text stringlengths 17 3.36M | source stringlengths 3 333 | __index_level_0__ int64 0 518k |
|---|---|---|
We present an algorithm for generating Poisson-disc patterns taking O(N) time to generate $N$ points. The method is based on a grid of regions which can contain no more than one point in the final pattern, and uses an explicit model of point arrival times under a uniform Poisson process. | Linear-Time Poisson-Disk Patterns | 9,900 |
We describe a technique for bundled curve representations in parallel-coordinates plots and present a controlled user study evaluating their effectiveness. Replacing the traditional C^0 polygonal lines by C^1 continuous piecewise Bezier curves makes it easier to visually trace data points through each coordinate axis. The resulting Bezier curves can then be bundled to visualize data with given cluster structures. Curve bundles are efficient to compute, provide visual separation between data clusters, reduce visual clutter, and present a clearer overview of the dataset. A controlled user study with 14 participants confirmed the effectiveness of curve bundling for parallel-coordinates visualization: 1) compared to polygonal lines, it is equally capable of revealing correlations between neighboring data attributes; 2) its geometric cues can be effective in displaying cluster information. For some datasets curve bundling allows the color perceptual channel to be applied to other data attributes, while for complex cluster patterns, bundling and color can represent clustering far more clearly than either alone. | Evaluation of a Bundling Technique for Parallel Coordinates | 9,901 |
This paper presents a survey of ocean simulation and rendering methods in computer graphics. To model and animate the ocean's surface, these methods mainly rely on two main approaches: on the one hand, those which approximate ocean dynamics with parametric, spectral or hybrid models and use empirical laws from oceanographic research. We will see that this type of methods essentially allows the simulation of ocean scenes in the deep water domain, without breaking waves. On the other hand, physically-based methods use Navier-Stokes Equations (NSE) to represent breaking waves and more generally ocean surface near the shore. We also describe ocean rendering methods in computer graphics, with a special interest in the simulation of phenomena such as foam and spray, and light's interaction with the ocean surface. | A Survey of Ocean Simulation and Rendering Techniques in Computer
Graphics | 9,902 |
Without careful long-term preservation digital data may be lost to a number of factors, including physical media decay, lack of suitable decoding equipment, and the absence of software. When raw data can be read but lack suitable annotations as to provenance, the ability to interpret them is more straightforward if they can be assessed through simple visual techniques. In this regard digital images are a special case since their data have a natural representation on two-dimensional media surfaces. This paper presents a novel binary image pixel encoding that produces an approximate analog rendering of encoded images when the image bits are arranged spatially in an appropriate manner. This simultaneous digital and analog representation acts to inseparably annotate bits as image data, which may contribute to the longevity of so-encoded images. | A self-rendering digital image encoding | 9,903 |
We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to perform either matrix computation or foot point projection in every iteration. As a result, our method is much faster than existing methods. | Fast B-spline Curve Fitting by L-BFGS | 9,904 |
Compared with full volume rendering, isosurface rendering has several well recognized advantages in efficiency and accuracy. However, standard isosurface rendering has some limitations in effectiveness. First, it uses a monotone colored approach and can only visualize the geometry features of an isosurface. The lack of the capability to illustrate the material property and the internal structures behind an isosurface has been a big limitation of this method in applications. Another limitation of isosurface rendering is the difficulty to reveal physically meaningful structures, which are hidden in one or multiple isosurfaces. As such, the application requirements of extract and recombine structures of interest can not be implemented effectively with isosurface rendering. In this work, we develop an enhanced isosurface rendering technique to improve the effectiveness while maintaining the performance efficiency of the standard isosurface rendering. First, an isosurface color enhancement method is proposed to illustrate the neighborhood density and to reveal some of the internal structures. Second, we extend the structure extraction capability of isosurface rendering by enabling explicit scene exploration within a 3D-view, using surface peeling, voxel-selecting, isosurface segmentation, and multi-surface-structure visualization. Our experiments show that the color enhancement not only improves the visual fidelity of the rendering, but also reveals the internal structures without significant increase of the computational cost. Explicit scene exploration is also demonstrated as a powerful tool in some application scenarios, such as displaying multiple abdominal organs. | Efficient and Effective Volume Visualization with Enhanced Isosurface
Rendering | 9,905 |
We present GLSL implementations of Perlin noise and Perlin simplex noise that run fast enough for practical consideration on current generation GPU hardware. The key benefits are that the functions are purely computational, i.e. they use neither textures nor lookup tables, and that they are implemented in GLSL version 1.20, which means they are compatible with all current GLSL-capable platforms, including OpenGL ES 2.0 and WebGL 1.0. Their performance is on par with previously presented GPU implementations of noise, they are very convenient to use, and they scale well with increasing parallelism in present and upcoming GPU architectures. | Efficient computational noise in GLSL | 9,906 |
Image resampling is a necessary component of any operation that changes the size of an image or its geometry. Methods tuned for natural image upsampling (roughly speaking, image enlargement) are analyzed and developed with a focus on their ability to preserve diagonal features and suppress overshoots. Monotone, locally bounded and almost monotone "direct" interpolation and filtering methods, as well as face split and vertex split surface subdivision methods, alone or in combination, are studied. Key properties are established by way of proofs and counterexamples as well as numerical experiments involving 1D curve and 2D diagonal data resampling. In addition, the Remez minimax method for the computation of low-cost polynomial approximations of low-pass filter kernels tuned for natural image downsampling (roughly speaking, image reduction) is refactored for relative error minimization in the presence of roots in the interior of the interval of approximation and so that even and odd functions are approximated with like polynomials. The accuracy and frequency response of the approximations are tabulated and plotted against the original, establishing their rapid convergence. | Numerical Analysis of Diagonal-Preserving, Ripple-Minimizing and
Low-Pass Image Resampling Methods | 9,907 |
We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The method represents a significant breakthrough in the practical computation of distance on a wide variety of geometric domains, since the resulting linear systems can be prefactored once and subsequently solved in near-linear time. In practice, distance can be updated via the heat method an order of magnitude faster than with state-of-the-art methods while maintaining a comparable level of accuracy. We provide numerical evidence that the method converges to the exact geodesic distance in the limit of refinement; we also explore smoothed approximations of distance suitable for applications where more regularity is required. | Geodesics in Heat | 9,908 |
Flow fields are often represented by a set of static arrows to illustrate scientific vulgarization, documentary film, meteorology, etc. This simple schematic representation lets an observer intuitively interpret the main properties of a flow: its orientation and velocity magnitude. We propose to generate dynamic versions of such representations for 2D unsteady flow fields. Our algorithm smoothly animates arrows along the flow while controlling their density in the domain over time. Several strategies have been combined to lower the unavoidable popping artifacts arising when arrows appear and disappear and to achieve visually pleasing animations. Disturbing arrow rotations in low velocity regions are also handled by continuously morphing arrow glyphs to semi-transparent discs. To substantiate our method, we provide results for synthetic and real velocity field datasets. | Visualizing 2D Flows with Animated Arrow Plots | 9,909 |
It is a common sense to apply the VFC (view frustum culling) of spatial object to bounding cube of the object in 3D graphics. The accuracy of VFC can not be guaranteed even in cube rotated three-dimensionally. In this paper is proposed a method which is able to carry out more precise and fast VFC of any spatial object in the image domain of cube by an analytic mapping, and is demonstrated the effect of the method for terrain block on global surface. | Fast View Frustum Culling of Spatial Object by Analytical Bounding Bin | 9,910 |
The Block Transform Coded, JPEG- a lossy image compression format has been used to keep storage and bandwidth requirements of digital image at practical levels. However, JPEG compression schemes may exhibit unwanted image artifacts to appear - such as the 'blocky' artifact found in smooth/monotone areas of an image, caused by the coarse quantization of DCT coefficients. A number of image filtering approaches have been analyzed in literature incorporating value-averaging filters in order to smooth out the discontinuities that appear across DCT block boundaries. Although some of these approaches are able to decrease the severity of these unwanted artifacts to some extent, other approaches have certain limitations that cause excessive blurring to high-contrast edges in the image. The image deblocking algorithm presented in this paper aims to filter the blocked boundaries. This is accomplished by employing smoothening, detection of blocked edges and then filtering the difference between the pixels containing the blocked edge. The deblocking algorithm presented has been successful in reducing blocky artifacts in an image and therefore increases the subjective as well as objective quality of the reconstructed image. | An algorithm for improving the quality of compacted JPEG image by
minimizes the blocking artifacts | 9,911 |
This paper presents the nearest neighbor value (NNV) algorithm for high resolution (H.R.) image interpolation. The difference between the proposed algorithm and conventional nearest neighbor algorithm is that the concept applied, to estimate the missing pixel value, is guided by the nearest value rather than the distance. In other words, the proposed concept selects one pixel, among four directly surrounding the empty location, whose value is almost equal to the value generated by the conventional bilinear interpolation algorithm. The proposed method demonstrated higher performances in terms of H.R. when compared to the conventional interpolation algorithms mentioned. | Nearest Neighbor Value Interpolation | 9,912 |
In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing. | Gap Processing for Adaptive Maximal Poisson-Disk Sampling | 9,913 |
We consider the problem of finding a color scale which performs well when converted to a grayscale. We assume that each color is converted to a shade of gray with the same intensity as the color. We also assume that the color scales have a linear variation of intensity and hue, and find scales which maximize the average chroma (or "colorfulness") of the colors. We find two classes of solutions, which traverse the color wheel in opposite directions. The two classes of scales start with hues near cyan and red. The average chroma of the scales are 65-77% those of the pure colors. | Color scales that are effective in both color and grayscale | 9,914 |
We establish several fundamental properties of analysis-suitable T-splines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended T-mesh of an analysis-suitable T-spline, is contained in the corresponding analysis-suitable T-spline space. This is accomplished through the theory of perturbed analysis-suitable T-spline spaces and a simple topological dimension formula. Second, we establish the theory of analysis-suitable local refinement and describe the conditions under which two analysis-suitable T-spline spaces are nested. Last, we demonstrate that these results can be used to establish basic approximation results which are critical for analysis. | Analysis-suitable T-splines: characterization, refineability, and
approximation | 9,915 |
Real-time generation of natural-looking floor plans is vital in games with dynamic environments. This paper presents an algorithm to generate suburban house floor plans in real-time. The algorithm is based on the work presented in [1]. However, the corridor placement is redesigned to produce floor plans similar to real houses. Moreover, an optimization stage is added to find a corridor placement with the minimum used space, an approach that is designed to mimic the real-life practices to minimize the wasted spaces in the design. The results show very similar floor plans to the ones designed by an architect. | A Novel Algorithm for Real-time Procedural Generation of Building Floor
Plans | 9,916 |
When representing a solid object there are alternatives to the use of traditional explicit (surface meshes) or implicit (zero crossing of implicit functions) methods. Skeletal representations encode shape information in a mixed fashion: they are composed of a set of explicit primitives, yet they are able to efficiently encode the shape's volume as well as its topology. I will discuss, in two dimensions, how symmetry can be used to reduce the dimensionality of the data (from a 2D solid to a 1D curve), and how this relates to the classical definition of skeletons by Medial Axis Transform. While the medial axis of a 2D shape is composed of a set of curves, in 3D it results in a set of sheets connected in a complex fashion. Because of this complexity, medial skeletons are difficult to use in practical applications. Curve skeletons address this problem by strictly requiring their geometry to be one dimensional, resulting in an intuitive yet powerful shape representation. In this report I will define both medial and curve skeletons and discuss their mutual relationship. I will also present several algorithms for their computation and a variety of scenarios where skeletons are employed, with a special focus on geometry processing and shape analysis. | Skeletal Representations and Applications | 9,917 |
We formalize the notion of sampling a function using k-d darts. A k-d dart is a set of independent, mutually orthogonal, k-dimensional subspaces called k-d flats. Each dart has d choose k flats, aligned with the coordinate axes for efficiency. We show that k-d darts are useful for exploring a function's properties, such as estimating its integral, or finding an exemplar above a threshold. We describe a recipe for converting an algorithm from point sampling to k-d dart sampling, assuming the function can be evaluated along a k-d flat. We demonstrate that k-d darts are more efficient than point-wise samples in high dimensions, depending on the characteristics of the sampling domain: e.g. the subregion of interest has small volume and evaluating the function along a flat is not too expensive. We present three concrete applications using line darts (1-d darts): relaxed maximal Poisson-disk sampling, high-quality rasterization of depth-of-field blur, and estimation of the probability of failure from a response surface for uncertainty quantification. In these applications, line darts achieve the same fidelity output as point darts in less time. We also demonstrate the accuracy of higher dimensional darts for a volume estimation problem. For Poisson-disk sampling, we use significantly less memory, enabling the generation of larger point clouds in higher dimensions. | k-d Darts: Sampling by k-Dimensional Flat Searches | 9,918 |
Polyhedral meshes (PM) - meshes having planar faces - have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate. Previous methods start with a smooth surface and then apply elaborate meshing schemes to create polyhedral meshes approximating the surface. In this paper, we describe a reverse approach: given the topology of a mesh, we explore the space of possible planar meshes with that topology. Our approach is based on a complete characterization of the maximal linear spaces of polyhedral meshes contained in the curved manifold of polyhedral meshes with a given topology. We show that these linear spaces can be described as nullspaces of differential operators, much like harmonic functions are nullspaces of the Laplacian operator. An analysis of this operator provides tools for global and local design of a polyhedral mesh, which fully expose the geometric possibilities and limitations of the given topology. | On Linear Spaces of Polyhedral Meshes | 9,919 |
Glyph-based visualization is an effective tool for depicting multivariate information. Since sorting is one of the most common analytical tasks performed on individual attributes of a multi-dimensional data set, this motivates the hypothesis that introducing glyph sorting would significantly enhance the usability of glyph-based visualization. In this paper, we present a glyph-based conceptual framework as part of a visualization process for interactive sorting of multivariate data. We examine several technical aspects of glyph sorting and provide design principles for developing effective, visually sortable glyphs. Glyphs that are visually sortable provide two key benefits: 1) performing comparative analysis of multiple attributes between glyphs and 2) to support multi-dimensional visual search. We describe a system that incorporates focus and context glyphs to control sorting in a visually intuitive manner and for viewing sorted results in an Interactive, Multi-dimensional Glyph (IMG) plot that enables users to perform high-dimensional sorting, analyse and examine data trends in detail. To demonstrate the usability of glyph sorting, we present a case study in rugby event analysis for comparing and analysing trends within matches. This work is undertaken in conjunction with a national rugby team. From using glyph sorting, analysts have reported the discovery of new insight beyond traditional match analysis. | Glyph Sorting: Interactive Visualization for Multi-dimensional Data | 9,920 |
The Generalized Cornu Spiral (GCS) was first proposed by Ali et al. in 1995 [9]. Due to the monotonocity of its curvature function, the surface generated with GCS segments has been considered as a high quality surface and it has potential applications in surface design [2]. In this paper, the analysis of GCS segment is carried out by determining its aesthetic value using the log curvature Graph (LCG) as proposed by Kanaya et al.[10]. The analysis of LCG supports the claim that GCS is indeed a generalized aesthetic curve. | The Logarithmic Curvature Graphs of Generalised Cornu Spirals | 9,921 |
A method to construct transition curves using a family of the quartic Bezier spiral is described. The transition curves discussed are S-shape and C-shape of contact, between two separated circles. A spiral is a curve of monotone increasing or monotone decreasing curvature of one sign. Thus, a spiral cannot have an inflection point or curvature extreme. The family of quartic Bezier spiral form which is introduced has more degrees of freedom and will give a better approximation. It is proved that the methods of constructing transition curves can be simplified by the transformation process and the ratio of two radii has no restriction, which extends the application area, and it gives a family of transition curves that allow more flexible curve designs. | G2 Transition curve using Quartic Bezier Curve | 9,922 |
In this paper, we analyze the planar cubic Alternative curve to determine the conditions for convex, loops, cusps and inflection points. Thus cubic curve is represented by linear combination of three control points and basis function that consist of two shape parameters. By using algebraic manipulation, we can determine the constraint of shape parameters and sufficient conditions are derived which ensure that the curve is a strictly convex, loops, cusps and inflection point. We conclude the result in a shape diagram of parameters. The simplicity of this form makes characterization more intuitive and efficient to compute. | Characterization of Planar Cubic Alternative curve | 9,923 |
The log-aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design. The discrete log-aesthetic filter based on the formulation of the log-aesthetic curve has successfully been introduced not to impose strong constraints on the designer's activity, to let him/her design freely and to embed the properties of the log-aesthetic curves for complicated ones with both increasing and decreasing curvature. In this paper, in order to define the log-aesthetic surface and develop surface filters based on its formulation, at first we reformulate the log-aesthetic curve with variational principle. Then we propose several new functionals to be minimized for free-form surfaces and define the log-aesthetic surface. Furthermore we propose new discrete surface filters based on the log-aesthetic surface formulation | Variational Formulation of the Log-Aesthetic Surface and Development of
Discrete Surface Filters | 9,924 |
In this paper, we proposed a new form of type-2 fuzzy data points(T2FDPs) that is normal type-2 data points(NT2FDPs). These brand-new forms of data were defined by using the definition of normal type-2 triangular fuzzy number(NT2TFN). Then, we applied fuzzification(alpha-cut) and type-reduction processes towards NT2FDPs after they had been redefined based on the situation of NT2FDPs. Furthermore, we redefine the defuzzification definition along with the new definitions of fuzzification process and type-reduction method to obtain crisp type-2 fuzzy solution data points. For all these processes from the defining the NT2FDPs to defuzzification of NT2FDPs, we demonstrate through curve representation by using the rational B-spline curve function as the example form modeling these NT2FDPs. | Normal type-2 Fuzzy Rational B-Spline Curve | 9,925 |
The research on developing planar curves to produce visually pleasing products (ranges from electric appliances to car body design) and indentifying/modifying planar curves for special purposes namely for railway design, highway design and robot trajectories have been progressing since 1970s. The pattern of research in this field of study has branched to five major groups namely curve synthesis, fairing process, improvement in control of natural spiral, construction of new type of planar curves and, natural spiral fitting & approximation techniques. The purpose of is this paper is to briefly review recent progresses in Computer Aided Geometric Design (CAGD) focusing on the topics states above. | Various Types of Aesthetic Curves | 9,926 |
An improvised algorithm is proposed based on the work of Yoshimoto and Harada. The improvised algorithm results a graph which is called LDGC or Logarithmic Distribution Graph of Curvature. This graph has the capability to identify the beauty of monotonic planar curves with less effort as compared to LDDC by Yoshimoto and Harada. | An Improvised Algorithm to Identify The Beauty of A Planar Curve | 9,927 |
In this paper, we proposed another new form of type-2 fuzzy data points(T2FDPs) that is perfectly normal type-2 data points(PNT2FDPs). These kinds of brand-new data were defined by using the existing type-2 fuzzy set theory(T2FST) and type-2 fuzzy number(T2FN) concept since we dealt with the problem of defining complex uncertainty data. Along with this restructuring, we included the fuzzification(alpha-cut operation), type-reduction and defuzzification processes against PNT2FDPs. In addition, we used interpolation B-soline curve function to demonstrate the PNT2FDPs. | Perfectly normal type-2 fuzzy interpolation B-spline curve | 9,928 |
In many graphics applications, the computation of exact geodesic distance is very important. However, the high computational cost of the existing geodesic algorithms means that they are not practical for large-scale models or time-critical applications. To tackle this challenge, we propose the parallel Chen-Han (or PCH) algorithm, which extends the classic Chen-Han (CH) discrete geodesic algorithm to the parallel setting. The original CH algorithm and its variant both lack a parallel solution because the windows (a key data structure that carries the shortest distance in the wavefront propagation) are maintained in a strict order or a tightly coupled manner, which means that only one window is processed at a time. We propose dividing the CH's sequential algorithm into four phases, window selection, window propagation, data organization, and events processing so that there is no data dependence or conflicts in each phase and the operations within each phase can be carried out in parallel. The proposed PCH algorithm is able to propagate a large number of windows simultaneously and independently. We also adopt a simple yet effective strategy to control the total number of windows. We implement the PCH algorithm on modern GPUs (such as Nvidia GTX 580) and analyze the performance in detail. The performance improvement (compared to the sequential algorithms) is highly consistent with GPU double-precision performance (GFLOPS). Extensive experiments on real-world models demonstrate an order of magnitude improvement in execution time compared to the state-of-the-art. | Parallel Chen-Han (PCH) Algorithm for Discrete Geodesics | 9,929 |
In this paper we discuss the variety of planar spiral segments and their applications in objects in both the real and artificial world. The discussed curves with monotonic curvature function are well-known in geometric modelling and computer aided geometric design as fair curves, and they are very significant in aesthetic shape modelling. Fair curve segments are used for two-point G1 and G2 Hermite interpolation, as well as for generating aesthetic splines. | On the variety of planar spirals and their applications in computer
aided design | 9,930 |
This article studies families of curves with monotonic curvature function (MC-curves) and their applications in geometric modelling and aesthetic design. Aesthetic analysis and assessment of the structure and plastic qualities of pseudospirals, which are curves with monotonic curvature function, are conducted for the first time in the field of geometric modelling from the position of technical aesthetics laws. The example of car body surface modelling with the use of aesthetics splines is given. | MC-curves and aesthetic measurements for pseudospiral curve segments | 9,931 |
High-dimensional transfer function design is widely used to provide appropriate data classification for direct volume rendering of various datasets. However, its design is a complicated task. Parallel coordinate plot (PCP), as a powerful visualization tool, can efficiently display high-dimensional geometry and accurately analyze multivariate data. In this paper, we propose to combine parallel coordinates with dimensional reduction methods to guide high-dimensional transfer function design. Our pipeline has two major advantages: (1) combine and display extracted high-dimensional features in parameter space; and (2) select appropriate high-dimensional parameters, with the help of dimensional reduction methods, to obtain sophisticated data classification as transfer function for volume rendering. In order to efficiently design high-dimensional transfer functions, the combination of both parallel coordinate components and dimension reduction results is necessary to generate final visualization results. We demonstrate the capability of our method for direct volume rendering using various CT and MRI datasets. | Parallel Coordinates Guided High Dimensional Transfer Function Design | 9,932 |
We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizing the approximation error between the input shape and the shape represented by the medial axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of medial axis transforms of 2D shapes. | Computing a Compact Spline Representation of the Medial Axis Transform
of a 2D Shape | 9,933 |
We present a novel methodology that utilizes 4-Dimensional (4D) space deformation to simulate a magnification lens on versatile volume datasets and textured solid models. Compared with other magnification methods (e.g., geometric optics, mesh editing), 4D differential geometry theory and its practices are much more flexible and powerful for preserving shape features (i.e., minimizing angle distortion), and easier to adapt to versatile solid models. The primary advantage of 4D space lies at the following fact: we can now easily magnify the volume of regions of interest (ROIs) from the additional dimension, while keeping the rest region unchanged. To achieve this primary goal, we first embed a 3D volumetric input into 4D space and magnify ROIs in the 4th dimension. Then we flatten the 4D shape back into 3D space to accommodate other typical applications in the real 3D world. In order to enforce distortion minimization, in both steps we devise the high dimensional geometry techniques based on rigorous 4D geometry theory for 3D/4D mapping back and forth to amend the distortion. Our system can preserve not only focus region, but also context region and global shape. We demonstrate the effectiveness, robustness, and efficacy of our framework with a variety of models ranging from tetrahedral meshes to volume datasets. | 4-Dimensional Geometry Lens: A Novel Volumetric Magnification Approach | 9,934 |
In this paper we describe a new technique to generate and use surfels for rendering of highly complex, polygonal 3D scenes in real time. The basic idea is to approximate complex parts of the scene by rendering a set of points (surfels). The points are computed in a preprocessing step and offer two important properties: They are placed only on the visible surface of the scene's geometry and they are distributed and sorted in such a way, that every prefix of points is a good visual representation of the approximated part of the scene. An early evaluation of the method shows that it is capable of rendering scenes consisting of several billions of triangles with high image quality. | Progressive Blue Surfels | 9,935 |
We present a novel methodology based on geometric approach to simulate magnification lens effects. Our aim is to promote new applications of powerful geometric modeling techniques in visual computing. Conventional image processing/visualization methods are computed in two dimensional space (2D). We examine this conventional 2D manipulation from a completely innovative perspective of 3D geometric processing. Compared with conventional optical lens design, 3D geometric method are much more capable of preserving shape features and minimizing distortion. We magnify an area of interest to better visualize the interior details, while keeping the rest of area without perceivable distortion. We flatten the mesh back into 2D space for viewing, and further applications in the screen space. In both steps, we devise an iterative deformation scheme to minimize distortion around both focus and context region, while avoiding the noncontinuous transition region between the focus and context areas. Particularly, our method allows the user to flexibly modify the ROI shapes to accommodate complex feature. The user can also easily specify a spectrum of metrics for different visual effects. Various experimental results demonstrate the effectiveness, robustness, and efficiency of our framework. | A New 3D Geometric Approach to Focus and Context Lens Effect Simulation | 9,936 |
In this paper, we address the following research problem: How can we generate a meaningful split grammar that explains a given facade layout? To evaluate if a grammar is meaningful, we propose a cost function based on the description length and minimize this cost using an approximate dynamic programming framework. Our evaluation indicates that our framework extracts meaningful split grammars that are competitive with those of expert users, while some users and all competing automatic solutions are less successful. | Inverse Procedural Modeling of Facade Layouts | 9,937 |
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. This dissertation systematically trailblazes a novel volumetric modeling framework to represent 3D solids. The need to explore more efficient and robust 3D modeling framework has gained the prominence. Although the traditional surface representation (e.g., triangle mesh) has many attractive properties, it is incapable of expressing the interior space and materials. Such a serious drawback overshadows many potential modeling and analysis applications. Consequently volumetric modeling techniques become the well-known solution to this problem. Nevertheless, many unsolved research issues remain when developing an efficient modeling paradigm for existing 3D models: complex geometry (fine details and extreme concaveness), arbitrary topology, heterogenous materials, large-scale data storage and processing, etc. | A Survey of Spline-based Volumetric Data Modeling Framework and Its
Applications | 9,938 |
In this dissertation, we concentrate on the challenging research issue of developing a spline-based modeling framework, which converts the conventional data (e.g., surface meshes) to tensor-product trivariate splines. This methodology can represent both boundary/volumetric geometry and real volumetric physical attributes in a compact and continuous fashion. The regular tensor-product structure enables our new developed methods to be embedded into the industry standard seamlessly. These properties make our techniques highly preferable in many physically-based applications including mechanical analysis, shape deformation and editing, virtual surgery training, etc. | A Spline-based Volumetric Data Modeling Framework and Its Applications | 9,939 |
Barycentric coordinates are frequently used as interpolants to shade computer graphics images. A simple equation transforms barycentric coordinates from screen space into eye space in order to undo the perspective transformation and permit accurate interpolative shading of texture maps. This technique is amenable to computation using a block-normalized integer representation. | Barycentric Coordinates as Interpolants | 9,940 |
Volume approximation is an important problem found in many applications of computer graphics, vision, and image processing. The problem is about computing an accurate and compact approximate representation of 3D volumes using some simple primitives. In this study, we propose a new volume representation, called medial meshes, and present an efficient method for its computation. Specifically, we use the union of a novel type of simple volume primitives, which are spheres and the convex hulls of two or three spheres, to approximate a given 3D shape. We compute such a volume approximation based on a new method for medial axis simplification guided by Hausdorff errors. We further demonstrate the superior efficiency and accuracy of our method over existing methods for medial axis simplification. | Medial Meshes for Volume Approximation | 9,941 |
A flexible, scalable and affordable virtual reality software system architecture is proposed. This solution can be easily implemented on different hardware configurations: on a single computer or on a computer cluster. The architecture is aimed to be integrated in the workflow for solving engineering tasks and oriented towards presenting implicit object properties through multiple sensorial channels (visual, audio and haptic). Implicit properties represent hidden object features (i.e. magnetization, radiation, humidity, toxicity, etc.) which cannot be perceived by the observer through his or her senses but require specialized equipment in order to expand the sensory ability of the observer. Our approach extends the underlying general scene graph structure incorporating additional effects nodes for implicit properties representation. | Affordable Virtual Reality System Architecture for Representation of
Implicit Object Properties | 9,942 |
The applicability of Virtual Reality for evaluating engineering analysis results is beginning to receive increased appreciation in the last years. The problem many engineers are still facing is how to import their model together with the analysis results in a virtual reality environment for exploration and results validation. In this paper we propose an algorithm for transforming model data and results from finite element analysis (FEA) solving application to a format easily interpretable by a virtual reality application. The algorithm includes also steps for reducing the face-count of the resulting mesh by eliminating faces from the inner part of the model in the cases when only the surfaces of the model is analyzed. We also describe a possibility for simultaneously assessing multiple analysis results relying on multimodal results presentation by stimulating different senses of the operator. | Post-processing of Engineering Analysis Results for Visualization in VR
Systems | 9,943 |
In this article we present Zahir, a framework for experimentation in Computer Graphics that provides a group of object-oriented base components that take care of common tasks in rendering techniques and algorithms, specially those of Non Photo-realistic Rendering (NPR). These components allow developers to implement rendering techniques and algorithms over static and animated meshes. Currently, Zahir is being used in a Master's Thesis and as support material in the undergraduate Computer Graphics course in University of Chile. | Zahir: a Object-Oriented Framework for Computer Graphics | 9,944 |
A comprehensive framework for detection and characterization of overlapping intrinsic symmetry over 3D shapes is proposed. To identify prominent symmetric regions which overlap in space and vary in form, the proposed framework is decoupled into a Correspondence Space Voting procedure followed by a Transformation Space Mapping procedure. In the correspondence space voting procedure, significant symmetries are first detected by identifying surface point pairs on the input shape that exhibit local similarity in terms of their intrinsic geometry while simultaneously maintaining an intrinsic distance structure at a global level. Since different point pairs can share a common point, the detected symmetric shape regions can potentially overlap. To this end, a global intrinsic distance-based voting technique is employed to ensure the inclusion of only those point pairs that exhibit significant symmetry. In the transformation space mapping procedure, the Functional Map framework is employed to generate the final map of symmetries between point pairs. The transformation space mapping procedure ensures the retrieval of the underlying dense correspondence map throughout the 3D shape that follows a particular symmetry. Additionally, the formulation of a novel cost matrix enables the inner product to succesfully indicate the complexity of the underlying symmetry transformation. The proposed transformation space mapping procedure is shown to result in the formulation of a semi-metric symmetry space where each point in the space represents a specific symmetry transformation and the distance between points represents the complexity between the corresponding transformations. Experimental results show that the proposed framework can successfully process complex 3D shapes that possess rich symmetries. | Detection and Characterization of Intrinsic Symmetry | 9,945 |
We propose a new gradient-domain technique for processing registered EM image stacks to remove the inter-image discontinuities while preserving intra-image detail. To this end, we process the image stack by first performing anisotropic diffusion to smooth the data along the slice axis and then solving a screened-Poisson equation within each slice to re-introduce the detail. The final image stack is both continuous across the slice axis (facilitating the tracking of information between slices) and maintains sharp details within each slice (supporting automatic feature detection). To support this editing, we describe the implementation of the first multigrid solver designed for efficient gradient domain processing of large, out-of-core, voxel grids. | Gradient-Domain Processing for Large EM Image Stacks | 9,946 |
This work presents an analysis of Higher Order Singular Value Decomposition (HO-SVD) applied to lossy compression of 3D mesh animations. We describe strategies for choosing a number of preserved spatial and temporal components after tensor decomposition. Compression error is measured using three metrics (MSE, Hausdorff, MSDM). Results are compared with a method based on Principal Component Analysis (PCA) and presented on a set of animations with typical mesh deformations. | Compression of animated 3D models using HO-SVD | 9,947 |
A fundamental tool in shape analysis is the virtual embedding of the Riemannian manifold describing the geometry of a shape into Euclidean space. Several methods have been proposed to embed isometric shapes in flat domains while preserving distances measured on the manifold. Recently, attention has been given to embedding shapes into the eigenspace of the Lapalce-Beltrami operator. The Laplace-Beltrami eigenspace preserves the diffusion distance, and is invariant under isometric transformations. However, Laplace-Beltrami eigenfunctions computed independently for different shapes are often incompatible with each other. Applications involving multiple shapes, such as pointwise correspondence, would greatly benefit if their respective eigenfunctions were somehow matched. Here, we introduce a statistical approach for matching eigenfunctions. We consider the values of the eigenfunctions over the manifold as sampling of random variables, and try to match their multivariate distributions. Comparing distributions is done indirectly, using high order statistics. We show that the permutation and sign ambiguities of low order eigenfunctions, can be inferred by minimizing the difference of their third order moments. The sign ambiguities of antisymmetric eigenfunctions can be resolved by exploiting isometric invariant relations between the gradients of the eigenfunctions and the surface normal. We present experiments demonstrating the success of the proposed method applied to feature point correspondence. | Matching LBO eigenspace of non-rigid shapes via high order statistics | 9,948 |
We present a novel BSSRDF for rendering translucent materials. Angular effects lacking in previous BSSRDF models are incorporated by using a dual-beam formulation. We employ a Placzek's Lemma interpretation of the method of images and discard diffusion theory. Instead, we derive a plane-parallel transformation of the BSSRDF to form the associated BRDF and optimize the image confiurations such that the BRDF is close to the known analytic solutions for the associated albedo problem. This ensures reciprocity, accurate colors, and provides an automatic level-of-detail transition for translucent objects that appear at various distances in an image. Despite optimizing the subsurface fluence in a plane-parallel setting, we find that this also leads to fairly accurate fluence distributions throughout the volume in the original 3D searchlight problem. Our method-of-images modifications can also improve the accuracy of previous BSSRDFs. | A Dual-Beam Method-of-Images 3D Searchlight BSSRDF | 9,949 |
Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact of popular integration methods, we consider a scenario where soft and hard constraints are added to a custom designed deformable linear object. Since the goal for this class of simulation methods is to attain interactive frame-rates, we present the drawbacks of using explicit integration methods over inherently stable, implicit integrators. To help numerical solver designers better understand the impact of an integrator on a certain simulated world, we have conceived a method of benchmarking the efficiency of an integrator with respect to its speed, stability and symplecticity. | On the impact of explicit or semi-implicit integration methods over the
stability of real-time numerical simulations | 9,950 |
In this paper, we present an approach to reconstruct 3-D human motion from multi-cameras and track human skeleton using the reconstructed human 3-D point (voxel) cloud. We use an improved and more robust algorithm, probabilistic shape from silhouette to reconstruct human voxel. In addition, the annealed particle filter is applied for tracking, where the measurement is computed using the reprojection of reconstructed voxel. We use two different ways to accelerate the approach. For the CPU only acceleration, we leverage Intel TBB to speed up the hot spot of the computational overhead and reached an accelerating ratio of 3.5 on a 4-core CPU. Moreover, we implement an intensively paralleled version via GPU acceleration without TBB. Taking account all data transfer and computing time, the GPU version is about 400 times faster than the original CPU implementation, leading the approach to run at a real-time speed. | Digitize Your Body and Action in 3-D at Over 10 FPS: Real Time Dense
Voxel Reconstruction and Marker-less Motion Tracking via GPU Acceleration | 9,951 |
This paper presents a method for extraction and analysis of curve--type structures which consist of disconnected components. Such structures are found in electron--microscopy (EM) images of metal nanograins, which are widely used in the field of nanosensor technology. The topography of metal nanograins in compound nanomaterials is crucial to nanosensor characteristics. The method of completing such templates consists of three steps. In the first step, a local Gaussian filter is used with different weights for each neighborhood. In the second step, an adaptive morphology operation is applied to detect the endpoints of curve segments and connect them. In the last step, pruning is employed to extract a curve which optimally fits the template. | A local Gaussian filter and adaptive morphology as tools for completing
partially discontinuous curves | 9,952 |
A composite quadric model (CQM) is an object modeled by piecewise linear or quadric patches. We study the continuous detection problem of a special type of CQM objects which are commonly used in CAD/CAM, that is, the boundary surfaces of such a CQM intersect only in straight line segments or conic curve segments. We present a framework for continuous collision detection (CCD) of this special type of CQM (which we also call CQM for brevity) in motion. We derive algebraic formulations and compute numerically the first contact time instants and the contact points of two moving CQMs in $\mathbb R^3$. Since it is difficult to process CCD of two CQMs in a direct manner because they are composed of semi-algebraic varieties, we break down the problem into subproblems of solving CCD of pairs of boundary elements of the CQMs. We present procedures to solve CCD of different types of boundary element pairs in different dimensions. Some CCD problems are reduced to their equivalents in a lower dimensional setting, where they can be solved more efficiently. | Continuous Collision Detection for Composite Quadric Models | 9,953 |
We consider the problem of establishing dense correspondences within a set of related shapes of strongly varying geometry. For such input, traditional shape matching approaches often produce unsatisfactory results. We propose an ensemble optimization method that improves given coarse correspondences to obtain dense correspondences. Following ideas from minimum description length approaches, it maximizes the compactness of the induced shape space to obtain high-quality correspondences. We make a number of improvements that are important for computer graphics applications: Our approach handles meshes of general topology and handles partial matching between input of varying topology. To this end we introduce a novel part-based generative statistical shape model. We develop a novel analysis algorithm that learns such models from training shapes of varying topology. We also provide a novel synthesis method that can generate new instances with varying part layouts and subject to generic variational constraints. In practical experiments, we obtain a substantial improvement in correspondence quality over state-of-the-art methods. As example application, we demonstrate a system that learns shape families as assemblies of deformable parts and permits real-time editing with continuous and discrete variability. | Compact Part-Based Shape Spaces for Dense Correspondences | 9,954 |
We propose connectivity-preserving geometry images (CGIMs), which map a three-dimensional mesh onto a rectangular regular array of an image, such that the reconstructed mesh produces no sampling errors, but merely round-off errors. We obtain a V-matrix with respect to the original mesh, whose elements are vertices of the mesh, which intrinsically preserves the vertex-set and the connectivity of the original mesh in the sense of allowing round-off errors. We generate a CGIM array by using the Cartesian coordinates of corresponding vertices of the V-matrix. To reconstruct a mesh, we obtain a vertex-set and an edge-set by collecting all the elements with different pixels, and all different pairwise adjacent elements from the CGIM array respectively. Compared with traditional geometry images, CGIMs achieve minimum reconstruction errors with an efficient parametrization-free algorithm via elementary permutation techniques. We apply CGIMs to lossy compression of meshes, and the experimental results show that CGIMs perform well in reconstruction precision and detail preservation. | Connectivity-preserving Geometry Images | 9,955 |
In this paper the problem of matching Forward Kinematics (FK) motion of a 3 Dimensional (3D) joint chain to the Inverse Kinematics (IK) movement and vice versa has been addressed. The problem lies at the heart of animating a 3D character having controller and manipulator based rig for animation within any 3D modeling and animation software. The seamless matching has been achieved through the use of pseudo-inverse of Jacobian Matrix. The Jacobian Matrix is used to determine the rotation values of each joint of character body part such as arms, between the inverse kinematics and forward kinematics motion. Then moving the corresponding kinematic joint system to the desired place, automatically eliminating the jumping or popping effect which would reduce the complexity of the system. | Forward and Inverse Kinematics Seamless Matching Using Jacobian | 9,956 |
For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions, classical diffusion approximation suffers from non-physical radiative fluxes which leads to a poor match to correct light transport. In particular, this prevents the application of classical diffusion approximation to heterogeneous media, where opaque material is embedded within transparent regions. To address this limitation, we introduce flux-limited diffusion, a technique from the astrophysics domain. This method provides a better approximation to light transport than classical diffusion approximation, particularly when applied to heterogeneous media, and hence broadens the applicability of diffusion-based techniques. We provide an algorithm for flux-limited diffusion, which is validated using the transport theory for a point light source in an infinite homogeneous medium. We further demonstrate that our implementation of flux-limited diffusion produces more accurate renderings of multiple scattering in various heterogeneous datasets than classical diffusion approximation, by comparing both methods to ground truth renderings obtained via volumetric path tracing. | Flux-Limited Diffusion for Multiple Scattering in Participating Media | 9,957 |
The generation of fractals and study of the dynamics of polynomials is one of the emerging and interesting field of research nowadays. We introduce in this paper the dynamics of polynomials z^ n - z + c = 0 for n>=2 and applied Jungck Ishikawa Iteration to generate new Relative Superior Mandelbrot sets and Relative Superior Julia sets. In order to solve this function by Jungck type iterative schemes, we write it in the form of Sz = Tz, where the function T, S are defined as Tz = z^ n + c and Sz = z. Only mathematical explanations are derived by applying Jungck Ishikawa Iteration for polynomials in the literature but in this paper we have generated Relative Mandelbrot sets and Relative Julia sets. | New Julia and Mandelbrot Sets for Jungck Ishikawa Iterates | 9,958 |
This research paper addresses the problem of generating involuntary and precise animation of quadrupeds with automatic rigging system of various character types. The technique proposed through this research is based on a two tier animation control curve with base simulation being driven through dynamic mathematical model using procedural algorithm and the top layer with a custom user controlled animation provided with intuitive Graphical User Interface (GUI). The character rig is based on forward and inverse kinematics driven through trigonometric based motion equations. The User is provided with various manipulators and attributes to control and handle the locomotion gaits of the characters and choose between various types of simulated motions from walking, running, trotting, ambling and galloping with complete custom controls to easily extend the base simulation as per requirements. | Expression driven Trignometric based Procedural Animation of Quadrupeds | 9,959 |
A recent development, called isogeometric analysis, provides a unified approach for design, analysis and optimization of functional products in industry. Traditional volume rendering methods for inspecting the results from the numerical simulations cannot be applied directly to isogeometric models. We present a novel approach for interactive visualization of isogeometric analysis results, ensuring correct, i.e., pixel-accurate geometry of the volume including its bounding surfaces. The entire OpenGL pipeline is used in a multi-stage algorithm leveraging techniques from surface rendering, order-independent transparency, as well as theory and numerical methods for ordinary differential equations. We showcase the efficiency of our approach on different models relevant to industry, ranging from quality inspection of the parametrization of the geometry, to stress analysis in linear elasticity, to visualization of computational fluid dynamics results. | Interactive Isogeometric Volume Visualization with Pixel-Accurate
Geometry | 9,960 |
We present Piko, a framework for designing, optimizing, and retargeting implementations of graphics pipelines on multiple architectures. Piko programmers express a graphics pipeline by organizing the computation within each stage into spatial bins and specifying a scheduling preference for these bins. Our compiler, Pikoc, compiles this input into an optimized implementation targeted to a massively-parallel GPU or a multicore CPU. Piko manages work granularity in a programmable and flexible manner, allowing programmers to build load-balanced parallel pipeline implementations, to exploit spatial and producer-consumer locality in a pipeline implementation, and to explore tradeoffs between these considerations. We demonstrate that Piko can implement a wide range of pipelines, including rasterization, Reyes, ray tracing, rasterization/ray tracing hybrid, and deferred rendering. Piko allows us to implement efficient graphics pipelines with relative ease and to quickly explore design alternatives by modifying the spatial binning configurations and scheduling preferences for individual stages, all while delivering real-time performance that is within a factor six of state-of-the-art rendering systems. | Piko: A Design Framework for Programmable Graphics Pipelines | 9,961 |
We present a generalization of the bilateral filter that can be applied to feature-preserving smoothing of signals on images, meshes, and other domains within a single unified framework. Our discretization is competitive with state-of-the-art smoothing techniques in terms of both accuracy and speed, is easy to implement, and has parameters that are straightforward to understand. Unlike previous bilateral filters developed for meshes and other irregular domains, our construction reduces exactly to the image bilateral on rectangular domains and comes with a rigorous foundation in both the smooth and discrete settings. These guarantees allow us to construct unconditionally convergent mean-shift schemes that handle a variety of extremely noisy signals. We also apply our framework to geometric edge-preserving effects like feature enhancement and show how it is related to local histogram techniques. | A General Framework for Bilateral and Mean Shift Filtering | 9,962 |
This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family $h$ of rigid motions. Our extension allows the input solid to have sharp features, i.e., to be of class G0 wherein, the unit outward normal to the solid may be discontinuous. In the earlier framework, the solid to be swept was restricted to be G1, and thus this is a significant and useful extension of that work. This naturally requires a precise description of the geometry of the surface generated by the sweep of a sharp edge supported by two intersecting smooth faces. We uncover the geometry along with the related issues like parametrization, self-intersection and singularities via a novel mathematical analysis. Correct trimming of such a surface is achieved by a delicate analysis of the interplay between the cone of normals at a sharp point and its trajectory under $h$. The overall topology is explicated by a key lifting theorem which allows us to compute the adjacency relations amongst entities in the swept volume by relating them to corresponding adjacencies in the input solid. Moreover, global issues related to body-check such as orientation are efficiently resolved. Many examples from a pilot implementation illustrate the efficiency and effectiveness of our framework. | Incorporating Sharp Features in the General Solid Sweep Framework | 9,963 |
Jacobson et al. [JKSH13] hypothesized that the local coherency of the generalized winding number function could be used to correctly determine consistent facet orientations in polygon meshes. We report on an approach to consistently orienting facets in polygon meshes by minimizing the Dirichlet energy of generalized winding numbers. While the energy can be concisely formulated and efficiently computed, we found that this approach is fundamentally flawed and is unfortunately not applicable for most handmade meshes shared on popular mesh repositories such as Google 3D Warehouse. | Consistently Orienting Facets in Polygon Meshes by Minimizing the
Dirichlet Energy of Generalized Winding Numbers | 9,964 |
We present a sketch-based modeling system suitable for detail editing, based on a multilevel representation for surfaces. The main advantage of this representation allowing for the control of local (details) and global changes of the model. We used an adaptive mesh (4-8 mesh) and developed a label theory to construct a manifold structure, which is responsible for controlling local editing of the model. The overall shape and global modifications are defined by a variational implicit surface (Hermite RBF). Our system assembles the manifold structures to allow the user to add details without changing the overall shape, as well as edit the overall shape while repositioning details coherently. | DASS: Detail Aware Sketch-Based Surface Modeling | 9,965 |
Search-based texture synthesis algorithms are sensitive to the order in which texture samples are generated; different synthesis orders yield different textures. Unfortunately, most polygon rasterizers and ray tracers do not guarantee the order with which surfaces are sampled. To circumvent this problem, textures are synthesized beforehand at some maximum resolution and rendered using texture mapping. We describe a search-based texture synthesis algorithm in which samples can be generated in arbitrary order, yet the resulting texture remains identical. The key to our algorithm is a pyramidal representation in which each texture sample depends only on a fixed number of neighboring samples at each level of the pyramid. The bottom (coarsest) level of the pyramid consists of a noise image, which is small and predetermined. When a sample is requested by the renderer, all samples on which it depends are generated at once. Using this approach, samples can be generated in any order. To make the algorithm efficient, we propose storing texture samples and their dependents in a pyramidal cache. Although the first few samples are expensive to generate, there is substantial reuse, so subsequent samples cost less. Fortunately, most rendering algorithms exhibit good coherence, so cache reuse is high. | Order-Independent Texture Synthesis | 9,966 |
Background: Visualization of multi-channel microscopy data plays a vital role in biological research. With the ever-increasing resolution of modern microscopes the data set size of the scanned specimen grows steadily. On commodity hardware this size easily exceeds the available main memory and the even more limited GPU memory. Common volume rendering techniques require the entire data set to be present in the GPU memory. Existing out-of-core rendering approaches for large volume data sets either are limited to single-channel volumes, or require a computer cluster, or have long preprocessing times. Results: We introduce a ray-casting technique for rendering large volumetric multi-channel microscopy data streams on commodity hardware. The volumetric data is managed at different levels of detail by an octree structure. In contrast to previous octree-based techniques, the octree is built incrementally and therefore supports streamed microscopy data as well as data set sizes exceeding the available main memory. Furthermore, our approach allows the user to interact with the partially rendered data set at all stages of the octree construction. After a detailed description of our method, we present performance results for different multi-channel data sets with a size of up to 24 GB on a standard desktop PC. Conclusions: Our rendering technique allows biologists to visualize their scanned specimen on their standard desktop computers without high-end hardware requirements. Furthermore, the user can interact with the data set during the initial loading to explore the already loaded parts, change rendering parameters like color maps or adjust clipping planes. Thus, the time of biologists being idle is reduced. Also, streamed data can be visualized to detect and stop flawed scans early during the scan process. | Visualization of Large Volumetric Multi-Channel Microscopy Data Streams
on Standard PCs | 9,967 |
Results: We present an application that enables the quantitative analysis of multichannel 5-D (x, y, z, t, channel) and large montage confocal fluorescence microscopy images. The image sequences show stem cells together with blood vessels, enabling quantification of the dynamic behaviors of stem cells in relation to their vascular niche, with applications in developmental and cancer biology. Our application automatically segments, tracks, and lineages the image sequence data and then allows the user to view and edit the results of automated algorithms in a stereoscopic 3-D window while simultaneously viewing the stem cell lineage tree in a 2-D window. Using the GPU to store and render the image sequence data enables a hybrid computational approach. An inference-based approach utilizing user-provided edits to automatically correct related mistakes executes interactively on the system CPU while the GPU handles 3-D visualization tasks. Conclusions: By exploiting commodity computer gaming hardware, we have developed an application that can be run in the laboratory to facilitate rapid iteration through biological experiments. There is a pressing need for visualization and analysis tools for 5-D live cell image data. We combine accurate unsupervised processes with an intuitive visualization of the results. Our validation interface allows for each data set to be corrected to 100% accuracy, ensuring that downstream data analysis is accurate and verifiable. Our tool is the first to combine all of these aspects, leveraging the synergies obtained by utilizing validation information from stereo visualization to improve the low level image processing tasks. | Visualization and Correction of Automated Segmentation, Tracking and
Lineaging from 5-D Stem Cell Image Sequences | 9,968 |
Background: Because of the difficulties involved in learning and using 3D modeling and rendering software, many scientists hire programmers or animators to create models and animations. This both slows the discovery process and provides opportunities for miscommunication. Working with multiple collaborators, we developed a set of design goals for a tool that would enable them to directly construct models and animations. Results: We present SketchBio, a tool that incorporates state-of-the-art bimanual interaction and drop shadows to enable rapid construction of molecular structures and animations. It includes three novel features: crystal by example, pose-mode physics, and spring-based layout that accelerate operations common in the formation of molecular models. We present design decisions and their consequences, including cases where iterative design was required to produce effective approaches. Conclusions: The design decisions, novel features, and inclusion of state-of-the-art techniques enabled SketchBio to meet all of its design goals. These features and decisions can be incorporated into existing and new tools to improve their effectiveness | SketchBio: A Scientist's 3D Interface for Molecular Modeling and
Animation | 9,969 |
Analysis of high dimensional data is a common task. Often, small multiples are used to visualize 1 or 2 dimensions at a time, such as in a scatterplot matrix. Associating data points between different views can be difficult though, as the points are not fixed. Other times, dimensional reduction techniques are employed to summarize the whole dataset in one image, but individual dimensions are lost in this view. In this paper, we present a means of augmenting a dimensional reduction plot with isocontours to reintroduce the original dimensions. By applying this to each dimension in the original data, we create multiple views where the points are consistent, which facilitates their comparison. Our approach employs a combination of a novel, graph-based projection technique with a GPU accelerated implementation of moving least squares to interpolate space between the points. We also present evaluations of this approach both with a case study and with a user study. | A Moving Least Squares Based Approach for Contour Visualization of
Multi-Dimensional Data | 9,970 |
Blue noise sampling has proved useful for many graphics applications, but remains underexplored in high-dimensional spaces due to the difficulty of generating distributions and proving properties about them. We present a blue noise sampling method with good quality and performance across different dimensions. The method, spoke-dart sampling, shoots rays from prior samples and selects samples from these rays. It combines the advantages of two major high-dimensional sampling methods: the locality of advancing front with the dimensionality-reduction of hyperplanes, specifically line sampling. We prove that the output sampling is saturated with high probability, with bounds on distances between pairs of samples and between any domain point and its nearest sample. We demonstrate spoke-dart applications for approximate Delaunay graph construction, global optimization, and robotic motion planning. Both the blue-noise quality of the output distribution and the adaptability of the intermediate processes of our method are useful in these applications. | Spoke-Darts for High-Dimensional Blue-Noise Sampling | 9,971 |
Harmonic surface deformation is a well-known geometric modeling method that creates plausible deformations in an interactive manner. However, this method is susceptible to artifacts, in particular close to the deformation handles. These artifacts often correlate with strong gradients of the deformation energy.In this work, we propose a novel formulation of harmonic surface deformation, which incorporates a regularization of the deformation energy. To do so, we build on and extend a recently introduced generic linear regularization approach. It can be expressed as a change of norm for the linear optimization problem, i.e., the regularization is baked into the optimization. This minimizes the implementation complexity and has only a small impact on runtime. Our results show that a moderate use of regularization suppresses many deformation artifacts common to the well-known harmonic surface deformation method, without introducing new artifacts. | Regularized Harmonic Surface Deformation | 9,972 |
Continuous collision detection (CCD) and response methods are widely adopted in dynamics simulation of deformable models. They are history-based, as their success is strictly based on an assumption of a collision-free state at the start of each time interval. On the other hand, in many applications surfaces have normals defined to designate their orientation (i.e. front- and back-face), yet CCD methods are totally blind to such orientation identification (thus are orientation-free). We notice that if such information is utilized, many penetrations can be untangled. In this paper we present a history-free method for separation of two penetrating meshes, where at least one of them has clarified surface orientation. This method first computes all edge-face (E-F) intersections with discrete collision detection (DCD), and then builds a number of penetration stencils. On response, the stencil vertices are relocated into a penetration-free state, via a global displacement minimizer. Our method is very effective for handling penetration between two meshes, being it an initial configuration or in the middle of physics simulation. The major limitation is that it is not applicable to self-collision within one mesh at the time being. | History-free Collision Response for Deformable Surfaces | 9,973 |
The physical world consists of spatially varying media, such as the atmosphere and the ocean, in which light and sound propagates along non-linear trajectories. This presents a challenge to existing ray-tracing based methods, which are widely adopted to simulate propagation due to their efficiency and flexibility, but assume linear rays. We present a novel algorithm that traces analytic ray curves computed from local media gradients, and utilizes the closed-form solutions of both the intersections of the ray curves with planar surfaces, and the travel distance. By constructing an adaptive unstructured mesh, our algorithm is able to model general media profiles that vary in three dimensions with complex boundaries consisting of terrains and other scene objects such as buildings. We trace the analytic ray curves using the adaptive unstructured mesh, which considerably improves the efficiency over prior methods. We highlight the algorithm's application on simulation of sound and visual propagation in outdoor scenes. | Tracing Analytic Ray Curves for Light and Sound Propagation in
Non-linear Media | 9,974 |
The production of animation is a resource intensive process in game companies. Therefore, techniques to synthesize animations have been developed. However, these procedural techniques offer limited adaptability by animation artists. In order to solve this, a fuzzy neural network model of the animation is proposed, where the parameters can be tuned either by machine learning techniques that use motion capture data as training data or by the animation artist himself. This paper illustrates how this real time procedural animation system can be developed, taking the human gait on flat terrain and inclined surfaces as example. Currently, the parametric model is capable of synthesizing animations for various limb sizes and step sizes. | Real-time animation of human characters with fuzzy controllers | 9,975 |
We present some notes on the definition of mathematical design as well as on the methods of mathematical modeling which are used in the process of the artistic design of the environment and its components. For the first time in the field of geometric modeling, we perform an aesthetic analysis of planar Bernstein-Bezier curves from the standpoint of the laws of technical aesthetics. The shape features of the curve segments' geometry were evaluated using the following criteria: conciseness-integrity, expressiveness, proportional consistency, compositional balance, structural organization, imagery, rationality, dynamism, scale, flexibility and harmony. In the non-Russian literature, Bernstein-Bezier curves using a monotonic curvature function (i.e., a class A Bezier curve) are considered to be fair (i.e., beautiful) curves, but their aesthetic analysis has never been performed. The aesthetic analysis performed by the authors of this work means that this is no longer the case. To confirm the conclusions of the authors' research, a survey of the "aesthetic appropriateness" of certain Bernstein-Bezier curve segments was conducted among 240 children, aged 14-17. The results of this survey have shown themselves to be in full accordance with the authors' results. | A mathematical design and evaluation of Bernstein-Bezier curves' shape
features using the laws of technical aesthetics | 9,976 |
Finding nearly accurate distance between two or more nearly intersecting three-dimensional (3D) objects is vital especially for collision determination such as in virtual surgeon simulation and real-time car crash simulation. Instead of performing broad phase collision detection, we need to check for accuracy of detection by running narrow phase collision detection. One of the important elements for narrow phase collision detection is to determine the precise distance between two or more nearly intersecting objects or polygons in order to prepare the area for potential colliding. Distance computation plays important roles in determine the exact point of contact between two or more nearly intersecting polygons where the preparation for collision detection is determined at the earlier stage. In this paper, we describes our current works of determining the distance between objects using dynamic pivot point that will be used as reference point to reduce the complexity searching for potential point of contacts. By using Axis-Aligned Bounding Box for each polygon, we calculate a dynamic pivot point that will become our reference point to determine the potential candidates for distance computation. The test our finding distance will be simplified by using our method instead of performing unneeded operations. Our method provides faster solution than the previous method where it helps to determine the point of contact efficiently and faster than the other method. | Efficient Distance Computation Algorithm between Nearly Intersected
Objects Using Dynamic Pivot Point in Virtual Environment Application | 9,977 |
One of the most efficient ways of generating goal-directed walking motions is synthesising the final motion based on footprints. Nevertheless, current implementations have not examined the generation of continuous motion based on footprints, where different behaviours can be generated automatically. Therefore, in this paper a flexible approach for footprint-driven locomotion composition is presented. The presented solution is based on the ability to generate footprint-driven locomotion, with flexible features like jumping, running, and stair stepping. In addition, the presented system examines the ability of generating the desired motion of the character based on predefined footprint patterns that determine which behaviour should be performed. Finally, it is examined the generation of transition patterns based on the velocity of the root and the number of footsteps required to achieve the target behaviour smoothly and naturally. | Footprint-Driven Locomotion Composition | 9,978 |
As humans, we regularly associate shape of an object with its built material. In the context of geometric modeling, however, this interrelation between form and material is rarely explored. In this work, we propose a novel data-driven reforming (i.e., reshaping) algorithm that adapts an input multi-component model for a target fabrication material. The algorithm adapts both the part geometry and the inter-part topology of the input shape to better align with material specific fabrication requirements. As output, we produce the reshaped model along with respective part dimensions and inter-part junction specifications. We evaluate our algorithm on a range of man-made models and demonstrate non-trivial model reshaping examples focusing only on metal and wooden materials. We also appraise the output of our algorithm using a user study. | Mesh2Fab: Reforming Shapes for Material-specific Fabrication | 9,979 |
Being able to reverse engineer from point cloud data to obtain 3D models is important in modeling. As our main contribution, we present a new method to obtain a tensor product B-spline representation from point cloud data by fitting surfaces to appropriately segmented data. By blending multiple local fits our method is more efficient than existing techniques, with the ability to deal with more detail by efficiently introducing a high number of knots. Further point cloud data obtained by digitizing 3D data, typically presents many associated complications like noise and missing data. As our second contribution, we propose an end-to-end framework for smoothing, hole filling, parameterization, knot selection and B-spline fitting that addresses these issues, works robustly with large irregularly shaped data containing holes and is straightforward to implement. | Reverse Engineering Point Clouds to Fit Tensor Product B-Spline Surfaces
by Blending Local Fits | 9,980 |
This paper presents an application of photogrammetry on ceramic fragments from two excavation sites located north-west of France. The restitution by photogrammetry of these different fragments allowed reconstructions of the potteries in their original state or at least to get to as close as possible. We used the 3D reconstructions to compute some metrics and to generate a presentation support by using a 3D printer. This work is based on affordable tools and illustrates how 3D technologies can be quite easily integrated in archaeology process with limited financial resources. 1. INTRODUCTION Today, photogrammetry and 3D modelling are an integral part of the methods used in archeology and heritage management. They provide answers to scientific needs in the fields of conservation, preservation, restoration and mediation of architectural, archaeological and cultural heritage [2] [6] [7] [9]. Photogrammetry on ceramic fragments was one of the first applications contemporary of the development of this technique applied in the archaeological community [3]. More recently and due to its democratization, it was applied more generally to artifacts [5]. Finally joined today by the rise of 3D printing [8] [10], it can restore fragmented artifacts [1] [12]. These examples target one or several particular objects and use different types of equipment that can be expensive. These aspects can put off uninitiated archaeologists. So it would be appropriate to see if these techniques could be generalized to a whole class of geometrically simple and common artifacts, such as ceramics. From these observations, associated to ceramics specialists with fragments of broken ceramics, we aimed at arranging different tools and methods, including photogrammetry, to explore opportunities for a cheap and attainable reconstruction methodology and its possible applications. Our first objective was to establish a protocol for scanning fragments with photogrammetry, and for reconstruction of original ceramics. We used the digital reconstitutions of the ceramics we got following our process to calculate some metrics and to design and 3D print a display for the remaining fragments of one pottery. | Ceramics Fragments Digitization by Photogrammetry, Reconstructions and
Applications | 9,981 |
In this paper, we present a novel approach to the problem of merging of B\'ezier curves with respect to the $L_2$-norm. We give illustrative examples to show that the solution of the conventional merging problem may not be suitable for further modification and applications. As in the case of the degree reduction problem, we apply the so-called restricted area approach -- proposed recently in (P. Gospodarczyk, Computer-Aided Design 62 (2015), 143--151) -- to avoid certain defects and make the resulting curve more useful. A method of solving the new problem is based on box-constrained quadratic programming approach. | Merging of Bézier curves with box constraints | 9,982 |
Halo is one of the most important basic elements in cosmology simulation, which merges from small clumps to ever larger objects. The processes of the birth and merging of the halos play a fundamental role in studying the evolution of large scale cosmological structures. In this paper, a visual analysis system is developed to interactively identify and explore the evolution histories of thousands of halos. In this system, an intelligent structure-aware selection method in What You See Is What You Get manner is designed to efficiently define the interesting region in 3D space with 2D hand-drawn lasso input. Then the exact information of halos within this 3D region is identified by data mining in the merger tree files. To avoid visual clutter, all the halos are projected in 2D space with a MDS method. Through the linked view of 3D View and 2D graph, Users can interactively explore these halos, including the tracing path and evolution history tree. | Interactive Visual Exploration of Halos in Large Scale Cosmology
Simulation | 9,983 |
We present a new approach to the problem of $G^{k,l}$-constrained ($k,l \leq 3$) multi-degree reduction of B\'{e}zier curves with respect to the least squares norm. First, to minimize the least squares error, we consider two methods of determining the values of geometric continuity parameters. One of them is based on quadratic and nonlinear programming, while the other uses some simplifying assumptions and solves a system of linear equations. Next, for prescribed values of these parameters, we obtain control points of the multi-degree reduced curve, using the properties of constrained dual Bernstein basis polynomials. Assuming that the input and output curves are of degree $n$ and $m$, respectively, we determine these points with the complexity $O(mn)$, which is significantly less than the cost of other known methods. Finally, we give several examples to demonstrate the effectiveness of our algorithms. | $G^{k,l}$-constrained multi-degree reduction of Bézier curves | 9,984 |
This paper provides a tutorial and survey for a specific kind of illustrative visualization technique: feature lines. We examine different feature line methods. For this, we provide the differential geometry behind these concepts and adapt this mathematical field to the discrete differential geometry. All discrete differential geometry terms are explained for triangulated surface meshes. These utilities serve as basis for the feature line methods. We provide the reader with all knowledge to re-implement every feature line method. Furthermore, we summarize the methods and suggest a guideline for which kind of surface which feature line algorithm is best suited. Our work is motivated by, but not restricted to, medical and biological surface models. | Feature Lines for Illustrating Medical Surface Models: Mathematical
Background and Survey | 9,985 |
Marching surfaces is a method for isosurface extraction and approximation based on a $G^1$ multi-sided patch interpolation scheme. Given a 3D grid of scalar values, an underlying curve network is formed using second order information and cubic Hermite splines. Circular arc fitting defines the tangent vectors for the Hermite curves at specified isovalues. Once the boundary curve network is formed, a loop of curves is determined for each grid cell and then interpolated with multi-sided surface patches, which are $G^1$ continuous at the joins. The data economy of the method and its continuity preserving properties provide an effective compression scheme, ideal for indirect volume rendering on mobile devices, or collaborating on the Internet, while enhancing visual fidelity. The use of multi-sided patches enables a more natural way to approximate the isosurfaces than using a fixed number of sides or polygons as is proposed in the literature. This assertion is supported with comparisons to the traditional Marching Cubes algorithm and other $G^1$ methods. | Marching Surfaces: Isosurface Approximation using G$^1$ Multi-Sided
Surfaces | 9,986 |
When animation of a humanoid figure is to be generated at run-time, instead of by replaying pre-composed motion clips, some method is required of specifying the avatar's movements in a form from which the required motion data can be automatically generated. This form must be of a more abstract nature than raw motion data: ideally, it should be independent of the particular avatar's proportions, and both writable by hand and suitable for automatic generation from higher-level descriptions of the required actions. We describe here the development and implementation of such a scripting language for the particular area of sign languages of the deaf, called SiGML (Signing Gesture Markup Language), based on the existing HamNoSys notation for sign languages. We conclude by suggesting how this work may be extended to more general animation for interactive virtual reality applications. | Avatar-independent scripting for real-time gesture animation | 9,987 |
We present a multi-scale approach to sketch-based shape retrieval. It is based on a novel multi-scale shape descriptor called Pyramidof- Parts, which encodes the features and spatial relationship of the semantic parts of query sketches. The same descriptor can also be used to represent 2D projected views of 3D shapes, allowing effective matching of query sketches with 3D shapes across multiple scales. Experimental results show that the proposed method outperforms the state-of-the-art method, whether the sketch segmentation information is obtained manually or automatically by considering each stroke as a semantic part. | Sketch-based Shape Retrieval using Pyramid-of-Parts | 9,988 |
The midpoint method or technique is a measurement and as each measurement it has a tolerance, but worst of all it can be invalid, called Out-of-Control or OoC. The core of all midpoint methods is the accurate measurement of the difference of the squared distances of two points to the polar of their midpoint with respect to the conic. When this measurement is valid, it also measures the difference of the squared distances of these points to the conic, although it may be inaccurate, called Out-of-Accuracy or OoA. The primary condition is the necessary and sufficient condition that a measurement is valid. It is comletely new and it can be checked ultra fast and before the actual measurement starts. Modeling an incremental algorithm, shows that the curve must be subdivided into piecewise monotonic sections, the start point must be optimal, and it explains that the 2D-incremental method can find, locally, the global Least Square Distance. Locally means that there are at most three candidate points for a given monotonic direction; therefore the 2D-midpoint method has, locally, at most three measurements. When all the possible measurements are invalid, the midpoint method cannot be applied, and in that case the ultra fast OoC-rule selects the candidate point. This guarantees, for the first time, a 100% stable, ultra-fast, berserkless midpoint algorithm, which can be easily transformed to hardware. | Relative Squared Distances to a Conic Berserkless 8-Connected Midpoint
Algorithm | 9,989 |
Character rigging is a process of endowing a character with a set of custom manipulators and controls making it easy to animate by the animators. These controls consist of simple joints, handles, or even separate character selection windows.This research paper present an automated rigging system for quadruped characters with custom controls and manipulators for animation.The full character rigging mechanism is procedurally driven based on various principles and requirements used by the riggers and animators. The automation is achieved initially by creating widgets according to the character type. These widgets then can be customized by the rigger according to the character shape, height and proportion. Then joint locations for each body parts are calculated and widgets are replaced programmatically.Finally a complete and fully operational procedurally generated character control rig is created and attached with the underlying skeletal joints. The functionality and feasibility of the rig was analyzed from various source of actual character motion and a requirements criterion was met. The final rigged character provides an efficient and easy to manipulate control rig with no lagging and at high frame rate. | Analysis of Design Principles and Requirements for Procedural Rigging of
Bipeds and Quadrupeds Characters with Custom Manipulators for Animation | 9,990 |
Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing. | Data-Driven Shape Analysis and Processing | 9,991 |
The exploding growth of digital data in the information era and its immeasurable potential value has called for different types of data-driven techniques to exploit its value for further applications. Information visualization and data mining are two research field with such goal. While the two communities advocates different approaches of problem solving, the vision of combining the sophisticated algorithmic techniques from data mining as well as the intuitivity and interactivity of information visualization is tempting. In this paper, we attempt to survey recent researches and real world systems integrating the wisdom in two fields towards more effective and efficient data analytics. More specifically, we study the intersection from a data mining point of view, explore how information visualization can be used to complement and improve different stages of data mining through established theories for optimized visual presentation as well as practical toolsets for rapid development. We organize the survey by identifying three main stages of typical process of data mining, the preliminary analysis of data, the model construction, as well as the model evaluation, and study how each stage can benefit from information visualization. | On Integrating Information Visualization Techniques into Data Mining: A
Review | 9,992 |
We present a flexible illustrative line style model for the visualization of streamline data. Our model partitions view-oriented line strips into parallel bands whose basic visual properties can be controlled independently. We thus extend previous line stylization techniques specifically for visualization purposes by allowing the parametrization of these bands based on the local line data attributes. Moreover, our approach supports emphasis and abstraction by introducing line style transfer functions that map local line attribute values to complete line styles. With a flexible GPU implementation of this line style model we enable the interactive exploration of visual representations of streamlines. We demonstrate the effectiveness of our model by applying it to 3D flow field datasets. | Interactive Illustrative Line Styles and Line Style Transfer Functions
for Flow Visualization | 9,993 |
We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function $f$ on that domain; suitable functions have exactly one critical point, a maximum, in the domain, and the gradient of the function on the boundary points inward. Because every integral curve intersects the boundary exactly once, Integral Curve Coordinates provide a natural bijective mapping from one domain to another given a bijection of the boundary. Our approach can be applied to shapes in any dimension, provided that the boundary of the shape (or cage) is topologically equivalent to an $n$-sphere. We present a simple algorithm for generating a suitable function space for $f$ in any dimension. We demonstrate our approach in 2D and describe a practical (simple and robust) algorithm for tracing integral curves on a (piecewise-linear) triangulated regular grid. | Bijective Deformations in $\mathbb{R}^n$ via Integral Curve Coordinates | 9,994 |
In this paper, we use the blending functions of Lupa\c{s} type (rational) $(p,q)$-Bernstein operators based on $(p,q)$-integers for construction of Lupa\c{s} $(p,q)$-B$\acute{e}$zier curves (rational curves) and surfaces (rational surfaces) with shape parameters. We study the nature of degree elevation and degree reduction for Lupa\c{s} $(p,q)$-B$\acute{e}$zier Bernstein functions. Parametric curves are represented using Lupa\c{s} $(p,q)$-Bernstein basis. We introduce affine de Casteljau algorithm for Lupa\c{s} type $(p,q)$-Bernstein B$\acute{e}$zier curves. The new curves have some properties similar to $q$-B$\acute{e}$zier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain $(u, v) \in [0, 1] \times [0, 1] $ depending on four parameters. We also study the de Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain. We get $q$-B$\acute{e}$zier surfaces for $(u, v) \in [0, 1] \times [0, 1] $ when we set the parameter $p_1=p_2=1.$ In comparison to $q$-B$\acute{e}$zier curves and surfaces based on Lupa\c{s} $q$-Bernstein polynomials, our generalization gives us more flexibility in controlling the shapes of curves and surfaces. We also show that the $(p,q)$-analogue of Lupa\c{s} Bernstein operator sequence $L^{n}_{p_n,q_n}(f,x)$ converges uniformly to $f(x)\in C[0,1]$ if and only if $0<q_n<p_n\leq1$ such that $\lim\limits_{n\to\infty} q_n=1, $ $\lim\limits_{n\to\infty} p_n=1$ and $\lim\limits_{n\to\infty}p_n^n=a,$ $\lim\limits_{n\to\infty}q_n^n=b$ with $0<a,b\leq1.$ On the other hand, for any $p>0$ fixed and $p \neq 1,$ the sequence $L^{n}_{p,q}(f,x)$ converges uniformly to $f(x)~ \in C[0,1]$ if and only if $f(x)=ax+b$ for some $a, b \in \mathbb{R}.$ | B$\acute{e}$zier curves based on Lupaş $(p,q)$-analogue of Bernstein
polynomials in CAGD | 9,995 |
Recent work on octree-based finite-element systems has developed a multigrid solver for Poisson equations on meshes. While the idea of defining a regularly indexed function space has been successfully used in a number of applications, it has also been noted that the richness of the function space is limited because the function values can be coupled across locally disconnected regions. In this work, we show how to enrich the function space by introducing functions that resolve the coupling while still preserving the nesting hierarchy that supports multigrid. A spectral analysis reveals the superior quality of the resulting Laplace-Beltrami operator and applications to surface flow demonstrate that our new solver more efficiently converges to the correct solution. | A Connectivity-Aware Multi-level Finite-Element System for Solving
Laplace-Beltrami Equations | 9,996 |
We present in this paper a new family of implicit function for synthesizing a wide variety of 3D surfaces. The basis of this family consists of the usual functions that are: the function rectangular pulses, the function saw-tooth pulses, the function of triangular pulses, the staircase function and the power function. By combining these common functions, named constituent functions, in one implicit function and by varying some parameters of this function we can synthesize a wide variety of 3D surfaces with the possibility to set their deformations. | A wide diversity of 3D surfaces Generator using a new implicit function | 9,997 |
Ray tracing on GPUs is becoming quite common these days. There are many publicly available documents on how to implement basic ray tracing on GPUs for spheres and implicit surfaces. We even have some general frameworks for ray tracing on GPUs. We however hardly find details on how to implement more complex ray tracing algorithms themselves that are commonly used for photorealistic rendering. This paper explains an implementation of a stand-alone rendering system on GPUs which supports the bounding volume hierarchy and stochastic progressive photon mapping. The key characteristic of the system is that it uses only GLSL shaders without relying on any platform dependent feature. The system can thus run on many platforms that support OpenGL, making photorealistic rendering on GPUs widely accessible. This paper also sketches practical ideas for stackless traversal and pseudorandom number generation which both fit well with the limited system configuration. | Implementing a Photorealistic Rendering System using GLSL | 9,998 |
Information Visualization techniques are built on a context with many factors related to both vision and cognition, making it difficult to draw a clear picture of how data visually turns into comprehension. In the intent of promoting a better picture, here, we survey concepts on vision, cognition, and Information Visualization organized in a theorization named Visual Expression Process. Our theorization organizes the basis of visualization techniques with a reduced level of complexity; still, it is complete enough to foster discussions related to design and analytical tasks. Our work introduces the following contributions: (1) a Theoretical compilation of vision, cognition, and Information Visualization; (2) Discussions supported by vast literature; and (3) Reflections on visual-cognitive aspects concerning use and design. We expect our contributions will provide further clarification about how users and designers think about InfoVis, leveraging the potential of systems and techniques. | A survey on Information Visualization in light of Vision and Cognitive
sciences | 9,999 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.