correct coordinate: u α = ( 1 − α ) u 0 z 0 + α u 1 z 1 ( 1 − α ) 1 z 0 + α 1 z 1 {\displaystyle u_{\alpha }={\frac {(1-\alpha ){\frac {u_{0}}{z_{0}}}+\alpha {\frac {u_{1}}{z_{1}}}}{(1-\alpha ){\frac {1}{z_{0}}}+\alpha {\frac {1}{z_{1}}}}}} 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality and precision trade-offs, which can be applied to both software and hardware. Classic software texture mappers generally only performed simple texture mapping with one lighting effect at most (typically applied through a lookup table), and the perspective correctness was about 16 times more expensive.[compared to?] The Doom engine restricted the world to vertical walls and horizontal floors and ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors and ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom while using the same rendering technique. Some engines were able to render texture mapped heightmaps (e.g. Nova Logic's Voxel Space, and the engine for Outcast) via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals: keeping the arithmetic mill busy at all times and producing faster arithmetic results.[vague] For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware and had a relatively high triangle throughput compared to its peers. Software renderers generally prefer screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2D affine interpolation), thus lessening the overhead further. Another reason is that affine texture mapping does not fit into the low number of CPU registers of the x86 CPU; the 68000 and RISC processors are much more suited for that approach. A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. As the polygons are rendered independently, it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z, but the effort seems not to be worth it.[original research?] One other technique is to approximate the perspective with a faster calculation, such as a polynomial. A second uses the 1 z i {\textstyle {\frac {1}{z_{i}}}} value of the last two drawn pixels to linearly extrapolate the next value. For the latter, the division is then done starting from those values so that all that has to be divided is a small remainder. However, the amount of bookkeeping needed makes this technique too slow on most systems.[citation needed] A third technique, used by the Build Engine (used, most notably, in Duke Nukem 3D), builds on the constant distance trick used by the Doom engine by finding and rendering along the line of constant distance for arbitrary polygons. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG) and professional graphics workstations (such as Silicon Graphics) and broadcast digital video effects machines such as the Ampex ADO. Texture mapping hardware later appeared in arcade cabinets, consumer video game consoles, and PC video cards in the mid-1990s. In flight simulations, texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. Additionally, texture mapping was implemented so that real-time processing of prefiltered texture patterns stored in memory could be accessed by the video processor in real-time. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU. Some hardware implementations combine texture mapping with hidden-surface determination in tile-based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting. On earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen: Of these methods, inverse texture mapping has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive. The primary advantage of this method is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage is that the memory access pattern in the texture space will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness. Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer. This was used by some hardware, such as the 3DO, the Sega Saturn and the NV1. The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see the § Affine texture mapping section above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness. UV mapping became an important technique for 3D modelling and assisted in clipping the texture correctly when the primitive went past the edge of the screen, but existing hardware did not provide effective implementations of this. These shortcomings could have been addressed with further development, but GPU design has mostly shifted toward using the inverse mapping technique. Applications Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks: It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results. Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Exposé in Mac OS X. See also References Software External links |
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[SOURCE: https://en.wikipedia.org/wiki/Texture_mapping#cite_ref-7] | [TOKENS: 4408] |
Contents Texture mapping Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV space). Semantic Texture mapping can multiply refer to (1) the task of unwrapping a 3D model (converting the surface of a 3D model into a 2D texture map), (2) applying a 2D texture map onto the surface of a 3D model, and (3) the 3D software algorithm that performs both tasks. A texture map refers to a 2D image ("texture") that adds visual detail to a 3D model. The image can be stored as a raster graphic. A texture that stores a specific property—such as bumpiness, reflectivity, or transparency—is also referred to as a color map or roughness map. The coordinate space that converts from a 3D model's 3D space into a 2D space for sampling from the texture map is variously called UV space, UV coordinates, or texture space. Algorithm The following is a simplified explanation of how an algorithm could work to render an image: History The original technique was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. Texture maps A texture map is an image applied ("mapped") to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3D model formats or material definitions, and assembled into resource bundles. They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources (which may be located in device memory) as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping. Texture maps usually contain RGB color data (either stored as direct color, compressed formats, or indexed color), and sometimes an additional channel for alpha blending (RGBA) especially for billboards and decal overlay textures. It is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity. Multiple texture maps (or channels) may be combined for control over specularity, normals, displacement, or subsurface scattering, e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered a modern evolution of tile map graphics). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning or digital photography, designed in image manipulation software such as GIMP or Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush. This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2D case is also known as UV coordinates). This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3D space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface (which is important for render mapping and light mapping, also known as baking). Texture mapping maps the model surface (or screen space during rasterization) into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on the screen) are calculated from the texels (texture pixels) is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination) into a surface texture (possibly on a low-resolution model). This technique is called baking (or render mapping) and is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games (e.g. Messiah) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps in a process called surface caching. Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Rasterisation algorithms Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility, and performance. Affine texture mapping linearly interpolates texture coordinates across a surface, making it the fastest form of texture mapping. Some software and hardware (such as the original PlayStation) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed-point UV coordinates or by an incremental error algorithm akin to Bresenham's line algorithm. In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (as shown in the figure: the checker box texture appears bent), especially as primitives near the camera. This distortion can be reduced by subdividing polygons into smaller polygons. Using quad primitives for rectangular objects can look less incorrect than if those rectangles were split into triangles. However, since interpolating four points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the forward texture mapping used by the Nvidia NV1, offered efficient quad primitives. With perspective correction, triangles become equivalent to quad primitives and this advantage disappears. For rectangular objects that are at right angles to the viewer (like floors and walls), the perspective only needs to be corrected in one direction across the screen rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor. Affine linear interpolation across that horizontal span will look correct because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space rather than simply interpolating coordinates in 2D screen space. While achieving the correct visual effect, perspective correct texturing is more expensive to calculate. To perform perspective correction of the texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, it is possible to take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across the surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} , and v {\displaystyle v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to produce a perspective correct texture mapping. To do this, the reciprocals at each vertex of the geometry (three points for a triangle) are calculated. Vertex n {\displaystyle n} has reciprocals u n z n {\displaystyle {\frac {u_{n}}{z_{n}}}} , v n z n {\displaystyle {\frac {v_{n}}{z_{n}}}} , and 1 z n {\displaystyle {\frac {1}{z_{n}}}} . Then, linear interpolation can be done on these reciprocals between the n {\displaystyle n} vertices (e.g., using barycentric coordinates), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} and 1 z i {\displaystyle {\frac {1}{z_{i}}}} (reciprocal z i {\displaystyle z_{i}} ). However, as our division by z {\displaystyle z} altered their coordinate system, this u i , v i {\displaystyle u_{i},v_{i}} cannot be used as texture coordinates. To correct back to the u , v {\displaystyle u,v} space, the corrected z {\displaystyle z} is calculated by taking the reciprocal once again: z c o r r e c t = 1 1 z i {\displaystyle z_{correct}={\frac {1}{\frac {1}{z_{i}}}}} . This is then used to correct the u i , v i {\displaystyle u_{i},v_{i}} coordinates: u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that the difference from pixel to pixel between texture coordinates is smaller in parts of the polygon that are closer to the viewer (stretching the texture wider) and is larger in parts that are farther away (compressing the texture). Affine texture mapping directly interpolates a texture coordinate u α {\displaystyle u_{\alpha }} between two endpoints u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} : u α = ( 1 − α ) u 0 + α u 1 {\displaystyle u_{\alpha }=(1-\alpha )u_{0}+\alpha u_{1}} where 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1} . Perspective correct mapping interpolates after dividing by depth z {\displaystyle z} , then uses its interpolated reciprocal to recover the correct coordinate: u α = ( 1 − α ) u 0 z 0 + α u 1 z 1 ( 1 − α ) 1 z 0 + α 1 z 1 {\displaystyle u_{\alpha }={\frac {(1-\alpha ){\frac {u_{0}}{z_{0}}}+\alpha {\frac {u_{1}}{z_{1}}}}{(1-\alpha ){\frac {1}{z_{0}}}+\alpha {\frac {1}{z_{1}}}}}} 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality and precision trade-offs, which can be applied to both software and hardware. Classic software texture mappers generally only performed simple texture mapping with one lighting effect at most (typically applied through a lookup table), and the perspective correctness was about 16 times more expensive.[compared to?] The Doom engine restricted the world to vertical walls and horizontal floors and ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors and ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom while using the same rendering technique. Some engines were able to render texture mapped heightmaps (e.g. Nova Logic's Voxel Space, and the engine for Outcast) via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals: keeping the arithmetic mill busy at all times and producing faster arithmetic results.[vague] For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware and had a relatively high triangle throughput compared to its peers. Software renderers generally prefer screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2D affine interpolation), thus lessening the overhead further. Another reason is that affine texture mapping does not fit into the low number of CPU registers of the x86 CPU; the 68000 and RISC processors are much more suited for that approach. A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. As the polygons are rendered independently, it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z, but the effort seems not to be worth it.[original research?] One other technique is to approximate the perspective with a faster calculation, such as a polynomial. A second uses the 1 z i {\textstyle {\frac {1}{z_{i}}}} value of the last two drawn pixels to linearly extrapolate the next value. For the latter, the division is then done starting from those values so that all that has to be divided is a small remainder. However, the amount of bookkeeping needed makes this technique too slow on most systems.[citation needed] A third technique, used by the Build Engine (used, most notably, in Duke Nukem 3D), builds on the constant distance trick used by the Doom engine by finding and rendering along the line of constant distance for arbitrary polygons. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG) and professional graphics workstations (such as Silicon Graphics) and broadcast digital video effects machines such as the Ampex ADO. Texture mapping hardware later appeared in arcade cabinets, consumer video game consoles, and PC video cards in the mid-1990s. In flight simulations, texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. Additionally, texture mapping was implemented so that real-time processing of prefiltered texture patterns stored in memory could be accessed by the video processor in real-time. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU. Some hardware implementations combine texture mapping with hidden-surface determination in tile-based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting. On earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen: Of these methods, inverse texture mapping has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive. The primary advantage of this method is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage is that the memory access pattern in the texture space will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness. Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer. This was used by some hardware, such as the 3DO, the Sega Saturn and the NV1. The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see the § Affine texture mapping section above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness. UV mapping became an important technique for 3D modelling and assisted in clipping the texture correctly when the primitive went past the edge of the screen, but existing hardware did not provide effective implementations of this. These shortcomings could have been addressed with further development, but GPU design has mostly shifted toward using the inverse mapping technique. Applications Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks: It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results. Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Exposé in Mac OS X. See also References Software External links |
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[SOURCE: https://en.wikipedia.org/wiki/Texture_mapping#cite_ref-17] | [TOKENS: 4408] |
Contents Texture mapping Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV space). Semantic Texture mapping can multiply refer to (1) the task of unwrapping a 3D model (converting the surface of a 3D model into a 2D texture map), (2) applying a 2D texture map onto the surface of a 3D model, and (3) the 3D software algorithm that performs both tasks. A texture map refers to a 2D image ("texture") that adds visual detail to a 3D model. The image can be stored as a raster graphic. A texture that stores a specific property—such as bumpiness, reflectivity, or transparency—is also referred to as a color map or roughness map. The coordinate space that converts from a 3D model's 3D space into a 2D space for sampling from the texture map is variously called UV space, UV coordinates, or texture space. Algorithm The following is a simplified explanation of how an algorithm could work to render an image: History The original technique was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. Texture maps A texture map is an image applied ("mapped") to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3D model formats or material definitions, and assembled into resource bundles. They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources (which may be located in device memory) as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping. Texture maps usually contain RGB color data (either stored as direct color, compressed formats, or indexed color), and sometimes an additional channel for alpha blending (RGBA) especially for billboards and decal overlay textures. It is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity. Multiple texture maps (or channels) may be combined for control over specularity, normals, displacement, or subsurface scattering, e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered a modern evolution of tile map graphics). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning or digital photography, designed in image manipulation software such as GIMP or Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush. This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2D case is also known as UV coordinates). This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3D space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface (which is important for render mapping and light mapping, also known as baking). Texture mapping maps the model surface (or screen space during rasterization) into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on the screen) are calculated from the texels (texture pixels) is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination) into a surface texture (possibly on a low-resolution model). This technique is called baking (or render mapping) and is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games (e.g. Messiah) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps in a process called surface caching. Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Rasterisation algorithms Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility, and performance. Affine texture mapping linearly interpolates texture coordinates across a surface, making it the fastest form of texture mapping. Some software and hardware (such as the original PlayStation) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed-point UV coordinates or by an incremental error algorithm akin to Bresenham's line algorithm. In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (as shown in the figure: the checker box texture appears bent), especially as primitives near the camera. This distortion can be reduced by subdividing polygons into smaller polygons. Using quad primitives for rectangular objects can look less incorrect than if those rectangles were split into triangles. However, since interpolating four points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the forward texture mapping used by the Nvidia NV1, offered efficient quad primitives. With perspective correction, triangles become equivalent to quad primitives and this advantage disappears. For rectangular objects that are at right angles to the viewer (like floors and walls), the perspective only needs to be corrected in one direction across the screen rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor. Affine linear interpolation across that horizontal span will look correct because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space rather than simply interpolating coordinates in 2D screen space. While achieving the correct visual effect, perspective correct texturing is more expensive to calculate. To perform perspective correction of the texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, it is possible to take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across the surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} , and v {\displaystyle v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to produce a perspective correct texture mapping. To do this, the reciprocals at each vertex of the geometry (three points for a triangle) are calculated. Vertex n {\displaystyle n} has reciprocals u n z n {\displaystyle {\frac {u_{n}}{z_{n}}}} , v n z n {\displaystyle {\frac {v_{n}}{z_{n}}}} , and 1 z n {\displaystyle {\frac {1}{z_{n}}}} . Then, linear interpolation can be done on these reciprocals between the n {\displaystyle n} vertices (e.g., using barycentric coordinates), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} and 1 z i {\displaystyle {\frac {1}{z_{i}}}} (reciprocal z i {\displaystyle z_{i}} ). However, as our division by z {\displaystyle z} altered their coordinate system, this u i , v i {\displaystyle u_{i},v_{i}} cannot be used as texture coordinates. To correct back to the u , v {\displaystyle u,v} space, the corrected z {\displaystyle z} is calculated by taking the reciprocal once again: z c o r r e c t = 1 1 z i {\displaystyle z_{correct}={\frac {1}{\frac {1}{z_{i}}}}} . This is then used to correct the u i , v i {\displaystyle u_{i},v_{i}} coordinates: u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that the difference from pixel to pixel between texture coordinates is smaller in parts of the polygon that are closer to the viewer (stretching the texture wider) and is larger in parts that are farther away (compressing the texture). Affine texture mapping directly interpolates a texture coordinate u α {\displaystyle u_{\alpha }} between two endpoints u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} : u α = ( 1 − α ) u 0 + α u 1 {\displaystyle u_{\alpha }=(1-\alpha )u_{0}+\alpha u_{1}} where 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1} . Perspective correct mapping interpolates after dividing by depth z {\displaystyle z} , then uses its interpolated reciprocal to recover the correct coordinate: u α = ( 1 − α ) u 0 z 0 + α u 1 z 1 ( 1 − α ) 1 z 0 + α 1 z 1 {\displaystyle u_{\alpha }={\frac {(1-\alpha ){\frac {u_{0}}{z_{0}}}+\alpha {\frac {u_{1}}{z_{1}}}}{(1-\alpha ){\frac {1}{z_{0}}}+\alpha {\frac {1}{z_{1}}}}}} 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality and precision trade-offs, which can be applied to both software and hardware. Classic software texture mappers generally only performed simple texture mapping with one lighting effect at most (typically applied through a lookup table), and the perspective correctness was about 16 times more expensive.[compared to?] The Doom engine restricted the world to vertical walls and horizontal floors and ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors and ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom while using the same rendering technique. Some engines were able to render texture mapped heightmaps (e.g. Nova Logic's Voxel Space, and the engine for Outcast) via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals: keeping the arithmetic mill busy at all times and producing faster arithmetic results.[vague] For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware and had a relatively high triangle throughput compared to its peers. Software renderers generally prefer screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2D affine interpolation), thus lessening the overhead further. Another reason is that affine texture mapping does not fit into the low number of CPU registers of the x86 CPU; the 68000 and RISC processors are much more suited for that approach. A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. As the polygons are rendered independently, it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z, but the effort seems not to be worth it.[original research?] One other technique is to approximate the perspective with a faster calculation, such as a polynomial. A second uses the 1 z i {\textstyle {\frac {1}{z_{i}}}} value of the last two drawn pixels to linearly extrapolate the next value. For the latter, the division is then done starting from those values so that all that has to be divided is a small remainder. However, the amount of bookkeeping needed makes this technique too slow on most systems.[citation needed] A third technique, used by the Build Engine (used, most notably, in Duke Nukem 3D), builds on the constant distance trick used by the Doom engine by finding and rendering along the line of constant distance for arbitrary polygons. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG) and professional graphics workstations (such as Silicon Graphics) and broadcast digital video effects machines such as the Ampex ADO. Texture mapping hardware later appeared in arcade cabinets, consumer video game consoles, and PC video cards in the mid-1990s. In flight simulations, texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. Additionally, texture mapping was implemented so that real-time processing of prefiltered texture patterns stored in memory could be accessed by the video processor in real-time. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU. Some hardware implementations combine texture mapping with hidden-surface determination in tile-based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting. On earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen: Of these methods, inverse texture mapping has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive. The primary advantage of this method is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage is that the memory access pattern in the texture space will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness. Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer. This was used by some hardware, such as the 3DO, the Sega Saturn and the NV1. The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see the § Affine texture mapping section above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness. UV mapping became an important technique for 3D modelling and assisted in clipping the texture correctly when the primitive went past the edge of the screen, but existing hardware did not provide effective implementations of this. These shortcomings could have been addressed with further development, but GPU design has mostly shifted toward using the inverse mapping technique. Applications Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks: It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results. Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Exposé in Mac OS X. See also References Software External links |
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Contents Texture mapping Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV space). Semantic Texture mapping can multiply refer to (1) the task of unwrapping a 3D model (converting the surface of a 3D model into a 2D texture map), (2) applying a 2D texture map onto the surface of a 3D model, and (3) the 3D software algorithm that performs both tasks. A texture map refers to a 2D image ("texture") that adds visual detail to a 3D model. The image can be stored as a raster graphic. A texture that stores a specific property—such as bumpiness, reflectivity, or transparency—is also referred to as a color map or roughness map. The coordinate space that converts from a 3D model's 3D space into a 2D space for sampling from the texture map is variously called UV space, UV coordinates, or texture space. Algorithm The following is a simplified explanation of how an algorithm could work to render an image: History The original technique was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. Texture maps A texture map is an image applied ("mapped") to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3D model formats or material definitions, and assembled into resource bundles. They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources (which may be located in device memory) as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping. Texture maps usually contain RGB color data (either stored as direct color, compressed formats, or indexed color), and sometimes an additional channel for alpha blending (RGBA) especially for billboards and decal overlay textures. It is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity. Multiple texture maps (or channels) may be combined for control over specularity, normals, displacement, or subsurface scattering, e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered a modern evolution of tile map graphics). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning or digital photography, designed in image manipulation software such as GIMP or Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush. This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2D case is also known as UV coordinates). This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3D space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface (which is important for render mapping and light mapping, also known as baking). Texture mapping maps the model surface (or screen space during rasterization) into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on the screen) are calculated from the texels (texture pixels) is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination) into a surface texture (possibly on a low-resolution model). This technique is called baking (or render mapping) and is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games (e.g. Messiah) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps in a process called surface caching. Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Rasterisation algorithms Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility, and performance. Affine texture mapping linearly interpolates texture coordinates across a surface, making it the fastest form of texture mapping. Some software and hardware (such as the original PlayStation) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed-point UV coordinates or by an incremental error algorithm akin to Bresenham's line algorithm. In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (as shown in the figure: the checker box texture appears bent), especially as primitives near the camera. This distortion can be reduced by subdividing polygons into smaller polygons. Using quad primitives for rectangular objects can look less incorrect than if those rectangles were split into triangles. However, since interpolating four points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the forward texture mapping used by the Nvidia NV1, offered efficient quad primitives. With perspective correction, triangles become equivalent to quad primitives and this advantage disappears. For rectangular objects that are at right angles to the viewer (like floors and walls), the perspective only needs to be corrected in one direction across the screen rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor. Affine linear interpolation across that horizontal span will look correct because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space rather than simply interpolating coordinates in 2D screen space. While achieving the correct visual effect, perspective correct texturing is more expensive to calculate. To perform perspective correction of the texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, it is possible to take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across the surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} , and v {\displaystyle v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to produce a perspective correct texture mapping. To do this, the reciprocals at each vertex of the geometry (three points for a triangle) are calculated. Vertex n {\displaystyle n} has reciprocals u n z n {\displaystyle {\frac {u_{n}}{z_{n}}}} , v n z n {\displaystyle {\frac {v_{n}}{z_{n}}}} , and 1 z n {\displaystyle {\frac {1}{z_{n}}}} . Then, linear interpolation can be done on these reciprocals between the n {\displaystyle n} vertices (e.g., using barycentric coordinates), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} and 1 z i {\displaystyle {\frac {1}{z_{i}}}} (reciprocal z i {\displaystyle z_{i}} ). However, as our division by z {\displaystyle z} altered their coordinate system, this u i , v i {\displaystyle u_{i},v_{i}} cannot be used as texture coordinates. To correct back to the u , v {\displaystyle u,v} space, the corrected z {\displaystyle z} is calculated by taking the reciprocal once again: z c o r r e c t = 1 1 z i {\displaystyle z_{correct}={\frac {1}{\frac {1}{z_{i}}}}} . This is then used to correct the u i , v i {\displaystyle u_{i},v_{i}} coordinates: u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that the difference from pixel to pixel between texture coordinates is smaller in parts of the polygon that are closer to the viewer (stretching the texture wider) and is larger in parts that are farther away (compressing the texture). Affine texture mapping directly interpolates a texture coordinate u α {\displaystyle u_{\alpha }} between two endpoints u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} : u α = ( 1 − α ) u 0 + α u 1 {\displaystyle u_{\alpha }=(1-\alpha )u_{0}+\alpha u_{1}} where 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1} . Perspective correct mapping interpolates after dividing by depth z {\displaystyle z} , then uses its interpolated reciprocal to recover the correct coordinate: u α = ( 1 − α ) u 0 z 0 + α u 1 z 1 ( 1 − α ) 1 z 0 + α 1 z 1 {\displaystyle u_{\alpha }={\frac {(1-\alpha ){\frac {u_{0}}{z_{0}}}+\alpha {\frac {u_{1}}{z_{1}}}}{(1-\alpha ){\frac {1}{z_{0}}}+\alpha {\frac {1}{z_{1}}}}}} 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality and precision trade-offs, which can be applied to both software and hardware. Classic software texture mappers generally only performed simple texture mapping with one lighting effect at most (typically applied through a lookup table), and the perspective correctness was about 16 times more expensive.[compared to?] The Doom engine restricted the world to vertical walls and horizontal floors and ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors and ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom while using the same rendering technique. Some engines were able to render texture mapped heightmaps (e.g. Nova Logic's Voxel Space, and the engine for Outcast) via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals: keeping the arithmetic mill busy at all times and producing faster arithmetic results.[vague] For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware and had a relatively high triangle throughput compared to its peers. Software renderers generally prefer screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2D affine interpolation), thus lessening the overhead further. Another reason is that affine texture mapping does not fit into the low number of CPU registers of the x86 CPU; the 68000 and RISC processors are much more suited for that approach. A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. As the polygons are rendered independently, it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z, but the effort seems not to be worth it.[original research?] One other technique is to approximate the perspective with a faster calculation, such as a polynomial. A second uses the 1 z i {\textstyle {\frac {1}{z_{i}}}} value of the last two drawn pixels to linearly extrapolate the next value. For the latter, the division is then done starting from those values so that all that has to be divided is a small remainder. However, the amount of bookkeeping needed makes this technique too slow on most systems.[citation needed] A third technique, used by the Build Engine (used, most notably, in Duke Nukem 3D), builds on the constant distance trick used by the Doom engine by finding and rendering along the line of constant distance for arbitrary polygons. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG) and professional graphics workstations (such as Silicon Graphics) and broadcast digital video effects machines such as the Ampex ADO. Texture mapping hardware later appeared in arcade cabinets, consumer video game consoles, and PC video cards in the mid-1990s. In flight simulations, texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. Additionally, texture mapping was implemented so that real-time processing of prefiltered texture patterns stored in memory could be accessed by the video processor in real-time. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU. Some hardware implementations combine texture mapping with hidden-surface determination in tile-based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting. On earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen: Of these methods, inverse texture mapping has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive. The primary advantage of this method is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage is that the memory access pattern in the texture space will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness. Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer. This was used by some hardware, such as the 3DO, the Sega Saturn and the NV1. The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see the § Affine texture mapping section above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness. UV mapping became an important technique for 3D modelling and assisted in clipping the texture correctly when the primitive went past the edge of the screen, but existing hardware did not provide effective implementations of this. These shortcomings could have been addressed with further development, but GPU design has mostly shifted toward using the inverse mapping technique. Applications Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks: It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results. Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Exposé in Mac OS X. See also References Software External links |
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[SOURCE: https://en.wikipedia.org/wiki/UVW_mapping] | [TOKENS: 379] |
Contents UVW mapping UVW mapping is a mathematical technique for coordinate mapping. In computer graphics, it most commonly maps an object's surface in R 2 {\displaystyle \mathbb {R} ^{2}} to a solid texture with UVW coordinates in R 3 {\displaystyle \mathbb {R} ^{3}} , in contrast to UV mapping, which maps surfaces in R 2 {\displaystyle \mathbb {R} ^{2}} to an image with UV coordinates in R 2 {\displaystyle \mathbb {R} ^{2}} . The UVW mapping is suitable for painting an object's surface based on a solid texture. This allows a marble texture to wrap a vase to appear as if it were carved from actual marble. "UVW", like the standard Cartesian coordinate system, has three dimensions; the third dimension allows texture maps to wrap in complex ways onto irregular surfaces. Each point in a UVW map corresponds to a point on the surface of the object. The graphic designer or programmer generates the specific mathematical function to implement the map, so that points on the texture are assigned to (XYZ) points on the target surface. Generally speaking, the more orderly the unwrapped polygons are, the easier it is for the texture artist to paint features onto the texture. Once the texture is finished, all that has to be done is to wrap the UVW map back onto the object, projecting the texture in a way that is far more flexible and advanced, preventing graphic artifacts that accompany more simplistic texture mappings such as planar projection. For this reason, UVW mapping is commonly used to texture map non-platonic solids, non-geometric primitives, and other irregularly shaped objects, such as characters and furniture. References External links This computer graphics–related article is a stub. You can help Wikipedia by adding missing information. |
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[SOURCE: https://en.wikipedia.org/wiki/Texture_mapping#cite_ref-12] | [TOKENS: 4408] |
Contents Texture mapping Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV space). Semantic Texture mapping can multiply refer to (1) the task of unwrapping a 3D model (converting the surface of a 3D model into a 2D texture map), (2) applying a 2D texture map onto the surface of a 3D model, and (3) the 3D software algorithm that performs both tasks. A texture map refers to a 2D image ("texture") that adds visual detail to a 3D model. The image can be stored as a raster graphic. A texture that stores a specific property—such as bumpiness, reflectivity, or transparency—is also referred to as a color map or roughness map. The coordinate space that converts from a 3D model's 3D space into a 2D space for sampling from the texture map is variously called UV space, UV coordinates, or texture space. Algorithm The following is a simplified explanation of how an algorithm could work to render an image: History The original technique was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing, mipmaps, and more complex mappings such as height mapping, bump mapping, normal mapping, displacement mapping, reflection mapping, specular mapping, occlusion mapping, and many other variations on the technique (controlled by a materials system) have made it possible to simulate near-photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. Texture maps A texture map is an image applied ("mapped") to the surface of a shape or polygon. This may be a bitmap image or a procedural texture. They may be stored in common image file formats, referenced by 3D model formats or material definitions, and assembled into resource bundles. They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency. Rendering APIs typically manage texture map resources (which may be located in device memory) as buffers or surfaces, and may allow 'render to texture' for additional effects such as post processing or environment mapping. Texture maps usually contain RGB color data (either stored as direct color, compressed formats, or indexed color), and sometimes an additional channel for alpha blending (RGBA) especially for billboards and decal overlay textures. It is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity. Multiple texture maps (or channels) may be combined for control over specularity, normals, displacement, or subsurface scattering, e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered a modern evolution of tile map graphics). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning or digital photography, designed in image manipulation software such as GIMP or Photoshop, or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush. This process is akin to applying patterned paper to a plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2D case is also known as UV coordinates). This may be done through explicit assignment of vertex attributes, manually edited in a 3D modelling package through UV unwrapping tools. It is also possible to associate a procedural transformation from 3D space to texture space with the material. This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider the distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique "injective" mapping from every piece of a surface (which is important for render mapping and light mapping, also known as baking). Texture mapping maps the model surface (or screen space during rasterization) into texture space; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at a time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders, for greater fidelity. Another multitexture technique is bump mapping, which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on the screen) are calculated from the texels (texture pixels) is governed by texture filtering. The cheapest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies. In the event of a texture coordinate being outside the texture, it is either clamped or wrapped. Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from a data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination) into a surface texture (possibly on a low-resolution model). This technique is called baking (or render mapping) and is most commonly used for light maps, but may also be used to generate normal maps and displacement maps. Some computer games (e.g. Messiah) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps in a process called surface caching. Baking can be used as a form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls. It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Rasterisation algorithms Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility, and performance. Affine texture mapping linearly interpolates texture coordinates across a surface, making it the fastest form of texture mapping. Some software and hardware (such as the original PlayStation) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed-point UV coordinates or by an incremental error algorithm akin to Bresenham's line algorithm. In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (as shown in the figure: the checker box texture appears bent), especially as primitives near the camera. This distortion can be reduced by subdividing polygons into smaller polygons. Using quad primitives for rectangular objects can look less incorrect than if those rectangles were split into triangles. However, since interpolating four points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as the forward texture mapping used by the Nvidia NV1, offered efficient quad primitives. With perspective correction, triangles become equivalent to quad primitives and this advantage disappears. For rectangular objects that are at right angles to the viewer (like floors and walls), the perspective only needs to be corrected in one direction across the screen rather than both. The correct perspective mapping can be calculated at the left and right edges of the floor. Affine linear interpolation across that horizontal span will look correct because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space rather than simply interpolating coordinates in 2D screen space. While achieving the correct visual effect, perspective correct texturing is more expensive to calculate. To perform perspective correction of the texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, it is possible to take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across the surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} , and v {\displaystyle v} , before the division, are not linear across the surface in screen space. It is therefore possible to linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to produce a perspective correct texture mapping. To do this, the reciprocals at each vertex of the geometry (three points for a triangle) are calculated. Vertex n {\displaystyle n} has reciprocals u n z n {\displaystyle {\frac {u_{n}}{z_{n}}}} , v n z n {\displaystyle {\frac {v_{n}}{z_{n}}}} , and 1 z n {\displaystyle {\frac {1}{z_{n}}}} . Then, linear interpolation can be done on these reciprocals between the n {\displaystyle n} vertices (e.g., using barycentric coordinates), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} and 1 z i {\displaystyle {\frac {1}{z_{i}}}} (reciprocal z i {\displaystyle z_{i}} ). However, as our division by z {\displaystyle z} altered their coordinate system, this u i , v i {\displaystyle u_{i},v_{i}} cannot be used as texture coordinates. To correct back to the u , v {\displaystyle u,v} space, the corrected z {\displaystyle z} is calculated by taking the reciprocal once again: z c o r r e c t = 1 1 z i {\displaystyle z_{correct}={\frac {1}{\frac {1}{z_{i}}}}} . This is then used to correct the u i , v i {\displaystyle u_{i},v_{i}} coordinates: u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that the difference from pixel to pixel between texture coordinates is smaller in parts of the polygon that are closer to the viewer (stretching the texture wider) and is larger in parts that are farther away (compressing the texture). Affine texture mapping directly interpolates a texture coordinate u α {\displaystyle u_{\alpha }} between two endpoints u 0 {\displaystyle u_{0}} and u 1 {\displaystyle u_{1}} : u α = ( 1 − α ) u 0 + α u 1 {\displaystyle u_{\alpha }=(1-\alpha )u_{0}+\alpha u_{1}} where 0 ≤ α ≤ 1 {\displaystyle 0\leq \alpha \leq 1} . Perspective correct mapping interpolates after dividing by depth z {\displaystyle z} , then uses its interpolated reciprocal to recover the correct coordinate: u α = ( 1 − α ) u 0 z 0 + α u 1 z 1 ( 1 − α ) 1 z 0 + α 1 z 1 {\displaystyle u_{\alpha }={\frac {(1-\alpha ){\frac {u_{0}}{z_{0}}}+\alpha {\frac {u_{1}}{z_{1}}}}{(1-\alpha ){\frac {1}{z_{0}}}+\alpha {\frac {1}{z_{1}}}}}} 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality and precision trade-offs, which can be applied to both software and hardware. Classic software texture mappers generally only performed simple texture mapping with one lighting effect at most (typically applied through a lookup table), and the perspective correctness was about 16 times more expensive.[compared to?] The Doom engine restricted the world to vertical walls and horizontal floors and ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors and ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for the depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom while using the same rendering technique. Some engines were able to render texture mapped heightmaps (e.g. Nova Logic's Voxel Space, and the engine for Outcast) via Bresenham-like incremental algorithms, producing the appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals: keeping the arithmetic mill busy at all times and producing faster arithmetic results.[vague] For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware and had a relatively high triangle throughput compared to its peers. Software renderers generally prefer screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along a line of pixels to simplify the set-up (compared to 2D affine interpolation), thus lessening the overhead further. Another reason is that affine texture mapping does not fit into the low number of CPU registers of the x86 CPU; the 68000 and RISC processors are much more suited for that approach. A different approach was taken for Quake, which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at the speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. As the polygons are rendered independently, it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z, but the effort seems not to be worth it.[original research?] One other technique is to approximate the perspective with a faster calculation, such as a polynomial. A second uses the 1 z i {\textstyle {\frac {1}{z_{i}}}} value of the last two drawn pixels to linearly extrapolate the next value. For the latter, the division is then done starting from those values so that all that has to be divided is a small remainder. However, the amount of bookkeeping needed makes this technique too slow on most systems.[citation needed] A third technique, used by the Build Engine (used, most notably, in Duke Nukem 3D), builds on the constant distance trick used by the Doom engine by finding and rendering along the line of constant distance for arbitrary polygons. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG) and professional graphics workstations (such as Silicon Graphics) and broadcast digital video effects machines such as the Ampex ADO. Texture mapping hardware later appeared in arcade cabinets, consumer video game consoles, and PC video cards in the mid-1990s. In flight simulations, texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. Additionally, texture mapping was implemented so that real-time processing of prefiltered texture patterns stored in memory could be accessed by the video processor in real-time. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers, or texture mapping units, to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn. As of 2016, texture mapping hardware is ubiquitous as most SOCs contain a suitable GPU. Some hardware implementations combine texture mapping with hidden-surface determination in tile-based deferred rendering or scanline rendering; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting. On earlier graphics hardware, there were two competing paradigms of how to deliver a texture to the screen: Of these methods, inverse texture mapping has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by the primitive. The primary advantage of this method is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage is that the memory access pattern in the texture space will not be linear if the texture is at an angle to the screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness. Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to a place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer. This was used by some hardware, such as the 3DO, the Sega Saturn and the NV1. The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of a quad looks less incorrect than the same quad split into two triangles (see the § Affine texture mapping section above). The NV1 hardware also allowed a quadratic interpolation mode to provide an even better approximation of perspective correctness. UV mapping became an important technique for 3D modelling and assisted in clipping the texture correctly when the primitive went past the edge of the screen, but existing hardware did not provide effective implementations of this. These shortcomings could have been addressed with further development, but GPU design has mostly shifted toward using the inverse mapping technique. Applications Beyond 3D rendering, the availability of texture mapping hardware has inspired its use for accelerating other tasks: It is possible to use texture mapping hardware to accelerate both the reconstruction of voxel data sets from tomographic scans, and to visualize the results. Many user interfaces use texture mapping to accelerate animated transitions of screen elements, e.g. Exposé in Mac OS X. See also References Software External links |
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[SOURCE: https://en.wikipedia.org/wiki/Ohio_State_University] | [TOKENS: 7423] |
Contents Ohio State University The Ohio State University (Ohio State, tOSU, or OSU) is a public, land-grant research university in Columbus, Ohio, United States. Founded in 1870, it is the flagship institution of the University System of Ohio. It is regarded as a "Public Ivy" and is consistently ranked among the best public universities in the United States. Ohio State is a member of the Association of American Universities and is classified "R1: Doctoral Universities – Very high research activity". The university is known for its political science department, one of the most influential globally and a major department within American politics; and applied science, where it specializes in artificial intelligence, computer science, biomedical research, and engineering. According to the National Science Foundation, in 2026 the university had research and development (R&D) expenditures of $1.58 billion, the 12th largest in the U.S. Ohio State consists of sixteen colleges, including of Arts and Sciences, Business, Dentistry, Engineering, Public Affairs, and Law, and offers study in a wide range of degree programs at the undergraduate and graduate levels. It has five satellite campuses in Lima, Mansfield, Marion, Newark, and Wooster. The university is one of the largest by enrollment in the United States, with over 50,000 undergraduate students and 15,000 graduate students. Its athletic teams compete in NCAA Division I as the Ohio State Buckeyes in the Big Ten Conference for the majority of sports. Past and present alumni and faculty of Ohio State include 6 Nobel Prize laureates, 9 Rhodes Scholars, 7 Churchill Scholars, 1 Fields Medalist, 8 Pulitzer Prize winners, 77 Goldwater scholars, 1 Costa Rican president, 1 U.S. vice president, 7 U.S. senators, 15 U.S. representatives, and 118 Olympic medalists. History The proposal of a manufacturing and agriculture university in central Ohio was initially met in the 1870s with hostility from the state's agricultural interests, and with competition for resources from Ohio University, which was chartered by the Northwest Ordinance and Miami University. The university was established in the year 1870 as a land-grant university. The university opened its doors to 24 students on September 17, 1873. In 1878, the first class of six men graduated. The first woman graduated the following year. Also in 1878, the Ohio legislature recognized an expanded scope for the university by changing its name to "the Ohio State University". In 1906, Ohio State president William Oxley Thompson, along with the university's supporters in the state legislature, put forth the Lybarger Bill with the aim of shifting virtually all higher education support to the continued development of Ohio State while funding only the "normal school" functions of the state's other public universities. Although the Lybarger Bill failed narrowly to gain passage, in its place the Eagleson Bill was passed as a compromise, which determined that all doctoral education and research functions would be the role of Ohio State, and that Miami University and Ohio University would not offer instruction beyond the master's degree level – an agreement that would remain in place until the 1950s. In 1916, Ohio State was elected into membership in the Association of American Universities. With the onset of the Great Depression, Ohio State would face many of the challenges affecting universities throughout America as budget support was slashed, and students without the means of paying tuition returned home to support families. By the mid-1930s, however, enrollment had stabilized due in large part to the role of the Federal Emergency Relief Administration and later the National Youth Administration. By the end of the decade, enrollment had still managed to grow to over 17,500. In 1934, the Ohio State Research Foundation was founded to bring in outside funding for faculty research projects. In 1938, a development office was opened to begin raising funds privately to offset reductions in state support. In 1952, Ohio State founded the interdisciplinary Mershon Center for International Security Studies, which it still houses. In 1986, Ohio State ended its historic open enrollment policy and moved towards selective admissions. The 2020s were marked by internal divisions over politics. In 2020, Kristina M. Johnson took office as the 16th president. Her tenure was marked by the university incorporating various diversity, equity, and inclusion policies, which led to criticism from conservatives. Along with other public universities in the state, DEI policies were banned in 2025 with the Advance Ohio Higher Education Act, which passed the Ohio State Legislature and was signed by Governor Mike DeWine. In 2023, Walter E. Carter Jr. took office as the 17th president. His tenure has been described as either more politically neutral or conservative than Johnson's, rolling back many of her perceived progressive policies. Protests at Ohio State University by pro-Palestinian demonstrators have occurred during the Gaza War, demanding "financial divestment, academic boycott, financial disclosure, acknowledging the genocide, and ending targeted policing". A solidarity encampment was constructed on OSU's South Oval on April 25, 2025 during which there were at least 36 arrests. In January 2025, the defense technology company Anduril Industries announced a series of Arsenal Projects, hyperscaling computer facilities for autonomous sensors and weapons. Anduril announced the construction of a manufacturing facility in Columbus, Ohio, to be named "Arsenal-1", with subsequent Arsenals planned. The facility has been noted for its close ties with Ohio State University, with Anduril Industries sponsoring the football program for the 2025 to 2026 year, close ties to the current college administration, and many of Anduril-1's employees hailing from its applied science programs at the university. Campuses Ohio State's 1,764-acre (7.14 km2) main campus is about 2.5 miles (4.0 km) north of Columbus' downtown. The historical center of campus is the Oval, a quad of about 11 acres (4.5 ha). The original campus was laid out in the English country style with University Hall overlooking what would become the Oval. From 1905 to 1913, the Olmsted brothers, who had designed New York City's Central Park, were contracted as architectural consultants. Under their leadership, a more formal landscape plan was created with its center axis through the Oval. This axis shifted the university's street grid 12.25 degrees from the City of Columbus' street grid. Construction of the main library in 1915 reinforced this grid shift. Ohio State's research library system has a combined collection of over 5.8 million volumes. Along with 21 libraries on its Columbus campus, the university has eight branches at off-campus research facilities and regional campuses, and a book storage depository near campus. In all, the Ohio State library system encompasses 55 branches and specialty collections. Some more significant collections include the Byrd Polar Research Center Archival Program, which has the archives of Admiral Richard E. Byrd and other polar research materials; the Hilandar Research Library, which has the world's largest collection of medieval Slavic manuscripts on microform; the Ohio State Cartoon Library & Museum, the world's largest repository of original cartoons; the Lawrence and Lee Theatre Research Institute. And the archives of Senator John Glenn Anchoring the traditional campus gateway at the eastern end of the Oval is the 1989 Wexner Center for the Arts. Designed by architects Peter Eisenman of New York and Richard Trott of Columbus, the center was funded in large part by Ohio State alumnus Les Wexner's gift of $25 million in the 1980s. The center was founded to encompass all aspects of visual and performing arts with a focus on new commissions and artist residencies. Part of its design was to pay tribute to the armory that formerly had the same location. Its groundbreaking deconstructivist architecture has resulted in it being lauded as one of the most important buildings of its generation. Its design has also been criticized as proving less than ideal for many of the art installations it has attempted to display. The centerpiece of the Wexner Center's permanent collection is Picasso's Nude on a Black Armchair, which was purchased by Wexner at auction for $45 million. To the south of the Oval is another, somewhat smaller expanse of green space commonly referred to as the South Oval. At its eastern end, it is anchored by the Ohio Union. To the west are Hale Hall, the Kuhn Honors House, Browning Amphitheatre (a traditional stone Greek theatre) and Mirror Lake. Knowlton Hall, dedicated in October 2004, is at the corner of West Woodruff Avenue and Tuttle Park Place, next to Ohio Stadium. Knowlton Hall along with the Fisher College of Business and Hitchcock Hall form an academic nucleus in the northwestern corner of North campus. Knowlton Hall was designed by Atlanta-based Mack Scogin Merrill Elam along with WSA Studio from Columbus. The Hall is home to the KSA Café, the disciplines of architecture, landscape architecture, city and regional planning, and about 550 undergraduate and graduate students. Knowlton Hall stands out from the general reddish-brown brick of Ohio State's campus with distinctive white marble tiles that cover the building's exterior. This unique wall cladding was requested by Austin E. Knowlton, the namesake of and main patron to the creation of Knowlton Hall. Knowlton also requested that five white marble columns be erected on the site, each column representing one of the classical orders of architecture. The campus is served by the Campus Area Bus Service. The Ohio State University at Lima (Ohio State Lima) is a regional campus in Lima, Ohio that was established in 1960. The Lima Campus Library has 76,000 volumes and 200+ journal subscriptions. Library databases also provide access to thousands of online journals. The university shares the campus with Rhodes State College. The Ohio State University at Mansfield was founded in 1958 as a land-grant college. It was created through a partnership between Mansfield-area citizens and the state of Ohio. Soon after the Ohio Board of Regents designated Mansfield as the site for an Ohio State regional campus, Mansfield-area citizens mounted a major campaign to acquire land for the campus. OSU-Mansfield, in 1989, hosted a weekend school for Japanese students. The Ohio State University at Marion (OSU Marion or OSUM) is a satellite campus in Marion, Ohio. The campus was founded in 1957. Its 187-acre (0.76 km2) campus is located 45 miles (72 km) north of Columbus and is shared with Marion Technical College. There are eight buildings on the campus. The Ohio State University at Newark is a satellite campus in Newark, Ohio. During its early years, classes were held at old Newark High School. In 1966, over one million dollars pledged by 7,000 local citizens to match funds from the state legislature supported the cost of buying 155 acres (0.63 km2) of land and constructing the first building, Founders Hall, which opened in 1968. The Ohio State University Agricultural Technical Institute is a satellite campus in Wooster, Ohio, established in 1969. It grants associate degrees from the university's College of Food, Agricultural, and Environmental Sciences. Organization and administration Ohio State is overseen by a 15-member Board of Trustees appointed by the Governor of Ohio. Ohio State was among the first group of four public universities to raise a $1 billion endowment when it passed the $1 billion mark in 1999. At the end of 2005, Ohio State's endowment stood at $1.73 billion, ranking it seventh among public universities and 27th among all American universities. In June 2006, the endowment passed the $2 billion mark. In recent decades, and in response to continually shrinking state funding, Ohio State has conducted two significant multi-year fundraising campaigns. The first concluded in 1987 and raised $460 million, a record at the time for a public university. The "Affirm Thy Friendship Campaign" took place between 1995 and 2000. With an initial goal of raising $850 million, the campaign's final tally was $1.23 billion, placing Ohio State among the small group of public universities to have successfully conducted a $1 billion campaign. At his welcoming ceremony, returning President E. Gordon Gee announced in the fall of 2007 that Ohio State would launch a $2.5 billion fundraising campaign. In 2019, celebrating the university's 150th year, President Michael V. Drake announced the "Time and Change Campaign" with a goal of raising $4.5 billion from 1 million individual donors. Academics Ohio State is the flagship university of the University System of Ohio. It is best known for its political science department and applied science programs, where it specializes in artificial intelligence, computer science, biomedical research, and engineering. According to the National Science Foundation, in 2026 the university had research and development (R&D) expenditures of $1.58 billion, ranking it 12th in the nation. Admissions to Ohio State are considered highly selective. In the Autumn 2025 admissions period, the middle 50 percent of composite scores for the SAT was 1360 to 1500. The composite scores for the ACT were 29 to 34. For the enrolled Spring 2025 class, Ohio State accepted 38,532 students out of 88,508 total for an approximate admission rate of 43.5%. OSU's freshman retention rate was 93.9% between 2021 and 2022, with 88% going on to graduate within six years. Ohio State is regarded as a Public Ivy and consistently ranked among the best public universities in the United States by major college and university rankings. In 2026, the university was ranked by Time the 5th best public university in the United States and 33rd globally. Similarly in its 2026 edition, U.S. News & World Report ranked Ohio State as 15th overall among public and 41th among all national universities. In 2026, the Center for World University Rankings ranked Ohio State 29th nationally and 55th out of 21,462 universities globally. The Academic Ranking of World Universities placed Ohio State 39–51 nationally and 82th globally for 2023. Times Higher Education World University Rankings ranks it 108th in the world. In 2024, QS World University Rankings ranked the university 151st in the world. In 1916, Ohio State became the first university in Ohio to be extended membership into the Association of American Universities, and remains the only public university in Ohio among the organization's 60 members. Bloomberg Businessweek ranked the undergraduate business program at Ohio State's Fisher College of Business as the 14th best in the nation in its 2016 rankings. In 2023, U.S. News & World Report ranked the college's political science, audiology, sociology, speech–language pathology, finance, accounting, public affairs, nursing, social work, healthcare administration and pharmacy programs as among the top 20 programs in the country. The university has obtained "national and geopolitical significance" during the 2020s Artificial Intelligence Cold War between the United States and China in generative AI. The Ohio Supercomputer Center (OSC) is a supercomputer facility located on the western end of the campus. Established in 1987, it partners with universities, labs and industries, providing high performance computing, cyberinfrastructure, research and computational science education services. In 2023, the university announced that it had obtained four H100 NVIDIA GPUs's for AI training at OSC, with a goal of continuous hyperscaling of advanced AI chips for the long term future. By early 2024, Ohio State had added 128 H100 into a new "Cardinal" supercomputing cluster across 32 nodes. The ongoing additions have made the OSC one of the most powerful academic supercomputers. In June 2025, the university became the first in the world to require all future students to take courses in artificial intelligence. In November of that same year, the university announced it would hire 100 tenure-track faculty with expertise in artificial intelligence (particularly in the fields of generative AI, large language models, machine learning, and deep learning) between then and 2030. Ohio State is a founding member of the Association of Universities for Research in Astronomy (AURA) is a consortium of universities and other institutions that operates astronomical observatories and telescopes. Established in October 10, 1957, with the encouragement of the National Science Foundation (NSF), AURA was incorporated by a group of seven U.S. universities: California, Chicago, Harvard, Indiana, Michigan, Ohio State, and Wisconsin. The first meeting of the board of directors took place in Ann Arbor, Michigan. Today, AURA has 47 member institutions in the United States and 3 international affiliate members. The Wow! signal was a strong narrowband radio signal detected on August 15, 1977, by Ohio State University's Big Ear radio telescope in Delaware, Ohio, then used to support the search for extraterrestrial intelligence. The signal appeared to come from the direction of the constellation Sagittarius and bore expected hallmarks of extraterrestrial origin. The "Wow! Signal" is considered by scientists to be one of the few compelling candidates for an intentional extraterrestrial radio transmission ever detected. Despite numerous follow-up searches and hypotheses, the signal has never recurred, and no explanation, terrestrial or otherwise, has been confirmed. While some researchers have suggested it could represent an extraterrestrial transmission, its single occurrence and lack of replication limit the strength of this interpretation. The Wow! signal has inspired SETI targeted searches, scientific discussion about rare astrophysical phenomena, and references in popular culture. The university is a prominent force in biomedical research. The Ohio State College of Medicine is on the southern edge of the central campus. It is home to the James Cancer Hospital, a cancer research institute and one of the National Cancer Institute's 41 comprehensive cancer centers, along with the Richard M. Ross Heart Hospital, a research institute for cardiovascular disease. Ohio State's "Buckeye Bullet" electric car broke the world record for the fastest speed by an electric vehicle on October 3, 2004, with a maximum speed of 271.737 mph (437.318 km/h) at the Bonneville Salt Flats in Utah. The vehicle also holds the U.S. record for fastest electric vehicle with a speed of 314.958 mph (506.876 km/h), and peak timed mile speed of 321.834 mph (517.942 km/h). A team of engineering students from the university's "Center for Automotive Research-Intelligent Transportation" (CAR-IT) designed, built and managed the vehicle. In 2007, Buckeye Bullet 2 was launched. This follow-up effort was a collaboration between Ohio State engineering students and engineers from the Ford Motor Company broke the land speed record once again in 2016. On September 19, 2016, the Buckeye Bullet 3 achieved a new world record with a speed of 341.4 mph (549.4 km/h), beating its own previous record of 308 mph (496 km/h). Roger Schroer was the driver for the record breaking run. Ohio State's political science program is ranked among the top programs globally. Political scientist Simon Hix ranked it 4th in the world in 2004, while a 2007 study in the academic journal PS: Political Science & Politics ranked it ninth in the United States. The National Science Foundation ranked Ohio State University 12th in 2026 among American universities for research and development expenditures with $1.58 billion. In a 2007 report released by the National Science Foundation, Ohio State's research expenditures for 2006 were $652 million, placing it seventh among public universities and 11th overall, also ranking third among all American universities for private industry-sponsored research. Research expenditures at Ohio State were $864 million in 2017. In 2006, Ohio State announced it would designate at least $110 million of its research efforts toward what it termed "fundamental concerns" such as research toward a cure for cancer, renewable energy sources and sustainable drinking water supplies. In 2021, President Kristina M. Johnson announced the university would invest at least $750 million over the next 10 years toward research and researchers. This was announced in conjunction with Ohio State's new Innovation District, which will be an interdisciplinary research facility and act as a hub for healthcare and technology research, serving Ohio State faculty and students as well as public and private partners. Construction of the facility was completed in 2023, as one of the first buildings in the District. Research facilities include Aeronautical/Astronautical Research Laboratory, Byrd Polar Research Center, Center for Automotive Research, (OSU CAR), Chadwick Arboretum, Biomedical Research Tower, Biological Sciences Building, CDME, Comprehensive Cancer Center, David Heart and Lung Research Institute, Electroscience Laboratory, Large Binocular Telescope (LBT, originally named the Columbus Project), Mershon Center for International Security Studies, Museum of Biological Diversity, National Center for the Middle Market, Stone Laboratory on Gibraltar Island, Center for Urban and Regional Analysis and Ohio Agricultural Research and Development Center. Student life The Office of Student Life has partnership affiliations with the Schottenstein Center, the Blackwell Inn and the Drake Events Center. Services supporting student wellness include the Wilce Student Health Center, named for university physician John Wilce, the Mary A. Daniels Student Wellness Center and the Counseling and Consultation Service. The RPAC is the main recreational facility on campus. The Wellness Center within the RPAC offers services such as nutrition counseling, financial coaching, HIV and STI testing, sexual assault services, and alcohol and other drug education. The Washington Monthly college rankings, which seek to evaluate colleges' contributions to American society based on factors of social mobility, research and service to the country by their graduates, placed Ohio State 61st among national universities in 2023. In June 2018, Ohio State dissolved its Sexual Civility and Empowerment unit and eliminated four positions in the unit due to concerns about mismanagement and a lack of support for survivors of sexual assault. This occurred after the unit was suspended in February 2018 and following an external review. The Columbus Dispatch and the school newspaper, The Lantern, reported that "[SCE] failed to properly report students' sexual-assault complaints" and that some victims were told that they were "'lying', 'delusional', 'suffering from mental illness', 'have an active imagination', that they 'didn't understand their own experience', and also 'fabricated their story'". With help from the Philadelphia law firm Cozen O'Connor, the university will be creating[when?] a new framework to handle sexual assault cases and reevaluating its Title IX program. On July 20, 2018, BBC News reported that over 100 male students, including athletes from 14 sports, had reported sexual misconduct by a deceased university team physician, Richard Strauss. The reports dated back to 1978, and included claims that he groped and took nude photographs of his patients. Four former wrestlers filed a lawsuit against Ohio State for ignoring complaints of "rampant sexual misconduct" by Strauss. U.S. representative Jim Jordan was named in the lawsuit and has since denied the former wrestlers' claims that he knew about the abuse while he was an assistant coach for eight years at the university.[better source needed] In May 2020, the university entered into a settlement and agreed to pay $40.9 million to the sexual abuse survivors. The Ohio Union was the first student union built by an American public university. It is dedicated to the enrichment of the student experience, on and off the university campus. The first Ohio Union, on the south edge of the South Oval, was constructed in 1909 and was later renamed Enarson Hall. The second Ohio Union was completed in 1950 and was prominently along High Street, southeast of the Oval. It was a center of student life for more than 50 years, providing facilities for student activities, organizations and events, and serving as an important meeting place for campus and community interaction. The union also housed many student services and programs, along with dining and recreational facilities. The second Ohio Union was demolished in February 2007 to make way for the new Ohio Union, which was finished in 2010. During this time, student activities were relocated to Ohio Stadium and other academic buildings. The university has over 1,000 student organizations; intercollegiate, club and recreational sports programs; student media organizations and publications, fraternities and sororities; and three student governments. Student organizations at Ohio State provide students with opportunities to get involved in a wide variety of interest areas including academic, social, religious, artistic, service-based, diversity and many more. There are over 1,000 registered student organizations that involve many thousands of students. The university's forensics team has won the state National Forensics Association tournament several times. Block "O" is currently the largest student-run organization on the campus of Ohio State. With over 2,400 annual members, Block "O" serves as the official student cheering section at athletic events for the university. According to the Student Organization Office in the Ohio Union, Agricultural Education Society is the oldest student organization on campus. The Men's Glee Club often disputes the claim, but after consultation with Ohio Union Staff, Agricultural Education Society was named as the university's oldest organization. Each year, students may sign up to participate in BuckeyeThon, Ohio State's student-led philanthropy. The organization hosts events throughout the year to support the hematology/oncology/bone marrow transplant unit at Nationwide Children's Hospital in Columbus. Each February, thousands of students and community members attend BuckeyeThon's signature event, a Dance Marathon consisting of two separate 12-hour shifts. In the past 15 years, students have raised over $5 million to support treatment, research, and various therapies at the hospital. Unique to BuckeyeThon is the use of an operational fund separate from the main philanthropic cancer fund. As a registered non-profit, BuckeyeThon is subject to university audit and issues gift receipts through the Foundation. Ohio State has several student-managed publications and media outlets. The Makio is the official yearbook. The Makio's sales plummeted by 60% during the early 1970s; the organization went bankrupt and stopped publication during the late 1970s. The book was revived from 1985 to 1994 and again in 2000, thanks to several student organizations. The Lantern is the school's daily newspaper and has operated as a laboratory newspaper[clarification needed] in the School of Communication (formerly the School of Journalism) since 1881. Mosaic is a literary magazine published by Ohio State, which features undergraduate fiction, poetry and art. The Sundial is a student-written and -published humor magazine. Founded in 1911, it is one of the oldest humor magazines in the country, but has not been published without large interruptions. Ohio State has two improvisational comedy groups that regularly perform around campus and across the U.S. There are two student-run radio stations: AROUSE, the music station, is home to over 100 student DJs, streaming music and independent content, and Scarlet and Gray Sports Radio. Students also operate a local cable TV channel known as Buckeye TV, which airs primarily on the campus closed cable system operated by the Office of the Chief Information Officer (OCIO). At the Ohio State University, three recognized student governments represent their constituents. Ohio State operates 41 on-campus residence halls divided into three geographic clusters: South Campus (site of the university's original dormitories), North Campus (largely constructed during the post-war enrollment boom) and West Campus ("The Towers"). The residence hall system has 40 smaller living and learning environments defined by social or academic considerations. Separate housing for graduate and professional students is maintained on the Southern tier of campus within the Gateway Residential Complex and the William H. Hall Student Residential Complex. Family housing is maintained at Buckeye Village at the far northern edge of campus beyond the athletic complex. Student Life University Housing also administers student residential housing on the OSU Newark, OSU Mansfield and OSU Agricultural Technical Institute (ATI) campuses. The Residence Hall Advisory Council (RHAC), which is a representative body of all students living in the university's residence halls, helps evaluate and improve the living conditions of the residence halls. Athletics Ohio State's intercollegiate sports teams are called the "Buckeyes" (derived from the colloquial term for people from the state of Ohio and after the state tree, the Ohio Buckeye, and participate in the NCAA's Division I in all sports and the Big Ten Conference in all but women's hockey. Ohio State currently has 36 varsity teams. Some of the sports figures who were student athletes at Ohio State include Jesse Owens, (track and field); John Havlicek, Jerry Lucas, and Katie Smith (basketball); Frank Howard (baseball); Jack Nicklaus (golf); Archie Griffin and Chic Harley (football running backs). Hall of Fame coaches at Ohio State have included Paul Brown and Woody Hayes (football), Fred Taylor (men's basketball). Notable sports figures in Ohio State history may be inducted into the Ohio State Varsity O Hall of Fame. The school colors are scarlet and gray. Notable team symbols include the Brutus Buckeye mascot and two fight songs: "Across the Field" and "Buckeye Battle Cry". In 2007, Sports Illustrated nicknamed Ohio State's athletic program as being "The Program" due to the unsurpassed facilities, an unparalleled number of men's and women's sports teams and their success, and the financial support of an impressive fan base. The Buckeyes are one of the most successful college football programs. As of 2025, the Ohio State football program is valued at $2–2.5 billion, the highest valuation nationally. With 990 wins as of the 2026 season, Ohio State ranks best all-time in winning percentage in the NCAA. The Buckeyes claim nine national championships: 1942, 1954, 1957, 1961, 1968, 1970, 2002, 2014, and 2024. At least one NCAA college football ranking considers Buckeyes national champions in the 1933, 1944, 1969, 1973, 1974, 1975, and 1998 seasons. The program has captured 41 conference championships (2 OAC and 39 Big Ten), 10 division championships, and has compiled 10 undefeated seasons, including six perfect seasons (no losses or ties). Seven players have received the Heisman Trophy (second all-time), with the program holding the distinction of having the only two-time winner (Archie Griffin) of the award. The team's rivalry against the University of Michigan has been termed as one of the fiercest, greatest, and most influential in North American sports. Ohio State is the only program in college football history to have never lost more than seven games in a single season. Ohio State is one of six universities – the University of Michigan, the University of Florida, Stanford University, UCLA and the University of California at Berkeley being the others – to have won national championships in all three major men's sports (baseball, basketball and football). Ohio State is also one of only two universities to appear in the national championship games in both football and men's basketball in the same calendar year (the other being the University of Florida). Ohio State has also won national championships in wrestling, men's volleyball, men's swimming and diving, men's outdoor track and field, men's golf, men's gymnastics, men's fencing, women's rowing, co-ed fencing and multiple synchronized swimming championships. The Ohio State equestrian team has won eight Intercollegiate Horse Show Association national championships. Since the inception of the Athletic Director's Cup, Ohio State has finished in the top 25 each year, including top-six finishes in three of the last five years. During the 2005–2006 school year, Ohio State became the first Big Ten team to win conference championships in football, men's basketball and women's basketball. Ohio State repeated the feat during the 2006–2007 school year, winning solo championships in all three sports. Traditions The Ohio State University Marching Band is famous for "Script Ohio", during which the band marches single-file through the curves of the word "Ohio", much like a pen writes the word, all while playing the French march "Le Regiment de Sambre et Meuse". "Across the Field", a fight song used by teams of all sports, has been played at events since 1915. "Buckeye Battle Cry", the second fight song which was first performed in 1928, is played as the marching band enters via the Ohio Stadium ramp. Ohio State operates a public television station, WOSU-TV (virtual channel 34/DT 16, a local PBS TV station), as well as two public radio stations, WOSU-FM 89.7(NPR/BBC news/talk) and WOSA-FM 101.1 (classical, "Classical 101") in Columbus. Notable people As of 2014, Ohio State has approximately 580,000 living alumni around the world. Past and present students and faculty include 6 Nobel Prize laureates, nine Rhodes Scholars, seven Churchill Scholars, 77 Goldwater scholars, one Fields Medalist and eight Pulitzer Prize winners. It also includes the current Vice President of the United States, JD Vance, seven U.S. Senators, and 15 U.S. Representatives. 118 Olympic medals have been awarded to those who attended Ohio State. Also included are Medal of Honor recipients, ambassadors, Fortune 500 CEOs, UFC champions, and members of the Forbes 400 list of the world's wealthiest individuals. Its alumni have been inducted into the Baseball Hall of Fame in Cooperstown, New York, the NFL Hall of Fame and the Basketball Hall of Fame. Its athletes have three times received the Sullivan Award as the nation's top amateur athlete. Roboticist James S. Albus was named a "Hero of US Manufacturing" by Fortune magazine in 1997. Howard Tucker, who as of April 2023 was the world's oldest living practicing doctor at 100, attended for both his undergraduate work and medical school. Notable alumni include: As of 2008, Ohio State's faculty included 21 members of the National Academy of Sciences or National Academy of Engineering, four members of the Institute of Medicine and 177 elected fellows of the American Association for the Advancement of Science. In 2009, 17 Ohio State faculty members were elected as AAAS Fellows. Each year since 2002, Ohio State has either led or been second among all American universities in the number of their faculty members elected as fellows to the AAAS. In surveys conducted in 2005 and 2006 by the Collaborative on Academic Careers in Higher Education (COACHE), Ohio State was rated as "exemplary" in four of the seven measured aspects of workplace satisfaction for junior faculty members at 31 universities: overall tenure practices, policy effectiveness, compensation and work-family balance. Notable past and present Ohio State faculty include: See also Notes References External links 40°00′00″N 83°00′45″W / 40.0000°N 83.0125°W / 40.0000; -83.0125 |
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[SOURCE: https://en.wikipedia.org/wiki/Relief_mapping_(computer_graphics)] | [TOKENS: 156] |
Contents Relief mapping (computer graphics) In computer graphics, relief mapping is a texture mapping technique first introduced in 2000 used to render the surface details of three-dimensional objects accurately and efficiently. It can produce accurate depictions of self-occlusion, self-shadowing, and parallax. It is a form of short-distance ray tracing done in a pixel shader.[citation needed] Relief mapping is highly comparable in both function and approach to another displacement texture mapping technique, Parallax occlusion mapping, considering that they both rely on ray tracing, though the two are not to be confused with each other, as parallax occlusion mapping uses reverse heightmap tracing. See also References External links This computer graphics–related article is a stub. You can help Wikipedia by adding missing information. |
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[SOURCE: https://en.wikipedia.org/wiki/Category:Computer_graphics] | [TOKENS: 90] |
Category:Computer graphics Computer graphics is the field of visual computing, where one utilizes computers both to generate visual images synthetically and to integrate or alter visual and spatial information sampled from the real world. Contents Subcategories This category has the following 44 subcategories, out of 44 total. Pages in category "Computer graphics" The following 200 pages are in this category, out of approximately 225 total. This list may not reflect recent changes. |
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