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Signed distance fields (SDFs) are a form of surface representation widely used in computer graphics, having applications in rendering, collision detection and modelling. In interactive media such as games, high-resolution SDFs are commonly produced offline and subsequently loaded into the application, representing rigid meshes only. This work develops a novel technique that combines jump flooding and ray tracing to generate approximate SDFs in real-time. Our approach can produce relatively accurate scene representation for rendering soft shadows while maintaining interactive frame rates. We extend our previous work with details on the design and implementation as well as visual quality and performance evaluation of the technique. | RTSDF: Real-time Signed Distance Fields for Soft Shadow Approximation in
Games | 10,800 |
We propose a novel framework for computing the medial axis transform of 3D shapes while preserving their medial features via restricted power diagram (RPD). Medial features, including external features such as the sharp edges and corners of the input mesh surface and internal features such as the seams and junctions of medial axis, are important shape descriptors both topologically and geometrically. However, existing medial axis approximation methods fail to capture and preserve them due to the fundamentally under-sampling in the vicinity of medial features, and the difficulty to build their correct connections. In this paper we use the RPD of medial spheres and its affiliated structures to help solve these challenges. The dual structure of RPD provides the connectivity of medial spheres. The surface restricted power cell (RPC) of each medial sphere provides the tangential surface regions that these spheres have contact with. The connected components (CC) of surface RPC give us the classification of each sphere, to be on a medial sheet, a seam, or a junction. They allow us to detect insufficient sphere sampling around medial features and develop necessary conditions to preserve them. Using this RPD-based framework, we are able to construct high quality medial meshes with features preserved. Compared with existing sampling-based or voxel-based methods, our method is the first one that can preserve not only external features but also internal features of medial axes. | Computing Medial Axis Transform with Feature Preservation via Restricted
Power Diagram | 10,801 |
Parametric Bidirectional Scattering Distribution Functions (BSDFs) are pervasively used because of their flexibility to represent a large variety of material appearances by simply tuning the parameters. While efficient evaluation of parametric BSDFs has been well-studied, high-quality importance sampling techniques for parametric BSDFs are still scarce. Existing sampling strategies either heavily rely on approximations, resulting in high variance, or solely perform sampling on a portion of the whole BSDF slice. Moreover, many of the sampling approaches are specifically paired with certain types of BSDFs. In this paper, we seek an efficient and general way for importance sampling parametric BSDFs. We notice that the nature of importance sampling is the mapping between a uniform distribution and the target distribution. Specifically, when BSDF parameters are given, the mapping that performs importance sampling on a BSDF slice can be simply recorded as a 2D image that we name as importance map. Following this observation, we accurately precompute the importance maps using a mathematical tool named optimal transport. Then we propose a lightweight neural network to efficiently compress the precomputed importance maps. In this way, we have brought parametric BSDF important sampling to the precomputation stage, avoiding heavy runtime computation. Since this process is similar to light baking where a set of images are precomputed, we name our method importance baking. Together with a BSDF evaluation network and a PDF (probability density function) query network, our method enables full multiple importance sampling (MIS) without any revision to the rendering pipeline. Our method essentially performs perfect importance sampling. Compared with previous methods, we demonstrate reduced noise levels on rendering results with a rich set of appearances. | BSDF Importance Baking: A Lightweight Neural Solution to Importance
Sampling General Parametric BSDFs | 10,802 |
Procedural terrain generation is the process of generating a digital representation of terrain using a computer program or procedure, with little to no human guidance. This paper proposes a procedural terrain generation algorithm based on a graph representation of fluvial erosion that offers several novel improvements over existing algorithms. Namely, the use of a height constraint map with two types of locally defined constraint strengths; the ability to specify a realistic erosion strength via level of rainfall; and the ability to carve realistic gorges. These novelties allow it to generate more varied and realistic terrain by integrating additional parameters and simulation processes, while being faster and offering more flexibility and ease of use to terrain designers due to the nature and intuitiveness of these new parameters and processes. This paper additionally reviews some common metrics used to evaluate terrain generators, and suggests a completely new one that contributes to a more holistic evaluation. | Visually Improved Erosion Algorithm for the Procedural Generation of
Tile-based Terrain | 10,803 |
Classically, rasterization techniques are performed for real-time rendering to meet the constraint of interactive frame rates. However, such techniques do not produce realistic results as compared to ray tracing approaches. Hence, hybrid rendering has emerged to improve the graphics fidelity of rasterization with ray tracing in real-time. We explore the approach of distributed rendering in incorporating real-time hybrid rendering into metaverse experiences for immersive graphics. In standalone extended reality (XR) devices, such ray tracing-enabled graphics is only feasible through pure cloud-based remote rendering systems that rely on low-latency networks to transmit real-time ray-traced data in response to interactive user input. Under high network latency conditions, remote rendering might not be able to maintain interactive frame rates for the client, adversely affecting the user experience. We adopt hybrid rendering via a distributed rendering approach by integrating ray tracing on powerful remote hardware with raster-based rendering on user access devices. With this hybrid approach, our technique can help standalone XR devices achieve ray tracing-incorporated graphics and maintain interactive frame rates even under high-latency conditions. | DHR: Distributed Hybrid Rendering for Metaverse Experiences | 10,804 |
Monte Carlo rendering algorithms often utilize correlations between pixels to improve efficiency and enhance image quality. For real-time applications in particular, repeated reservoir resampling offers a powerful framework to reuse samples both spatially in an image and temporally across multiple frames. While such techniques achieve equal-error up to 100 times faster for real-time direct lighting and global illumination, they are still far from optimal. For instance, unchecked spatiotemporal resampling often introduces noticeable correlation artifacts, while reservoirs holding more than one sample suffer from impoverishment in the form of duplicate samples. We demonstrate how interleaving Markov Chain Monte Carlo (MCMC) mutations with reservoir resampling helps alleviate these issues, especially in scenes with glossy materials and difficult-to-sample lighting. Moreover, our approach does not introduce any bias, and in practice we find considerable improvement in image quality with just a single mutation per reservoir sample in each frame. | Decorrelating ReSTIR Samplers via MCMC Mutations | 10,805 |
We present a realistic, robust, and computationally fast method of solving highly non-linear inverse kinematic problems with angular limits using the Gauss-Seidel iterative method. Our method is ideally suited towards character based interactive applications such as games. To achieve interactive simulation speeds, numerous acceleration techniques are employed, including spatial coherent starting approximations and projected angular clamping. The method has been tested on a continuous range of poses for animated articulated characters and successfully performed in all cases and produced good visual outcomes. | Real-Time Character Inverse Kinematics using the Gauss-Seidel Iterative
Approximation Method | 10,806 |
We propose an approach for generating crochet instructions (patterns) from an input 3D model. We focus on Amigurumi, which are knitted stuffed toys. Given a closed triangle mesh, and a single point specified by the user, we generate crochet instructions, which when knitted and stuffed result in a toy similar to the input geometry. Our approach relies on constructing the geometry and connectivity of a Crochet Graph, which is then translated into a crochet pattern. We segment the shape automatically into chrochetable components, which are connected using the join-as-you-go method, requiring no additional sewing. We demonstrate that our method is applicable to a large variety of shapes and geometries, and yields easily crochetable patterns. | AmiGo: Computational Design of Amigurumi Crochet Patterns | 10,807 |
Virtual Reality systems provide many opportunities for scientific research and consumer enjoyment; however, they are more demanding than traditional desktop applications and require a wired connection to desktops in order to enjoy maximum quality. Standalone options that are not connected to computers exist, yet they are powered by mobile GPUs, which provide limited power in comparison to desktop rendering. Alternative approaches to improve performance on mobile devices use server rendering to render frames for a client and treat the client largely as a display device. However, current streaming solutions largely suffer from high end-to-end latency due to processing and networking requirements, as well as underutilization of the client. We propose a networked split-rendering approach to achieve faster end-to-end image presentation rates on the mobile device while preserving image quality. Our proposed solution uses an image-space division of labour between the server-side GPU and the mobile client, and achieves a significantly faster runtime than client-only rendering and than using a thin-client approach, which is mostly reliant on the server. | An Image-Space Split-Rendering Approach to Accelerate Low-Powered
Virtual Reality | 10,808 |
We present a method for learning neural representations of flow maps from time-varying vector field data. The flow map is pervasive within the area of flow visualization, as it is foundational to numerous visualization techniques, e.g. integral curve computation for pathlines or streaklines, as well as computing separation/attraction structures within the flow field. Yet bottlenecks in flow map computation, namely the numerical integration of vector fields, can easily inhibit their use within interactive visualization settings. In response, in our work we seek neural representations of flow maps that are efficient to evaluate, while remaining scalable to optimize, both in computation cost and data requirements. A key aspect of our approach is that we can frame the process of representation learning not in optimizing for samples of the flow map, but rather, a self-consistency criterion on flow map derivatives that eliminates the need for flow map samples, and thus numerical integration, altogether. Central to realizing this is a novel neural network design for flow maps, coupled with an optimization scheme, wherein our representation only requires the time-varying vector field for learning, encoded as instantaneous velocity. We show the benefits of our method over prior works in terms of accuracy and efficiency across a range of 2D and 3D time-varying vector fields, while showing how our neural representation of flow maps can benefit unsteady flow visualization techniques such as streaklines, and the finite-time Lyapunov exponent. | Integration-free Learning of Flow Maps | 10,809 |
Step-and-project is a popular way to simulate non-penetrated deformable bodies in physically-based animation. First integrating the system in time regardless of contacts and post resolving potential intersections practically strike a good balance between plausibility and efficiency. However, existing methods could be defective and unsafe when the time step is large, taking risks of failures or demands of repetitive collision testing and resolving that severely degrade performance. In this paper, we propose a novel two-way method for fast and reliable continuous collision handling. Our method launches the optimization at both ends of the intermediate time-integrated state and the previous intersection-free state, progressively generating a piecewise-linear path and finally reaching a feasible solution for the next time step. Technically, our method interleaves between a forward step and a backward step at a low cost, until the result is conditionally converged. Due to a set of unified volume-based contact constraints, our method can flexibly and reliably handle a variety of codimensional deformable bodies, including volumetric bodies, cloth, hair and sand. The experiments show that our method is safe, robust, physically faithful and numerically efficient, especially suitable for large deformations or large time steps. | Fast GPU-Based Two-Way Continuous Collision Handling | 10,810 |
We propose a multi-class point optimization formulation based on continuous Wasserstein barycenters. Our formulation is designed to handle hundreds to thousands of optimization objectives and comes with a practical optimization scheme. We demonstrate the effectiveness of our framework on various sampling applications like stippling, object placement, and Monte-Carlo integration. We a derive multi-class error bound for perceptual rendering error which can be minimized using our optimization. We provide source code at https://github.com/iribis/filtered-sliced-optimal-transport. | Scalable multi-class sampling via filtered sliced optimal transport | 10,811 |
The request for high-quality solutions continually grows in a world where more and more tasks are executed through computers. This also counts for fields such as engineering, computer graphics, etc., which use meshes to solve their problems. A mesh is a combination of some elementary elements, for which hexahedral elements are a good choice thanks to their superior numerical features. The solutions reached using these meshes depend on the quality of the elements making up the mesh. The problem is that these individual elements can take on a shape which prevents accurate computations. Such elements are considered to be invalid. To allow users to get accurate results, the shape of these elements must therefore be changed to be considered valid. In this work, we combine the results of two papers to scan a mesh, identify possible invalid elements and then change the shape of these elements to make them valid. With this combination, we end up with a working algorithm. But there is room for improvement, which is why we introduce multiple improvements to speed up the algorithm as well as make it more robust. We then test our algorithm and compare it to another approach. This work, therefore, introduces a new efficient and robust approach to untangle invalid meshes. | Up to 58 Tets/Hex to untangle Hex meshes | 10,812 |
Ultrasound-guided spine interventions, such as lumbar-puncture procedures, often suffer from the reduced visibility of key anatomical features such as the inter-spinous process space, due to the complex shape of the self-shadowing vertebra. Therefore, we propose to design a wearable 3D ultrasound device capable of imaging the vertebra from multiple insonification angles to improve the 3D bone surface visualization for interventional guidance. In this work, we aim to equip the imaging platform with a reconstruction algorithm taking advantage of the redundant ultrasound beam angles. Specifically, we try to weight each beam's contribution for the same reconstructed voxel during the reconstruction process based on its incidence angle to the estimated bone surface. To validate our approach, we acquired multi-angle ultrasound image data on a spine phantom with a tracked phased array transducer. The results show that with the proposed method the bone surface contrast can be significantly enhanced, providing clearer visual guidance for the clinician to perform spine intervention. | Insonification Angle-based Ultrasound Volume Reconstruction for Spine
Intervention | 10,813 |
We propose a computational approach to find a minimal set of 360-degree camera placements that together sufficiently cover an indoor environment for the building documentation problem in the architecture, engineering, and construction (AEC) industries. Our approach, based on a simple integer programming (IP) problem formulation, solves very efficiently and globally optimally. We conducted a study of using panoramas to capture the appearances of a real-world indoor environment, in which we found that our computed solutions are better than human solutions decided by both non-professional and professional users. | Optimizing Placements of 360-degree Panoramic Cameras in Indoor
Environments by Integer Programming | 10,814 |
Computational methods to compute similarities between floor plans can help architects explore floor plans in large datasets to avoid duplication of designs and to search for existing plans that satisfy their needs. Recently, LayoutGMN delivered state-of-the-art performance for computing similarity scores between floor plans. However, the high computational costs of LayoutGMN make it unsuitable for the aforementioned applications. In this paper, we significantly reduced the times needed to query results computed by LayoutGMN by projecting the floor plans into a common low-dimensional (e.g., three) data space. The projection is done by optimizing for coordinates of floor plans with Euclidean distances mimicking their similarity scores originally calculated by LayoutGMN. Quantitative and qualitative evaluations show that our results match the distributions of the original LayoutGMN similarity scores. User study shows that our similarity results largely match human expectations. | Floor Plan Exploration Framework Based on Similarity Distances | 10,815 |
Monte Carlo integration is typically interpreted as an estimator of the expected value using stochastic samples. There exists an alternative interpretation in calculus where Monte Carlo integration can be seen as estimating a \emph{constant} function -- from the stochastic evaluations of the integrand -- that integrates to the original integral. The integral mean value theorem states that this \emph{constant} function should be the mean (or expectation) of the integrand. Since both interpretations result in the same estimator, little attention has been devoted to the calculus-oriented interpretation. We show that the calculus-oriented interpretation actually implies the possibility of using a more \emph{complex} function than a \emph{constant} one to construct a more efficient estimator for Monte Carlo integration. We build a new estimator based on this interpretation and relate our estimator to control variates with least-squares regression on the stochastic samples of the integrand. Unlike prior work, our resulting estimator is \emph{provably} better than or equal to the conventional Monte Carlo estimator. To demonstrate the strength of our approach, we introduce a practical estimator that can act as a simple drop-in replacement for conventional Monte Carlo integration. We experimentally validate our framework on various light transport integrals. The code is available at \url{https://github.com/iribis/regressionmc}. | Regression-based Monte Carlo Integration | 10,816 |
Recently, virtual reality (VR) technology has been widely used in medical, military, manufacturing, entertainment, and other fields. These applications must simulate different complex material surfaces, various dynamic objects, and complex physical phenomena, increasing the complexity of VR scenes. Current computing devices cannot efficiently render these complex scenes in real time, and delayed rendering makes the content observed by the user inconsistent with the user's interaction, causing discomfort. Foveated rendering is a promising technique that can accelerate rendering. It takes advantage of human eyes' inherent features and renders different regions with different qualities without sacrificing perceived visual quality. Foveated rendering research has a history of 31 years and is mainly focused on solving the following three problems. The first is to apply perceptual models of the human visual system into foveated rendering. The second is to render the image with different qualities according to foveation principles. The third is to integrate foveated rendering into existing rendering paradigms to improve rendering performance. In this survey, we review foveated rendering research from 1990 to 2021. We first revisit the visual perceptual models related to foveated rendering. Subsequently, we propose a new foveated rendering taxonomy and then classify and review the research on this basis. Finally, we discuss potential opportunities and open questions in the foveated rendering field. We anticipate that this survey will provide new researchers with a high-level overview of the state of the art in this field, furnish experts with up-to-date information and offer ideas alongside a framework to VR display software and hardware designers and engineers. | Foveated Rendering: a State-of-the-Art Survey | 10,817 |
Adaptive Mesh Refinement (AMR) is becoming a prevalent data representation for scientific visualization. Resulting from large fluid mechanics simulations, the data is usually cell centric, imposing a number of challenges for high quality reconstruction at sample positions. While recent work has concentrated on real-time volume and isosurface rendering on GPUs, the rendering methods used still focus on simple lighting models without scattering events and global illumination. As in other areas of rendering, key to real-time performance are acceleration data structures; in this work we analyze the major bottlenecks of data structures that were originally optimized for camera/primary ray traversal when used with the incoherent ray tracing workload of a volumetric path tracer, and propose strategies to overcome the challenges coming with this. | Beyond ExaBricks: GPU Volume Path Tracing of AMR Data | 10,818 |
Dynamics simulation with frictional contacts is important for a wide range of applications, from cloth simulation to object manipulation. Recent methods using smoothed lagged friction forces have enabled robust and differentiable simulation of elastodynamics with friction. However, the resulting frictional behavior can be inaccurate and may not converge to analytic solutions. Here we evaluate the accuracy of lagged friction models in comparison with implicit frictional contact systems. We show that major inaccuracies near the stick-slip threshold in such systems are caused by lagging of friction forces rather than by smoothing the Coulomb friction curve. Furthermore, we demonstrate how systems involving implicit or lagged friction can be correctly used with higher-order time integration and highlight limitations in earlier attempts. We demonstrate how to exploit forward-mode automatic differentiation to simplify and, in some cases, improve the performance of the inexact Newton method. Finally, we show that other complex phenomena can also be simulated effectively while maintaining smoothness of the entire system. We extend our method to exhibit stick-slip frictional behavior and preserve volume on compressible and nearly-incompressible media using soft constraints. | Implicit frictional dynamics with soft constraints | 10,819 |
The fairing curves and surfaces are used extensively in geometric design, modeling, and industrial manufacturing. However, the majority of conventional fairing approaches, which lack sufficient parameters to improve fairness, are based on energy minimization problems. In this study, we develop a novel progressive-iterative approximation method for fairing curve and surface generation (fairing-PIA). Fairing-PIA is an iteration method that can generate a series of curves (surfaces) by adjusting the control points of B-spline curves (surfaces). In fairing-PIA, each control point is endowed with an individual weight. Thus, the fairing-PIA has many parameters to optimize the shapes of curves and surfaces. Not only a fairing curve (surface) can be generated globally through fairing-PIA, but also the curve (surface) can be improved locally. Moreover, we prove the convergence of the developed fairing-PIA and show that the conventional energy minimization fairing model is a special case of fairing-PIA. Finally, numerical examples indicate that the proposed method is effective and efficient. | Fairing-PIA: Progressive iterative approximation for fairing curve and
surface generation | 10,820 |
Hardware-based triangle rasterization is still the prevalent method for generating images at real-time interactive frame rates. With the availability of a programmable graphics pipeline a large variety of techniques are supported for evaluating lighting and material properties of fragments. However, these techniques are usually restricted to evaluating local lighting and material effects. In addition, view-point changes require the complete processing of scene data to generate appropriate images. Reusing already rendered data in the frame buffer for a given view point by warping for a new viewpoint increases navigation fidelity at the expense of introducing artifacts for fragments previously hidden from the viewer. We present fragment-history volumes (FHV), a rendering technique based on a sparse, discretized representation of a 3d scene that emerges from recording all fragments that pass the rasterization stage in the graphics pipeline. These fragments are stored into per-pixel or per-octant lists for further processing; essentially creating an A-buffer. FHVs using per-octant fragment lists are view independent and allow fast resampling for image generation as well as for using more sophisticated approaches to evaluate material and lighting properties, eventually enabling global-illumination evaluation in the standard graphics pipeline available on current hardware. We show how FHVs are stored on the GPU in several ways, how they are created, and how they can be used for image generation at high rates. We discuss results for different usage scenarios, variations of the technique, and some limitations. | Fragment-History Volumes | 10,821 |
Feature lines are important geometric cues in characterizing the structure of a CAD model. Despite great progress in both explicit reconstruction and implicit reconstruction, it remains a challenging task to reconstruct a polygonal surface equipped with feature lines, especially when the input point cloud is noisy and lacks faithful normal vectors. In this paper, we develop a multistage algorithm, named RFEPS, to address this challenge. The key steps include (1)denoising the point cloud based on the assumption of local planarity, (2)identifying the feature-line zone by optimization of discrete optimal transport, (3)augmenting the point set so that sufficiently many additional points are generated on potential geometry edges, and (4) generating a polygonal surface that interpolates the augmented point set based on restricted power diagram. We demonstrate through extensive experiments that RFEPS, benefiting from the edge-point augmentation and the feature-preserving explicit reconstruction, outperforms state-of-the-art methods in terms of the reconstruction quality, especially in terms of the ability to reconstruct missing feature lines. | RFEPS: Reconstructing Feature-line Equipped Polygonal Surface | 10,822 |
Heatmap is a common geovisualization method that interpolates and visualizes a set of point observations on a map surface. Most of online web mapping libraries implement a one-pass heatmap algorithm using HTML5 canvas or WebGL for efficient heatmap generation. However, such implementation applies additive operations that accumulate the rendering of point weights on the map surface grid, making it inappropriate for visualizations that require the highlighting of both low and high weights. We introduce \textit{hilomap}, an online heatmap algorithm that highlights surface areas where points with both low and high trends are located. An HTML5 Canvas-based reference implementation on OpenLayers is presented and evaluated. | Online Heatmap Generation with Both High and Low Weights | 10,823 |
Clothing plays a vital role in real life and hence, is also important for virtual realities and virtual applications, such as online retail, virtual try-on, and real-time digital avatar interactions. However, choosing the correct parameters to generate realistic clothing requires expert knowledge and is often an arduous manual process. To alleviate this issue, we develop a pipeline for automatically determining the static material parameters required to simulate clothing of a particular material based on easily captured real-world fabrics. We use differentiable simulation to find an optimal set of parameters that minimizes the difference between simulated cloth and deformed target cloth. Our novel well-suited loss function is optimized through non-linear least squares. We designed our objective function to capture material-specific behavior, resulting in similar values for different wrinkle configurations of the same material. While existing methods carefully design experiments to isolate stretch parameters from bending modes, we embrace that stretching fabrics causes wrinkling. We estimate bending first, given that membrane stiffness has little effect on bending. Furthermore, our pipeline decouples the capture method from the optimization by registering a template mesh to the scanned data. These choices simplify the capture system and allow for wrinkles in scanned fabrics. We use a differentiable extended position-based dynamics (XPBD) cloth simulator, which is capable of real-time simulation. We demonstrate our method on captured data of three different real-world fabrics and on three digital fabrics produced by a third-party simulator. | Estimating Cloth Elasticity Parameters Using Position-Based Simulation
of Compliant Constrained Dynamics | 10,824 |
Precomputed Radiance Transfer (PRT) is widely used for real-time photorealistic effects. PRT disentangles the rendering equation into transfer and lighting, enabling their precomputation. Transfer accounts for the cosine-weighted visibility of points in the scene while lighting for emitted radiance from the environment. Prior art stored precomputed transfer in a tabulated manner, either in vertex or texture space. These values are fetched with interpolation at each point for shading. Vertex space methods require densely tessellated mesh vertices for high quality images. Texture space methods require non-overlapping and area-preserving UV mapping to be available. They also require a high-resolution texture to avoid rendering artifacts. In this paper, we propose a compact transfer representation that is learnt directly on scene geometry points. Specifically, we train a small multi-layer perceptron (MLP) to predict the transfer at sampled surface points. Our approach is most beneficial where inherent mesh storage structure and natural UV mapping are not available, such as Implicit Surfaces as it learns the transfer values directly on the surface. We demonstrate real-time, photorealistic renderings of diffuse and glossy materials on SDF geometries with PRT using our approach. | Real-Time Rendering of Arbitrary Surface Geometries using Learnt
Transfer | 10,825 |
Pixel art is a popular artistic style adopted in the gaming industry, and nowadays, it is often accompanied by modern rendering techniques. One example is dynamic lighting for the game sprites, for which normal mapping defines how the light interacts with the material represented by each pixel. Although there are different methods to generate normal maps for 3D games, applying them for pixel art may not yield correct results due to the style specificities. Therefore, this work compiles different normal map generation methods and study their applicability for pixel art, reducing the scarcity of existing material on the techniques and contributing to a qualitative analysis of the behavior of these methods in different case studies. | Analysis and Compilation of Normal Map Generation Techniques for Pixel
Art | 10,826 |
360{\deg} images and videos have become an economic and popular way to provide VR experiences using real-world content. However, the manipulation of the stereo panoramic content remains less explored. In this paper, we focus on the 360{\deg} image composition problem, and develop a solution that can take an object from a stereo image pair and insert it at a given 3D position in a target stereo panorama, with well-preserved geometry information. Our method uses recovered 3D point clouds to guide the composited image generation. More specifically, we observe that using only a one-off operation to insert objects into equirectangular images will never produce satisfactory depth perception and generate ghost artifacts when users are watching the result from different view directions. Therefore, we propose a novel per-view projection method that segments the object in 3D spherical space with the stereo camera pair facing in that direction. A deep depth densification network is proposed to generate depth guidance for the stereo image generation of each view segment according to the desired position and pose of the inserted object. We finally combine the synthesized view segments and blend the objects into the target stereo 360{\deg} scene. A user study demonstrates that our method can provide good depth perception and removes ghost artifacts. The per-view solution is a potential paradigm for other content manipulation methods for 360{\deg} images and videos. | 360° Stereo Image Composition with Depth Adaption | 10,827 |
In this demo, we present a novel technique for approximating topologically optimal scaffoldings for 3D printed objects using a Monte Carlo algorithm based on the foraging behavior of the Physarum polycephalum slime mold. As a case study, we have created a biologically inspired bicycle helmet using this technique that is designed to be effective in resisting impacts. We have created a prototype of this helmet and propose further studies that measure the effectiveness and validity of the design. | Scaffolding Generation using a 3D Physarum Polycephalum Simulation | 10,828 |
The task of crafting procedural programs capable of generating structurally valid 3D shapes easily and intuitively remains an elusive goal in computer vision and graphics. Within the graphics community, generating procedural 3D models has shifted to using node graph systems. They allow the artist to create complex shapes and animations through visual programming. Being a high-level design tool, they made procedural 3D modeling more accessible. However, crafting those node graphs demands expertise and training. We present GeoCode, a novel framework designed to extend an existing node graph system and significantly lower the bar for the creation of new procedural 3D shape programs. Our approach meticulously balances expressiveness and generalization for part-based shapes. We propose a curated set of new geometric building blocks that are expressive and reusable across domains. We showcase three innovative and expressive programs developed through our technique and geometric building blocks. Our programs enforce intricate rules, empowering users to execute intuitive high-level parameter edits that seamlessly propagate throughout the entire shape at a lower level while maintaining its validity. To evaluate the user-friendliness of our geometric building blocks among non-experts, we conducted a user study that demonstrates their ease of use and highlights their applicability across diverse domains. Empirical evidence shows the superior accuracy of GeoCode in inferring and recovering 3D shapes compared to an existing competitor. Furthermore, our method demonstrates superior expressiveness compared to alternatives that utilize coarse primitives. Notably, we illustrate the ability to execute controllable local and global shape manipulations. | GeoCode: Interpretable Shape Programs | 10,829 |
A new modification of the Hermite cubic rectangular patch is proposed: the S-Patch, which is based on the requirement that diagonal curves must be of degree 3 instead of degree 6 as it is in the case of the Hermite patch. Theoretical derivation of conditions is presented and some experimental results as well. The S-Patch is convenient for applications, where different tessellation of the u-v domain is needed, boundary and diagonal curves of different degrees are not acceptable. | S-patch: Modification of the Hermite parametric patch | 10,830 |
Bezier parametric patches are used in engineering practice quite often, especially in CAD/CAM systems oriented to mechanical design. In many cases quadrilateral meshes are used for tessellation of parameters domain. We propose a new modification of the Bezier cubic rectangular patch, the BS-patch, which is based on the requirement that diagonal curves must be of degree 3 instead of degree 6 as it is in the case of the Bezier patch. Theoretical derivation of conditions is presented and some experimental results as well. The BS-Patch is convenient for applications where for different tessellation of the u-v domain different degrees of diagonal curves are not acceptable. | BS-Patch: Constrained Bezier Parametric Patch | 10,831 |
Plasma fractals is a technique to generate random and realistic clouds, textures and terrains~-- traditionally using recursive subdivision. We demonstrate a new approach, based on iterative expansion. It gives a family of algorithms that includes the standard square-diamond algorithm and offers various interesting ways of extending it, and hence generating nicer pictures. The approach came about from exploring plasma fractals from the point of view of an array language (which we implemented as an embedded DSL in OCaml)~-- that is, from the perspective of declaring whole image transformations rather than fiddling with individual pixels. | Demo: New View on Plasma Fractals -- From the High Point of Array
Languages | 10,832 |
Bicubic four-sided patches are widely used in computer graphics, CAD/CAM systems etc. Their flexibility is high and enables to compress a surface description before final rendering. However, computer graphics hardware supports only triangular meshes. Therefore, four-sided bicubic patches are approximated by a triangular mesh. The border curves of a bicubic patch are of degree 3, while diagonal and anti-diagonal curves are of degree 6. Therefore the resulting shape and texturing depend on the actual mapping, i.e. how the tessellation of a bicubic patch is made. The proposed new modification of the Hermite bicubic patch, the HS-patch, is a result of additional restriction put on the Hermite bicubic patch formulation - the diagonal and anti-diagonal curves are of degree 3. This requirement leads to a new Hermite based bicubic four-sided patch with 12 control points and another 4 control points, i.e. twist vectors, are computed from those 12 control points. | HS-Patch: A New Hermite Smart Bicubic Patch Modification | 10,833 |
In this paper, we propose CIMS: a novel correction-interpolation method for smoke simulation. The basis of our method is to first generate a low frame rate smoke simulation, then increase the frame rate using temporal interpolation. However, low frame rate smoke simulations are inaccurate as they require increasing the time-step. A simulation with a larger time-step produces results different from that of the original simulation with a small time-step. Therefore, the proposed method corrects the large time-step simulation results closer to the corresponding small time-step simulation results using a U-Net-based DNN model. To obtain more precise results, we applied modeling concepts used in the image domain, such as optical flow and perceptual loss. By correcting the large time-step simulation results and interpolating between them, the proposed method can efficiently and accurately generate high frame rate smoke simulations. We conduct qualitative and quantitative analyses to confirm the effectiveness of the proposed model. Our analyses show that our method reduces the mean squared error of large time-step simulation results by more than 80% on average. Our method also produces results closer to the ground truth than the previous DNN-based methods; it is on average 2.04 times more accurate than previous works. In addition, the computation time of the proposed correction method barely affects the overall computation time. | CIMS: Correction-Interpolation Method for Smoke Simulation | 10,834 |
Computationally weak systems and demanding graphical applications are still mostly dependent on linear blendshapes for facial animations. The accompanying artifacts such as self-intersections, loss of volume, or missing soft tissue elasticity can be avoided by using physics-based animation models. However, these are cumbersome to implement and require immense computational effort. We propose neural volumetric blendshapes, an approach that combines the advantages of physics-based simulations with realtime runtimes even on consumer-grade CPUs. To this end, we present a neural network that efficiently approximates the involved volumetric simulations and generalizes across human identities as well as facial expressions. Our approach can be used on top of any linear blendshape system and, hence, can be deployed straightforwardly. Furthermore, it only requires a single neutral face mesh as input in the minimal setting. Along with the design of the network, we introduce a pipeline for the challenging creation of anatomically and physically plausible training data. Part of the pipeline is a novel hybrid regressor that densely positions a skull within a skin surface while avoiding intersections. The fidelity of all parts of the data generation pipeline as well as the accuracy and efficiency of the network are evaluated in this work. Upon publication, the trained models and associated code will be released. | Neural Volumetric Blendshapes: Computationally Efficient Physics-Based
Facial Blendshapes | 10,835 |
We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with respect to a goal function simultaneously leveraging a performant simulation model. The method is efficient, thus enabling differentiable simulations of high resolution geometries and degrees of freedom (DoFs). Collisions are naturally included in the framework. Our differentiable model allows a user to easily add additional optimization variables. Every control variable gradient requires the computation of only a few partial derivatives which can be computed using automatic differentiation code. We demonstrate the efficacy of the method with examples such as elastic material parameter estimation, initial value optimization, optimizing for underlying body shape and pose by only observing the clothing, and optimizing a time-varying external force sequence to match sparse keyframe shapes at specific times. Our approach demonstrates excellent efficiency and we demonstrate this on high resolution meshes with optimizations involving over 26 million degrees of freedom. Making an existing solver differentiable requires only a few modifications and the model is compatible with both modern CPU and GPU multi-core hardware. | DiffXPBD : Differentiable Position-Based Simulation of Compliant
Constraint Dynamics | 10,836 |
The surface reconstruction problem from sets of planar parallel slices representing cross sections through 3D objects is presented. The final result of surface reconstruction is always based on the correct estimation of the structure of the original object. This paper is a case study of the problem of the structure determination. We present a new approach, which is based on considering mutually orthogonal sets of slices. A new method for surface reconstruction from orthogonal slices is described and the benefit of orthogonal slices is discussed too. | Robust Surface Reconstruction from Orthogonal Slices | 10,837 |
In this paper four fundamental methods for an iso-surface extraction are compared, based on cell decomposition to tetrahedra. The methods are compared both on mathematically generated data sets as well as on real data sets. The comparison using mathematical data is made from different points of view such as area approximation, volume approximation. On the other hand, the Hausdorff distance and root mean square are used to compare methods on real data sets. The presented comparison can be helpful when deciding among tested methods which one to choose, as well as when we need to compare a newly developed method with other existing approaches. | A Comparison of Fundamental Methods for Iso-surface Extraction | 10,838 |
Presenting real-time rendering of 3D surfaces using radiance textures for fast synthesis of complex incidence-variable effects and environment interactions. This includes iridescence, parallax occlusion and interior mapping, (specular, regular, diffuse, total-internal) reflections with many bounces, refraction, subsurface scattering, transparency, and possibly more. This method divides textures into a matrix of radiance buckets, where each bucket represent some data at various incidence angles. Data can show final pixel color, or deferred rendering ambient occlusion, reflections, shadow map, etc. Resolution of the final synthesized output is the radiance bucket matrix size. Technique can be implemented with a simple fragment shader. The computational footprint of this technique is of simple diffuse-only graphics, but with visual fidelity of complex (off-line) ray-traced render at the cost of storage memory footprint. Balance between computational footprint and storage memory footprint can be easily achieved with variable compression ratio of repetitive radiance scene textures. | Radiance Textures for Rasterizing Ray-Traced Data | 10,839 |
We present a robust and efficient method for simulating Lagrangian solid-fluid coupling based on a new operator splitting strategy. We use variational formulations to approximate fluid properties and solid-fluid interactions, and introduce a unified two-way coupling formulation for SPH fluids and FEM solids using interior point barrier-based frictional contact. We split the resulting optimization problem into a fluid phase and a solid-coupling phase using a novel time-splitting approach with augmented contact proxies, and propose efficient custom linear solvers. Our technique accounts for fluids interaction with nonlinear hyperelastic objects of different geometries and codimensions, while maintaining an algorithmically guaranteed non-penetrating criterion. Comprehensive benchmarks and experiments demonstrate the efficacy of our method. | A Contact Proxy Splitting Method for Lagrangian Solid-Fluid Coupling | 10,840 |
Intersection algorithms are very important in computation of geometrical problems. Algorithms for a line intersection with linear or quadratic surfaces are quite efficient. However, algorithms for a line intersection with other surfaces are more complex and time consuming. In this case the object is usually closed into a simple bounding volume to speed up the cases when the given line cannot intersect the given object. In this paper new formulations of the line-torus intersection problem are given and new specification of the bounding volume for a torus is given as well. The presented approach is based on an idea of a line intersection with an envelope of rotating sphere that forms a torus. Due to this approach new bounding volume can be formulated which is more effective as it enables to detect cases when the line passes the "hole" of a torus, too. | Line-Torus Intersection for Ray Tracing: Alternative Formulations | 10,841 |
We present an adaptive extension of probe based global illumination solution that enhances the response to dynamic changes in the scene while while also enabling an order of magnitude increase in probe count. Our adaptive sampling strategy carefully places samples in regions where we detect time varying changes in radiosity either due to a change in lighting, geometry or both. Even with large number of probes, our technique robustly updates the irradiance and visibility cache to reflect the most up to date changes without stalling the overall algorithm. Our bandwidth aware approach is largely an improvement over the original \textit{Dynamic Diffuse Global Illumination} while also remaining orthogonal to the recent advancements in the technique. | Adaptive Dynamic Global Illumination | 10,842 |
We present a neural extension of basic shadow mapping for fast, high quality hard and soft shadows. We compare favorably to fast pre-filtering shadow mapping, all while producing visual results on par with ray traced hard and soft shadows. We show that combining memory bandwidth-aware architecture specialization and careful temporal-window training leads to a fast, compact and easy-to-train neural shadowing method. Our technique is memory bandwidth conscious, eliminates the need for post-process temporal anti-aliasing or denoising, and supports scenes with dynamic view, emitters and geometry while remaining robust to unseen objects. | Neural Shadow Mapping | 10,843 |
In animation, style can be considered as a distinctive layer over the content of a motion, allowing a character to achieve the same gesture in various ways. Editing existing animation to modify the style while keeping the same content is an interesting task, which can facilitate the re-use of animation data and cut down on production time. Existing animation edition methods either work directly on the motion data, providing precise but tedious tools, or manipulate semantic style categories, taking control away from the user. As a middle ground, we propose a new character motion edition paradigm allowing higher-level manipulations without sacrificing controllability. We describe the concept of pose metrics, objective value functions which can be used to edit animation, leaving the style interpretation up to the user. We then propose an edition pipeline to edit animation data using pose metrics. | Pose Metrics: a New Paradigm for Character Motion Edition | 10,844 |
We introduce a new Eulerian simulation framework for liquid animation that leverages both finite element and finite volume methods. In contrast to previous methods where the whole simulation domain is discretized either using the finite volume method or finite element method, our method spatially merges them together using two types of discretization being tightly coupled on its seams while enforcing second order accurate boundary conditions at free surfaces. We achieve our formulation via a variational form using new shape functions specifically designed for this purpose. By enabling a mixture of the two methods, we can take advantage of the best of two worlds. For example, finite volume method (FVM) result in sparse linear systems; however, complexity is encountered when unstructured grids such as tetrahedral or Voronoi elements are used. Finite element method (FEM), on the other hand, result in comparably denser linear systems, but the complexity remains the same even if unstructured elements are chosen; thereby facilitating spatial adaptivity. In this paper, we propose to use FVM for the majority parts to retain the sparsity of linear systems and FEM for parts where the grid elements are allowed to be freely deformed. An example of this application is locally moving grids. We show that by adapting the local grid movement to an underlying nearly rigid motion, numerical diffusion is noticeably reduced; leading to better preservation of structural details such as sharp edges, thin sheets and spindles of liquids. | A Combined Finite Element and Finite Volume Method for Liquid Simulation | 10,845 |
The IRMA project aims to design innovative methodologies for research in the field of historical and archaeological heritage based on a combination of medical imaging technologies and interactive 3D restitution modalities (virtual reality, augmented reality, haptics, additive manufacturing). These tools are based on recent research results from a collaboration between IRISA, Inrap and the company Image ET and are intended for cultural heritage professionals such as museums, curators, restorers and archaeologists. | From medical imaging to virtual reality for archaeology | 10,846 |
In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory Riemann-Hilbert problems. Such problems arise, in particular, in evaluating the long-time behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves here exclusively to the modified Korteweg de Vries (MKdV) equation, $$y_t-6y^2y_x+y_{xxx}=0,\qquad -\infty<x<\infty,\ t\ge0, y(x,t=0)=y_0(x),$$ but it will be clear immediately to the reader with some experience in the field, that the method extends naturally and easily to the general class of wave equations solvable by the inverse scattering method, such as the KdV, nonlinear Schr\"odinger (NLS), and Boussinesq equations, etc., and also to ``integrable'' ordinary differential equations such as the Painlev\'e transcendents. | A steepest descent method for oscillatory Riemann-Hilbert problems | 10,847 |
For all functions on an arbitrary open set $\Omega\subset\R^3$ with zero boundary values, we prove the optimal bound \[ \sup_{\Omega}|u| \leq (2\pi)^{-1/2} \left(\int_{\Omega}|\nabla u|^2 \,dx\, \int_{\Omega}|\Delta u|^2 \,dx\right)^{1/4}. \] The method of proof is elementary and admits generalizations. The inequality is applied to establish an existence theorem for the Burgers equation. | A sharp pointwise bound for functions with $L^2$-Laplacians on arbitrary
domains and its applications | 10,848 |
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions. | user's guide to viscosity solutions of second order partial differential
equations | 10,849 |
We consider the Einstein/Yang-Mills equations in $3+1$ space time dimensions with $\SU(2)$ gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is asymptotically flat and the total mass is finite. Thus, for non-abelian gauge fields the Yang/Mills repulsive force can balance the gravitational attractive force and prevent the formation of singularities in spacetime. | Smooth static solutions of the Einstein-Yang/Mills equation | 10,850 |
Given $\Bbb R^2, $ with a ``good'' complete metric, we show that the unique solution of the Ricci flow approaches a soliton at time infinity. Solitons are solutions of the Ricci flow, which move only by diffeomorphism. The Ricci flow on $\Bbb R^2$ is the limiting case of the porous medium equation when $m$ is zero. The results in the Ricci flow may therefore be interpreted as sufficient conditions on the initial data, which guarantee that the corresponding unique solution for the porous medium equation on the entire plane asymptotically behaves like a ``soliton-solution''. | A new result for the porous medium equation derived from the Ricci flow | 10,851 |
In this announcement we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We have shown that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is given which, when the additive constant is fixed, yields an approximation to the potential at a dense set of points. An estimate is presented for the error made by the formula. | A Formula for Finding a Potential from Nodal Lines | 10,852 |
A necessary and sufficient condition for local solvability is presented for the linear partial differential operators $-X^2-Y^2+ia(x)[X,Y]$ in $\bold R^3=\{(x,y,t)\}$, where $X=\partial_x,\; Y=\partial_y+x^k\partial_t$, and $a\in C^{\infty}(\bold R^1)$ is real valued, for each positive integer $k$. | Local Solvability For a Class of Partial Differential Operators With
Double Characteristics | 10,853 |
Examples are given of degenerate elliptic operators on smooth, compact manifolds that are not globally regular in $C^\infty$. These operators degenerate only in a rather mild fashion. Certain weak regularity results are proved, and an interpretation of global irregularity in terms of the associated heat semigroup is given. | Global Irregularity For Degenerate Elliptic Operators | 10,854 |
Local solvability is analyzed for natural families of partial differential operators having double characteristics. In some families the set of all operators that are not locally solvable is shown to have both infinite dimension and infinite codimension. | Infinite dimensional families of locally nonsolvable partial
differential operators | 10,855 |
This work is devoted to the study of a family of almost periodic one-dimensional Schr\"odinger equations. We define a monodromy matrix for this family. We study the asymptotic behavior of this matrix in the adiabatic case. Therefore, w develop a complex WKB method for adiabatic perturbations of periodic Schr\"odinger equations. At last, the study of the monodromy matrix enables us to get some spectral results for the initial family of almost periodic equations. | The monodromy matrix for a family of almost periodic Schrödinger
equations in the adiabatic case | 10,856 |
We prove local well-posedness results for the semi-linear wave equation for data in $H^\gamma$, $0 < \gamma < \frac{n-3}{2(n-1)}$, extending the previously known results for this problem. The improvement comes from an introduction of a two-scale Lebesgue space $X^{r,p}_k$. | Low regularity semi-linear wave equations | 10,857 |
We consider two variational evolution problems related to Monge-Kantorovich mass transfer. These problems provide models for collapsing sandpiles and for compression molding. We prove the following connection between these problems and nonlocal geometric curvature motion: The distance functions to surfaces moving according to certain nonlocal geometric laws are solutions of the variational evolution problems. Thus we do the first step of the proof of heuristics developed in earlier works. The main techniques we use are differential equations methods in the Monge-Kantorovich theory. | Variational evolution problems and nonlocal geometric motion | 10,858 |
The question of complete integrability of evolution equations associated to $n\times n$ first order isospectral operators is investigated using the inverse scattering method. It is shown that for $n>2$, e.g. for the three-wave interaction, additional (nonlinear) pointwise flows are necessary for the assertion of complete integrability. Their existence is demonstrated by constructing action-angle variables. This construction depends on the analysis of a natural 2-form and symplectic foliation for the groups GL(n) and SU(n).} | Complete Integrability of Completely Integrable Systems | 10,859 |
Using the scattering transform for $n^{th}$ order linear scalar operators, the Poisson bracket found by Gel'fand and Dikii, which generalizes the Gardner Poisson bracket for the KdV hierarchy, is computed on the scattering side. Action-angle variables are then constructed. Using this, complete integrability is demonstrated in the strong sense. Real action-angle variables are constructed in the self-adjoint case. | Action-Angle variables for the Gel'fand-Dikii flows | 10,860 |
If $u(t,x)$ is a solution of a one--dimensional, parabolic, second--order, linear partial differential equation (PDE), then it is known that, under suitable conditions, the number of zero--crossings of the function $u(t,\cdot)$ decreases (that is, does not increase) as time $t$ increases. Such theorems have applications to the study of blow--up of solutions of semilinear PDE, time dependent Sturm Liouville theory, curve shrinking problems and control theory. We generalise the PDE results by showing that the transition operator of a (possibly time--inhomogenous) one--dimensional diffusion reduces the number of zero--crossings of a function or even, suitably interpreted, a signed measure. Our proof is completely probabilistic and depends in a transparent manner on little more than the sample--path continuity of diffusion processes. | Transition operators of diffusions reduce zero-crossing | 10,861 |
In this paper we study the following nonlinear Maxwell's equations \\ $\varepsilon \E_{t}+\sigma(x,|\E|)\E= \g \vh +\F,\, \vh_{t}+\g \E=0$, where $\sigma(x,s)$ is a monotone graph of $s$. It is shown that the system has a unique weak solution. Moreover, the limit of the solution as $\varepsilon\rightarrow 0$ converges to the solution of quasi-stationary Maxwell's equations. | On a singular limit problem for nonlinear Maxwell's equations | 10,862 |
We study impact of a forced symmetry-breaking in boundary conditions on the bifurcation scenario of a semilinear elliptic partial differential equation. We show that for the square domain the orthogonality of eigenfunctions of the Laplacian may compensate partially the loss of symmetries in the boundary conditions and allows some solution to have more symmetries than the imposed boundary conditions. | Forced symmetry-breaking via boundary conditions | 10,863 |
Monge-Amp\`ere equations of the form, $u_{xx}u_{yy}-u_{xy}^2=F(u,u_x,u_y)$ arise in many areas of fluid and solid mechanics. Here it is shown that in the special case $F=u_y^4f(u, u_x/u_y)$, where $f$ denotes an arbitrary function, the Monge-Amp\`ere equation can be linearized by using a sequence of Amp\`ere, point, Legendre and rotation transformations. This linearization is a generalization of three examples from finite elasticity, involving plane strain and plane stress deformations of the incompressible perfectly elastic Varga material and also relates to a previous linearization of this equation due to Khabirov [7]. | On a class of linearizable Monge-Ampère equations | 10,864 |
The $x$-dependence of the symmetries of (1+1)-dimensional scalar translationally invariant evolution equations is described. The sufficient condition of (quasi)polynomiality in time $t$ of the symmetries of evolution equations with constant separant is found. The general form of time dependence of the symmetries of KdV-like non-linearizable evolution equations is presented. | On symmetries of KdV-like evolution equations | 10,865 |
We establish rigorously the existence of a three-parameter family of self-similar,globally bounded, and continuous weak solutions in two space dimensions to the compressible Euler equations with axisymmetry for gamma-law polytropic gases with gamma between 1 and 2, including 1. The initial data of these solutions have constant densities and outward-swirling velocities. We use the axisymmetry and self-similarity assumptions to reduce the equations to a system of three ordinary differential equations, from which we obtain detailed structures of solutions besides their existence. These solutions exhibit familiar structures seen in hurricanes and tornadoes. They all have finite local energy and vorticity with well-defined initial and boundary values. | Axisymmetric Solutions of the Euler Equations for Sub-Square Polytropic
Gases | 10,866 |
We prove local and global existence from large, rough initial data for a wave map between 1+1 dimensional Minkowski space and an analytic manifold. Included here is global existence for large data in the scale-invariant norm $\dot L^{1,1}$, and in the Sobolev spaces $H^s$ for $s > 3/4$. This builds on previous work in 1+1 dimensions of Pohlmeyer, Gu, Ginibre-Velo and Shatah. | Local and global well-posedness of wave maps on $\R^{1+1}$ for rough
data | 10,867 |
The concept of the theory of continuous groups of transformations has attracted the attention of applied mathematicians and engineers to solve many physical problems in the engineering sciences. Three applications are presented in this paper. The first one is the problem of time-dependent vertical temperature distribution in a stagnant lake. Two cases have been considered for the forms of the water parameters, namely water density and thermal conductivity. The second application is the unsteady free-convective boundary-layer flow on a non-isothermal vertical flat plate. The third application is the study of the dispersion of gaseous pollutants in the presence of a temperature inversion. The results are found in closed form and the effect of parameters are discussed. | Application of the group-theoretical method to physical problems | 10,868 |
This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form \ $\ds -\limfunc{div}\left(a\left(x, x/{\varepsilon _h},Du_h\right)\right)=f_h$ on $\Omega $ with Dirichlet boundary conditions. The sequence $(\varepsilon _h)$ tends to $0$ and the map $a(x,y,\xi )$ is periodic in $y$, monotone in $\xi $ and satisfies suitable continuity conditions. It is proved that $u_h\rightarrow u$ weakly in $H_0^{1,2}(\Omega )$, where $u$ is the solution of a homogenized problem \ $-\limfunc{div}(b(x,Du))=f$ on $\Omega $. We also prove some corrector results, i.e. we find $(P_h)$ such that $Du_h-P_h(Du)\rightarrow 0$ in $L^2(\Omega ,R^n)$. | Some homogenization and corrector results for nonlinear monotone
operators | 10,869 |
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as local symmetries of a related auxiliary system, are obtained. For some special nonlinearities new symmetry reductions and exact solutions are derived by using the nonclassical method. | Similarity reductions for a nonlinear diffusion equation | 10,870 |
Let $L$ be an infinitely degenerate second-order linear operator defined on a bounded smooth Euclidean domain. Under weaker conditions than those of H\"ormander, we show that the Dirichlet problem associated with $L$ has a unique smooth classical solution. The proof uses the Malliavin calculus. At present, there appears to be no proof of this result using classical analytic techniques. | The Dirichlet problem for superdegenerate differential operators | 10,871 |
A method for proving symmetrization inequalities for some elliptic p.d.e.'s on manifolds equipped with appropriate isoperimetric inequalities is outlined. The method is based on a modification of an approach of Baernstein. The question of what is the most general result that can be proved in this way is still open, and the author can be consulted if the reader is interested in this question. | From the Polya-Szego symmetrization inequality for Dirichlet integrals
to comparison theorems for p.d.e.'s on manifolds | 10,872 |
N-fold B\"acklund transformation for the Davey-Stewartson equation is constructed by using the analytic structure of the Lax eigenfunction in the complex eigenvalue plane. Explicit formulae can be obtained for a specified value of N. Lastly it is shown how generalized soliton solutions are generated from the trivial ones. | On the analytical approach to the N-fold Bäcklund transformation of
Davey-Stewartson equation | 10,873 |
The characteristic representation, or Goursat problem, for the Klein-Fock-Gordon equation with Volkov interaction [1] is regarded. It is shown that in this representation the explicit form of the Volkov propagator can be obtained. Using the characteristic representation technique, the Schwinger integral [2] in the Volkov problem can be calculated. | Fundamental solution of the Volkov problem (characteristic
representation) | 10,874 |
The endpoint Strichartz estimates for the Schr\"odinger equation are known to be false in two dimensions. However, if one averages the solution in $L^2$ in the angular variable, we show that the homogeneous endpoint and the retarded half-endpoint estimates hold, but the full retarded endpoint fails. In particular, the original versions of these estimates hold for radial data. | Spherically averaged endpoint Strichartz estimates for the
two-dimensional Schrödinger equation | 10,875 |
We show that the wave map equation in $\R^{1+1}$ is in general ill-posed in the critical space $\dot H^{1/2}$, and the Besov space $\dot B^{1/2,1}_2$. The problem is attributed to the bad behaviour of the one-dimensional bilinear expression $D^{-1}(f Dg)$ in these spaces. | Ill-posedness for one-dimensional wave maps at the critical regularity | 10,876 |
A codimension-three bifurcation, characterized by a pair of purely imaginary eigenvalues and a nonsemisimple double zero eigenvalue, arises in the study of a pair of weakly coupled nonlinear oscillators with Z_2 + Z_2 symmetry. The methodology is based on Arnold's ideas of versal deformations of matrices for the linear analysis, and Poincar\'e normal forms for the nonlinear analysis of the system. The stratified subvariety of primary bifurcations of codimensions one and two is identified in the parameter space. The analysis reveals different types of solutions in the state space, including equilibria, limit cycles, invariant tori and the possibility of homoclinic chaos. A mechanism is identified for energy transfer without strong resonance between two oscillation modes with widely separated frequencies. | Interactions of Andronov-Hopf and Bogdamov-Takens bifurcations | 10,877 |
The problem we are concerned with is whether singularities form in finite time in incompressible fluid flows. It is well known that the answer is ``no'' in the case of Euler and Navier-Stokes equations in dimension two. In dimension three it is still an open problem for these equations. In this paper we focus on a two-dimensional active scalar model for the 3D Euler vorticity equation. Constantin, Majda and Tabak suggested, by studying rigorous theorems and detailed numerical experiments, a general principle: ``If the level set topology in the temperature field for the 2D quasi-geostrophic active scalar in the region of strong scalar gradients does not contain a hyperbolic saddle, then no finite time singularity is possible.'' Numerical simulations showed evidence of singular behavior when the geometry of the level sets of the active scalar contain a hyperbolic saddle. There is a naturally associated notion of simple hyperbolic saddle breakdown. The main theorem we present in this paper shows that such breakdown cannot occur in finite time. We also show that the angle of the saddle cannot close in finite time and it cannot be faster than a double exponential in time. Using the same techniques, we see that analogous results hold for incompressible 2D and 3D Euler. | Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic
equation | 10,878 |
We derive an asymptotic solution of the Einstein field equations which describes the propagation of a thin, large amplitude gravitational wave into a curved space-time. The resulting equations have the same form as the colliding plane wave equations without one of the usual constraint equations. | Large amplitude gravitational waves | 10,879 |
This paper is concerned with the structure of the solutions to subcritical elliptic equations related to the Matukuma equation. In certain cases the complete structure of the solution set is known, and is comparable to that of the original Matukuma equation. Here we derive sufficient conditions for a more complicated solution set consisting of; (i) crossing solutions for small initial conditions and large initial conditions; (ii) at least one open interval of slowly decaying solutions; and (iii) at least two rapidly decaying solutions. As a consequence we obtain multiplicity results for rapidly decaying, or minimal solutions. | The structure of the solutions to semilinear equations at a critical
exponent | 10,880 |
For the quasilinear wave equation \partial_t^2u - \Delta u = u_t u_{tt}, we analyze the long-time behavior of classical solutions with small (not rotationally invariant) data. We give a complete asymptotic expansion of the lifespan and describe the solution close to the blowup point. It turns out that this solution is a ``blowup solution of cusp type,'' according to the terminology of the author. | Blowup of small data solutions for a quasilinear wave equation in two
space dimensions | 10,881 |
One of the fundamental unanswered questions in the general theory of relativity is whether ``naked'' singularities, that is singular events which are visible from infinity, may form with positive probability in the process of gravitational collapse. The conjecture that the answer to this question is in the negative has been called ``cosmic censorship.'' The present paper, which is a continuation previous work, addresses this question in the context of the spherical gravitational collapse of a scalar field. | The instability of naked singularities in the gravitational collapse of
a scalar field | 10,882 |
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of statics of hyper-elastic membranes under the regular hydrostatic load, we investigate peculiarities of deformation of a circular membrane whose mechanical characteristics are described by the Bidermann-type elastic potential. We develop an algorithm for solving a singular perturbation of nonlinear problem for the case of membrane loaded by heavy liquid. This algorithm enables us to obtain approximate solutions both in the presence of boundary layer and without it. The class of admissible functions, on which the variational method is realized, is chosen with account of the structure of formal asymptotic expansion of solutions of the corresponding linearized equations that have singularities in a small parameter at higher derivatives and in the independent variable. We give examples of calculations that illustrate possibilities of the method suggested for solving the problem under consideration. | Variational methods for solving nonlinear boundary problems of statics
of hyper-elastic membranes | 10,883 |
In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method. | Symmetries of a class of nonlinear fourth order partial differential
equations | 10,884 |
The purpose of this contribution is to show that some of the basic ideas of turbulence can be addressed in a deterministic setting instead of introducing random realizations of the fluid. Weak limits of oscillating sequences of solutions are considered and along the same line the Wigner transform replaces the Kolmogorov definition of the spectra of turbulence. One of the main issue is to show that, at least in some cases, this weak limit is the solution of an equation with an extra diffusion (the name turbulent diffusion appears naturally). In particular for a weak limit of solutions of the incompressible Euler equation (which is time reversible) such process would lead to the appearance of irreversibility. In the absence of proofs, following a program initiated by P. Lax, the diffusive property of the limit is analyzed, with the tools of Lax and Levermore or Jin Levermore and Mc Laughlin, on the zero dispersion limit of the Korteweg-deVries equation and of the Non Linear Schrodinger equation. The three authors are extremely happy to have the opportunity to publish this contribution in a volume dedicated to Walter Strauss as a mark of friendship and admiration for his achievement. They hope that this paper concerned with non linear fluid mechanics, non linear instabilities and inverse scattering, will find its place in the different domains that have interested Walter. | Weak Convergence and Deterministic Approach to Turbulent Diffusion | 10,885 |
In this letter, we report the existence of a novel type of explode-decay dromions, which are exponentially localized coherent structures whose amplitude varies with time, through Hirota method for a nonisospectral Davey-Stewartson equation I discussed recently by Jiang. Using suitable transformations, we also point out such solutions also exist for the isospectral Davey-Stewartson I equation itself for a careful choice of the potentials. | Explode-decay dromions in the non-isospectral Davey-Stewartson I (DSI)
equation | 10,886 |
A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schr\"odinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass of such a solution is shown to move along with the bicharacteristics of the basic symbol of the corresponding linear Schr\"odinger equation. The leading term of the asymptotic WKB-solution is constructed for the multidimensional NLSE. Special cases are considered for the standard one-dimensional NLSE and for NLSE in cylindrical coordinates. | Semiclassical solutions of the nonlinear Schrödinger equation | 10,887 |
This lecture notes cover a Part III (first year graduate) course that was given at Cambridge University over several years on pseudo-differential operators. The calculus on manifolds is developed and applied to prove propagation of singularities and the Hodge decomposition theorem. Problems are included. | Lectures on Pseudo-differential Operators | 10,888 |
We prove the doubling property of L-caloric measure corresponding to the second order parabolic equation in the whole space and in Lipschitz domains. For parabolic equations in the divergence form, a weaker form of the doubling property follows easily from a recent result, the backward Harnack inequality, and known estimates of Green's function. Our method works for both the divergence and nondivergence cases. Moreover, the backward Harnack inequality and estimates of Green's function are not needed in the course of proof. | Doubling properties for second order parabolic equations | 10,889 |
If we are given a smooth differential operator in the variable $x\in {\mathbb R}/2\pi {\mathbb Z},$ its normal form, as is well known, is the simplest form obtainable by means of the $\mbox{Diff}(S^1)$-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced $\mbox{Diff}(S^1)$-actions endowed with centrally extended Lie-Poisson brackets. After constructing a general expression for tranversal deformations of a Dirac type differential operator, we interpret it via the Lie-algebraic theory of induced $\mbox{Diff}(S^1)$-actions on a special Poisson manifold and determine its generic moment mapping. Using a Marsden-Weinstein reduction with respect to certain Casimir generated distributions, we describe a wide class of versally deformed Dirac type differential operators depending on complex parameters. | Versal deformations of a Dirac type differential operator | 10,890 |
It is possible to choose the parameters of a real quintic Ginzburg-Landau equation so that it possesses localized pulse-like solutions; Thual and Fauve have observed numerically that these pulses are stabilized by perturbations destroying the gradient structure of the real equation. For parameters such that the real part of the equations possesses pulses with a large shelf, we prove the existence of pulses by validated asymptotics, we find the expansion of the small eigenvalues of the operator and of their corresponding eigenvectors, and we give a sufficient condition for stabilization. This condition is generalized to any small non-gradient quintic perturbation of Ginzburg-Landau. | The Thual-Fauve pulse: skew stabilization | 10,891 |
In this note we obtain semiclassical resolvent estimates for non-trapping long range perturbations of the Laplacian on asymptotically Euclidean manifolds. Our proof is based on a positive commutator argument which differs from Mourre-type estimates by making the commutant also positive. The resolvent estimates, including the weighting of the Sobolev spaces in the estimates, are an immediate consequence. | Semiclassical estimates in asymptotically Euclidean scattering | 10,892 |
In this paper operator pencils $A(x,D,\lambda)$ are investigated which depend polynomially on the parameter $\lambda$ and act on a manifold with boundary. The operator A is assumed to satisfy the condition of N-ellipticity with parameter which is an ellipticity condition formulated with the use of the Newton polygon. We consider general boundary operators $B_1(x,D),...,B_m(x,D)$ and define N-ellipticity for the boundary value problem $(A,B_1,...,B_m)$ analogously to the Shapiro-Lopatinskii condition. It is shown that the boundary value problem is N-elliptic if and only if an a priori estimate holds, where the norms in the estimate are again defined in terms of the Newton polygon. These results are closely connected with singular perturbation theory and lead to uniform estimates for problems of Vishik-Lyusternik type containing a small parameter. | On elliptic operator pencils with general boundary conditions | 10,893 |
We consider the one-dimensional porous medium equation $u_t=\left (u^nu_x \right )_x+\frac{\mu}{x}u^nu_x$. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some cases this porous medium equation is connected with well known equations. With the introduction of a new dependent variable this partial differential equation can be equivalently written as a system of two equations. Point transformations are also sought for this auxiliary system. It turns out that in addition to the continuous point transformations that may be derived by Lie's method, a number of discrete transformations are obtained. In some cases the point transformations which are presented here for the single equation and for the auxiliary system form cyclic groups of finite order. | Continuous and discrete transformations of a one-dimensional porous
medium equation | 10,894 |
We consider the Cauchy problem for the wave equation in the whole space, R^n, with initial data which are distributions supported on finite sets. The main result is a precise description of the geometry of the sets of stationary points of the solutions to the wave equation. | Geometry of Stationary Sets for the Wave Equation in R^n, The Case of
Finitely Supported Initial Data, An Announcement | 10,895 |
We show that the full symbol of the Dirichlet to Neumann map of the k-form Laplace's equation on a Riemannian manifold (of dimension greater than 2) with boundary determines the full Taylor series, at the boundary, of the metric. This extends the result of Lee and Uhlmann for the case $k=0$. The proof avoids the computation of the full symbol by using the calculus of pseudo-differential operators parametrized by a boundary normal coordinate and recursively calculating the principal symbol of the difference of boundary operators. | An inverse boundary value problem for harmonic differential forms | 10,896 |
The authors show that bilinear estimates for null forms hold for Dirichlet-wave equations outside of convex obstacle. This generalizes results for the Euclidean case of Klainerman and Machedon, and of Sogge for the variable coefficient boundaryless case. The estimates are used to prove a local existence theorem for semilinear wave equations satisfying the null condition. | Null form estimates for (1/2,1/2) symbols and local existence for a
quasilinear Dirichlet-wave equation | 10,897 |
We study the conditions on the physical parameters in the Helfrich bending energy of lipid bilayer vesicles. Among embedded surfaces with a biconcave axisymmetric shape, the variation equation is analyzed in detail. This leads to simple conditions which guarantee the solution the information about the geometry. | An Analysis on the Shape Equation for Biconcave Axisymmetric Vesicles | 10,898 |
Let X be a compact manifold with boundary, and g a scattering metric on X, which may be either of short range or `gravitational' long range type. Thus, g gives X the geometric structure of a complete manifold with an asymptotically conic end. Let H be an operator of the form $H = \Delta + P$, where $\Delta$ is the Laplacian with respect to g and P is a self-adjoint first order scattering differential operator with coefficients vanishing at the boundary of X and satisfying a `gravitational' condition. We define a symbol calculus for Legendre distributions on manifolds with codimension two corners and use it to give a direct construction of the resolvent kernel of H, $R(\sigma + i0)$, for $\sigma$ on the positive real axis. In this approach, we do not use the limiting absorption principle at any stage; instead we construct a parametrix which solves the resolvent equation up to a compact error term and then use Fredholm theory to remove the error term. | The resolvent for Laplace-type operators on asymptotically conic spaces | 10,899 |
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