Rockhaven Waltz

https://digitalcommons.library.umaine.edu/mmb-me/1410/thumbnail.jp

Filtering Solid Gabor Noise

International audienceSolid noise is a fundamental tool in computer graphics. Surprisingly, no existing noise function supports both high-quality antialiasing and continuity across sharp edges. In this paper we show that a slicing approach is required to preserve continuity across sharp edges, and we present a new noise function that supports anisotropic filtering of sliced solid noise. This is made possible by individually filtering the slices of Gabor kernels, which requires the proper treatment of phase. This in turn leads to the introduction of the phase-augmented Gabor kernel and random-phase Gabor noise, our new noise function. We demonstrate that our new noise function supports both high-quality anti-aliasing and continuity across sharp edges, as well as anisotropy

Gabor Noise by Example

International audienceProcedural noise is a fundamental tool in Computer Graphics. However, designing noise patterns is hard. In this paper, we present Gabor noise by example, a method to estimate the parameters of bandwidth-quantized Gabor noise, a procedural noise function that can generate noise with an arbitrary power spectrum, from exemplar Gaussian textures, a class of textures that is completely characterized by their power spectrum. More specifically, we introduce (i) bandwidth-quantized Gabor noise, a generalization of Gabor noise to arbitrary power spectra that enables robust parameter estimation and efficient procedural evaluation; (ii) a robust parameter estimation technique for quantized-bandwidth Gabor noise, that automatically decomposes the noisy power spectrum estimate of an exemplar into a sparse sum of Gaussians using non-negative basis pursuit denoising; and (iii) an efficient procedural evaluation scheme for bandwidth-quantized Gabor noise, that uses multi-grid evaluation and importance sampling of the kernel parameters. Gabor noise by example preserves the traditional advantages of procedural noise, including a compact representation and a fast on-the-fly evaluation, and is mathematically well-founded. See project page at : http://graphics.cs.kuleuven.be/publications/GLLD12GNBE

Procedural Noise using Sparse Gabor Convolution

International audienceNoise is an essential tool for texturing and modeling. Designing interesting textures with noise calls for accurate spectral control, since noise is best described in terms of spectral content. Texturing requires that noise can be easily mapped to a surface, while high-quality rendering requires anisotropic filtering. A noise function that is procedural and fast to evaluate offers several additional advantages. Unfortunately, no existing noise combines all of these properties. In this paper we introduce a noise based on sparse convolution and the Gabor kernel that enables all of these properties. Our noise offers accurate spectral control with intuitive parameters such as orientation, principal frequency and bandwidth. Our noise supports two-dimensional and solid noise, but we also introduce setup-free surface noise. This is a method for mapping noise onto a surface, complementary to solid noise, that maintains the appearance of the noise pattern along the object and does not require a texture parameterization. Our approach requires only a few bytes of storage, does not use discretely sampled data, and is nonperiodic. It supports anisotropy and anisotropic filtering. We demonstrate our noise using an interactive tool for noise design

The

The tile packing problem is a challenging combinatorial puzzle based on tiles with colored edges or colored corners. In its different incarnations, the puzzle gives rise to a number of interesting problems. In this paper, we sketch the background of the tile packing problem and present solutions to the puzzle. We hope that this work will stimulate further interest in this puzzle amongst readers, and that the remaining open problems will eventually be solved

Tile-based methods in computer graphics

Many complex signals, such as point distributions and textures, cannot efficiently be synthesized and stored. In this dissertation we present tile-based methods to solve this problem. Instead of synthesizing a complex signal when needed, the signal is synthesized on forehand over a small set of tiles. Arbitrary large amounts of that signal can then efficiently be generated when needed by generating a stochastic tiling. Tile-based methods are traditionally based on Wang tiles. The colored edges of Wang tiles only constrain the four direct neighboring tiles, but not the four diagonally neighboring tiles. This problem introduces unwanted artifacts in the tiled signals, and complicates methods for synthesizing signals over a set of Wang tiles. To solve this problem we present corner tiles. Corner tiles are unit square tiles with colored corners rather than colored edges. The colored corners of corner tiles constrain all neighboring tiles. We revisit the most important applications of Wang tiles, and we show that corner tiles have substantial advantages for each of these applications. Stochastic tilings are traditionally generated using scanline stochastic tiling algorithms. However, these algorithms store the complete tiling and are therefore not efficient. To solve this problem, we present direct stochastic tiling algorithms for Wang tiles and corner tiles. These algorithms are capable of evaluating a stochastic tiling locally, without explicitely constructing and storing the tiling up to that point. We also introduce long-period hash functions to generate very large tilings. Poisson disk distributions and textures are two examples of complex signals. We present tile-based methods for generating Poisson disk distributions and for synthesizing textures. Tile-based methods not only allow to efficiently generate Poisson disk distributions and synthesize textures, but also enable new applications such as tile-based texture synthesis and a procedural object distribution function. This new texture basis function allows to distribute procedural objects over a procedural background, using intuitive parameters such as the scale, size and orientation of the objects. We also present an overview of applications of tiled Poisson disk distributions, and a detailed comparison of methods for generating Poisson disk distributions. We study corner tiles in the context of the tiling problem and aperiodic tile sets, and we construct several new aperiodic sets of Wang tiles and corner tiles. The tile-based methods we present in this dissertation are a valuable tool for computer graphics, and help to keep up with the continuously increasing demand for more complexity and realism in digitally synthesized images.Contents Preface iii Abstract v Contents vii 1 Introduction 1 1.1 Tile-Based Methods in Computer Graphics . . . . . . . . . . . 1 1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Wang Tiles and Corner Tiles 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Tilings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Tilings in Computer Graphics . . . . . . . . . . . . . . . . . . . 8 2.4 Wang Tiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Wang Tiles in Computer Graphics . . . . . . . . . . . . . . . . 9 2.6 Corner Tiles and the Corner Problem . . . . . . . . . . . . . . 9 2.7 Definitions, Conventions and Notations . . . . . . . . . . . . . . 10 2.8 Enumerating Wang Tile Sets and Corner Tile Sets . . . . . . . 12 2.9 Corner Tiles as Wang Tiles . . . . . . . . . . . . . . . . . . . . 14 2.10 Dominoes, Wang Cubes and Corner Cubes . . . . . . . . . . . 14 2.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Tiling Algorithms for Wang Tiles and Corner Tiles 17 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Scanline Stochastic Tiling Algorithms . . . . . . . . . . . . . . 17 3.2.1 A Scanline Stochastic Tiling Algorithm for Wang Tiles . 18 3.2.2 A Scanline Stochastic Tiling Algorithm for Corner Tiles 19 3.3 Direct Stochastic Tiling Algorithms . . . . . . . . . . . . . . . . 20 3.3.1 A Direct Stochastic Tiling Algorithm for Corner Tiles . 20 3.3.2 Direct Stochastic Tiling Algorithms for Wang Tiles . . . 21 3.4 Hash Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.4.1 Traditional Hash Functions Based on Permutation Tables 24 3.4.2 Long-Period Hash Functions Based on Permutation Tables 25 3.4.3 Hash Functions for Direct Stochastic Tiling Algorithms 27 3.4.4 Hash Functions for Procedural Texturing . . . . . . . . 28 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4 Tile-Based Methods for Generating Poisson Disk Distributions 31 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Poisson Disk Distributions . . . . . . . . . . . . . . . . . . . . . 31 4.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.2.2 History and Background . . . . . . . . . . . . . . . . . . 32 4.2.3 Radius Specification . . . . . . . . . . . . . . . . . . . . 33 4.2.4 Generation . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.3 Edge-Based Poisson Disk Tiles . . . . . . . . . . . . . . . . . . 35 4.4 Template Poisson Disk Tiles . . . . . . . . . . . . . . . . . . . . 44 4.5 Corner-Based Poisson Disk Tiles . . . . . . . . . . . . . . . . . 48 4.6 A Tile-Based Method for Generating Poisson Sphere Distributions 56 4.6.1 Poisson Sphere Distributions . . . . . . . . . . . . . . . 56 4.6.2 Three-Dimensional Corner Tiles . . . . . . . . . . . . . 57 4.6.3 Corner-Based Poisson Sphere Tiles . . . . . . . . . . . . 58 4.7 A Tile-Based Method for Generating Nonuniform Poisson Disk Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.7.1 Nonuniform Poisson Disk Distributions . . . . . . . . . 65 4.7.2 A Self-Similar Hierarchical Tile . . . . . . . . . . . . . . 65 4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5 Tile-Based Methods for Texture Synthesis 73 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.2 Texture Mapping and Texture Synthesis . . . . . . . . . . . . . 73 5.3 Tile-Based Texture Synthesis . . . . . . . . . . . . . . . . . . . 74 5.4 Tile-Based Texture Mapping . . . . . . . . . . . . . . . . . . . 78 5.5 The Tile Packing Problem . . . . . . . . . . . . . . . . . . . . . 81 5.5.1 The One-Dimensional Tile Packing Problem . . . . . . . 81 5.5.2 The Wang Tile Packing Problem . . . . . . . . . . . . . 83 5.5.3 The Corner Tile Packing Problem . . . . . . . . . . . . 84 5.5.4 Puzzles Derived from the Tile Packing Problem . . . . . 87 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6 A Comparison of Methods for Generating Poisson Disk Distributions 89 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 6.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6.2.1 Radius Analysis . . . . . . . . . . . . . . . . . . . . . . 90 6.2.2 Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . 90 6.2.3 Sampling Performance . . . . . . . . . . . . . . . . . . . 94 6.2.4 Timings . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.3 Dart Throwing . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.4 Relaxation Dart Throwing . . . . . . . . . . . . . . . . . . . . . 98 6.5 Lloyd’s Relaxation Scheme . . . . . . . . . . . . . . . . . . . . 100 6.6 Shade’s Poisson Disk Tiles . . . . . . . . . . . . . . . . . . . . . 102 6.7 Tiled Blue Noise Samples . . . . . . . . . . . . . . . . . . . . . 103 6.8 Fast Hierarchical Importance Sampling with Blue Noise Properties107 6.9 Edge-Based Poisson Disk Tiles . . . . . . . . . . . . . . . . . . 109 6.10 Template Poisson Disk Tiles . . . . . . . . . . . . . . . . . . . . 111 6.11 Corner-Based Poisson Disk Tiles . . . . . . . . . . . . . . . . . 114 6.12 Efficient Generation of Poisson Disk Sampling Patterns . . . . 117 6.13 A Spatial Data Structure for Fast Poisson Disk Sample Generation120 6.14 Recursive Wang Tiles for Real-Time Blue Noise . . . . . . . . . 122 6.15 A Comparison of Methods for Generating Poisson Sphere Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.16 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7 Applications of Poisson Disk Distributions 129 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.2 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.3 Non-Photorealistic Rendering . . . . . . . . . . . . . . . . . . . 132 7.4 Scientific Visualization . . . . . . . . . . . . . . . . . . . . . . . 134 7.5 Procedural Modeling, Geometric Object Distribution and Geometry Instancing . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.6 Procedural Texturing . . . . . . . . . . . . . . . . . . . . . . . . 136 7.6.1 History and Background . . . . . . . . . . . . . . . . . . 137 7.6.2 A 2D Procedural Object Distribution Function . . . . . 137 7.6.3 A 3D Procedural Object Distribution Function . . . . . 144 7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 8 Small Aperiodic Sets of Corner Tiles 147 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 8.2 History and Background . . . . . . . . . . . . . . . . . . . . . . 147 8.3 Construction of Aperiodic Corner Tile Sets from AperiodicWang Tile Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 8.3.1 Diagonal Translation . . . . . . . . . . . . . . . . . . . . 151 8.3.2 Horizontal and Vertical Translation . . . . . . . . . . . . 151 8.3.3 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.3.4 Subdivision . . . . . . . . . . . . . . . . . . . . . . . . . 154 8.4 Construction of AperiodicWang Tile Sets from Aperiodic Corner Tile Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 9 Conclusion 159 9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 9.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 9.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Bibliography 165 List of Publications 173 Biography 177nrpages: 177+xstatus: publishe

Wang Tiles in Computer Graphics

Many complex signals in computer graphics, such as point distributions and textures, cannot be efficiently synthesized and stored. This book presents tile-based methods based on Wang tiles and corner tiles to solve both these problems. Instead of synthesizing a complex signal when needed, the signal is synthesized beforehand over a small set of Wang tiles or corner tiles. Arbitrary large amounts of that signal can then efficiently be generated when needed by generating a stochastic tiling, and storing only a small set of tiles reduces storage requirements. A tile-based method for generating

Time and space efficient grids for ray tracing

The focus of research in acceleration structures for ray tracing recently shifted from render time to time to image, the sum of build time and render time, and also the memory footprint of acceleration structures now receives more attention. In this paper we revisit the grid acceleration structure in this setting. We present two efficient methods for representing and building a grid. The minimum storage method consist of a static data structure for representing a grid with minimal memory requirements, more specifically exactly one index per grid cell and exactly one index per object reference, and an algorithm for building that data structure in linear time. The hashed storage method consists of a static data structure for representing a grid that reduces memory requirements even further, by using perfect hashing based on row displacement compression, and a fast algorithm for building that data structure. We show that these methods are more efficient in both time and space than traditional methods based on linked lists and dynamic arrays. We also show that, for applications where time to image or memory usage is important, such as interactive ray tracing and rendering large models, the grid acceleration structure is very effective despite its simplicity.nrpages: 28status: publishe