Feature Adaptive Ray Tracing of Subdivision Surfaces

abstract: Subdivision surfaces have gained more and more traction since it became the standard surface representation in the movie industry for many years. And Catmull-Clark subdivision scheme is the most popular one for handling polygonal meshes. After its introduction, Catmull-Clark surfaces have been extended to several eminent ways, including the handling of boundaries, infinitely sharp creases, semi-sharp creases, and hierarchically defined detail. For ray tracing of subdivision surfaces, a common way is to construct spatial bounding volume hierarchies on top of input control mesh. However, a high-level refined subdivision surface not only requires a substantial amount of memory storage, but also causes slow and inefficient ray tracing. In this thesis, it presents a new way to improve the efficiency of ray tracing of subdivision surfaces, while the quality is not as good as general methods.Dissertation/ThesisMasters Thesis Computer Science 201

GPU Ray Tracing of Triangular Grid Primitives

Triangular grid primitives are a technique used to handle memory-intensive meshes more efficiently. They are also referred to as micro meshes in recent proprietary hardware implementations. This representation can reduce the memory footprint during ray tracing of subdivision surfaces or displacement maps that may result from mesh simplification. This paper presents a novel approach to accelerate GPU software ray tracing using a two-level bounding volume hierarchy (BVH) to store vertices in a non-redundant manner. The primary goal is to make the technology more accessible by focusing on standard GPU devices. The bottom-level BVH strictly follows the subdivision recursion, allowing for the side effect of rendering intermediate recursion depths. Our approach enables us to encode geometry and BVH using approximately 6.3 bytes per triangle, reducing standard representations by a factor of 4.5. Additionally, the construction time of the BVH is reduced. Our data structure achieves a peak performance impact of 16 % for a three-level subdivision

Subdivision Surface based One-Piece Representation

Subdivision surfaces are capable of modeling and representing complex shapes of arbi-trary topology. However, methods on how to build the control mesh of a complex surfaceare not studied much. Currently, most meshes of complicated objects come from trian-gulation and simplification of raster scanned data points, like the Stanford 3D ScanningRepository. This approach is costly and leads to very dense meshes.Subdivision surface based one-piece representation means to represent the final objectin a design process with only one subdivision surface, no matter how complicated theobject\u27s topology or shape. Hence the number of parts in the final representation isalways one.In this dissertation we present necessary mathematical theories and geometric algo-rithms to support subdivision surface based one-piece representation. First, an explicitparametrization method is presented for exact evaluation of Catmull-Clark subdivisionsurfaces. Based on it, two approaches are proposed for constructing the one-piece rep-resentation of a given object with arbitrary topology. One approach is to construct theone-piece representation by using the interpolation technique. Interpolation is a naturalway to build models, but the fairness of the interpolating surface is a big concern inprevious methods. With similarity based interpolation technique, we can obtain bet-ter modeling results with less undesired artifacts and undulations. Another approachis through performing Boolean operations. Up to this point, accurate Boolean oper-ations over subdivision surfaces are not approached yet in the literature. We presenta robust and error controllable Boolean operation method which results in a one-piecerepresentation. Because one-piece representations resulting from the above two methodsare usually dense, error controllable simplification of one-piece representations is needed.Two methods are presented for this purpose: adaptive tessellation and multiresolutionanalysis. Both methods can significantly reduce the complexity of a one-piece represen-tation and while having accurate error estimation.A system that performs subdivision surface based one-piece representation was im-plemented and a lot of examples have been tested. All the examples show that our ap-proaches can obtain very good subdivision based one-piece representation results. Eventhough our methods are based on Catmull-Clark subdivision scheme, we believe they canbe adapted to other subdivision schemes as well with small modifications

Isogeometric Approximation of Variational Problems for Shells

The interaction of applied geometry and numerical simulation is a growing field in the interplay of com- puter graphics, computational mechanics and applied mathematics known as isogeometric analysis. In this thesis we apply and analyze Loop subdivision surfaces as isogeometric tool because they provide great flexibility in handling surfaces of arbitrary topology combined with higher order smoothness. Compared with finite element methods, isogeometric methods are known to require far less degrees of freedom for the modeling of complex surfaces but at the same time the assembly of the isogeo- metric matrices is much more time-consuming. Therefore, we implement the isogeometric subdivision method and analyze the experimental convergence behavior for different quadrature schemes. The mid-edge quadrature combines robustness and efficiency, where efficiency is additionally increased via lookup tables. For the first time, the lookup tables allow the simulation with control meshes of arbitrary closed connectivity without an initial subdivision step, i.e. triangles can have more than one vertex with valence different from six. Geometric evolution problems have many applications in material sciences, surface processing and modeling, bio-mechanics, elasticity and physical simulations. These evolution problems are often based on the gradient flow of a geometric energy depending on first and second fundamental forms of the surface. The isogeometric approach allows a conforming higher order spatial discretization of these geometric evolutions. To overcome a time-error dominated scheme, we combine higher order space and time discretizations, where the time discretization based on implicit Runge-Kutta methods. We prove that the energy diminishes in every time-step in the fully discrete setting under mild time-step restrictions which is the crucial characteristic of a gradient flow. The overall setup allows for a general type of fourth-order energies. Among others, we perform experiments for Willmore flow with respect to different metrics. In the last chapter of this thesis we apply the time-discrete geodesic calculus in shape space to the space of subdivision shells. By approximating the squared Riemannian distance by a suitable energy, this approach defines a discrete path energy for a consistent computation of geodesics, logarithm and exponential maps and parallel transport. As approximation we pick up an elastic shell energy, which measures the deformation of a shell by membrane and bending contributions of its mid-surface. Bézier curves are a fundamental tool in computer-aided geometric design. We extend these to the subdivision shell space by generalizing the de Casteljau algorithm. The evaluation of Bézier curves depends on all input data. To solve this problem, we introduce B-splines and cardinal splines in shape space by gluing together piecewise Bézier curves in a smooth way. We show examples of quadratic and cubic Bézier curves, quadratic and cubic B-splines as well as cardinal splines in subdivision shell space

Hardware Accelerators for Animated Ray Tracing

Future graphics processors are likely to incorporate hardware accelerators for real-time ray tracing, in order to render increasingly complex lighting effects in interactive applications. However, ray tracing poses difficulties when drawing scenes with dynamic content, such as animated characters and objects. In dynamic scenes, the spatial datastructures used to accelerate ray tracing are invalidated on each animation frame, and need to be rapidly updated. Tree update is a complex subtask in its own right, and becomes highly expensive in complex scenes. Both ray tracing and tree update are highly memory-intensive tasks, and rendering systems are increasingly bandwidth-limited, so research on accelerator hardware has focused on architectural techniques to optimize away off-chip memory traffic. Dynamic scene support is further complicated by the recent introduction of compressed trees, which use low-precision numbers for storage and computation. Such compression reduces both the arithmetic and memory bandwidth cost of ray tracing, but adds to the complexity of tree update.This thesis proposes methods to cope with dynamic scenes in hardware-accelerated ray tracing, with focus on reducing traffic to external memory. Firstly, a hardware architecture is designed for linear bounding volume hierarchy construction, an algorithm which is a basic building block in most state-of-the-art software tree builders. The algorithm is rearranged into a streaming form which reduces traffic to one-third of software implementations of the same algorithm. Secondly, an algorithm is proposed for compressing bounding volume hierarchies in a streaming manner as they are output from a hardware builder, instead of performing compression as a postprocessing pass. As a result, with the proposed method, compression reduces the overall cost of tree update rather than increasing it. The last main contribution of this thesis is an evaluation of shallow bounding volume hierarchies, common in software ray tracing, for use in hardware pipelines. These are found to be more energy-efficient than binary hierarchies. The results in this thesis both confirm that dynamic scene support may become a bottleneck in real time ray tracing, and add to the state of the art on tree update in terms of energy-efficiency, as well as the complexity of scenes that can be handled in real time on resource-constrained platforms

Ray Tracing Gems

This book is a must-have for anyone serious about rendering in real time. With the announcement of new ray tracing APIs and hardware to support them, developers can easily create real-time applications with ray tracing as a core component. As ray tracing on the GPU becomes faster, it will play a more central role in real-time rendering. Ray Tracing Gems provides key building blocks for developers of games, architectural applications, visualizations, and more. Experts in rendering share their knowledge by explaining everything from nitty-gritty techniques that will improve any ray tracer to mastery of the new capabilities of current and future hardware. What you'll learn: The latest ray tracing techniques for developing real-time applications in multiple domains Guidance, advice, and best practices for rendering applications with Microsoft DirectX Raytracing (DXR) How to implement high-performance graphics for interactive visualizations, games, simulations, and more Who this book is for: Developers who are looking to leverage the latest APIs and GPU technology for real-time rendering and ray tracing Students looking to learn about best practices in these areas Enthusiasts who want to understand and experiment with their new GPU