پردازش مش چندضلعی

Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes. A supplemental contains downloads and additional information. Contents......Page 6 Preface......Page 10 1. Surface Representations......Page 13 1.1 Surface Definition and Properties......Page 15 1.2 Approximation Power......Page 17 1.3 Parametric Surface Representations......Page 19 1.4 Implicit Surface Representations......Page 25 1.5 Conversion Methods......Page 27 1.6 Summary and Further Reading......Page 32 2. Mesh Data Structures......Page 33 2.1 Face-Based Data Structures......Page 34 2.2 Edge-Based Data Structures......Page 36 2.3 Halfedge-Based Data Structure......Page 37 2.4 Directed-Edge Data Structure......Page 39 2.5 Summary and Further Reading......Page 40 3.1 Curves......Page 41 3.2 Surfaces......Page 43 3.3 Discrete Differential Operators......Page 52 3.4 Summary and Further Reading......Page 60 4. Smoothing......Page 61 4.1 Fourier Transform and Manifold Harmonics......Page 62 4.2 Diffusion Flow......Page 66 4.3 Fairing......Page 69 4.4 Summary and Further Reading......Page 73 5. Parameterization......Page 75 5.1 General Goals......Page 76 5.2 Parameterization of a Triangulated Surface......Page 78 5.3 Barycentric Mapping......Page 79 5.4 Conformal Mapping......Page 83 5.5 Methods Based on Distortion Analysis......Page 90 5.6 Summary and Further Reading......Page 94 6. Remeshing......Page 97 6.1 Local Structure......Page 98 6.2 Global Structure......Page 99 6.4 Voronoi Diagrams and Delaunay Triangulations......Page 101 6.5 Triangle-Based Remeshing......Page 104 6.6 Quad-dominant Remeshing......Page 116 6.7 Summary and Further Reading......Page 122 7. Simplification & Approximation......Page 123 7.1 Vertex Clustering......Page 125 7.2 Incremental Decimation......Page 127 7.3 Shape Approximation......Page 134 7.4 Out-of-Core Methods......Page 139 7.5 Summary and Further Reading......Page 142 8. Model Repair......Page 143 8.2 Types of Repair Algorithms......Page 144 8.3 Types of Input......Page 147 8.4 Surface-Oriented Algorithms......Page 151 8.5 Volumetric Repair Algorithms......Page 156 8.6 Summary and Further Reading......Page 162 9. Deformation......Page 163 9.1 Transformation Propagation......Page 165 9.2 Shell-Based Deformation......Page 167 9.3 Multi-Scale Deformation......Page 169 9.4 Differential Coordinates......Page 176 9.5 Freeform Deformation......Page 181 9.6 Radial Basis Functions......Page 185 9.7 Limitations of Linear Methods......Page 187 9.8 Summary and Further Reading......Page 189 A.1 Discretizing Poisson and Laplace Equations......Page 193 A.2 Data Structures for Sparse Matrices......Page 196 A.3 Iterative Solvers......Page 199 A.4 Sparse Direct Cholesky Solver......Page 205 A.5 Non-Symmetric Indefinite Systems......Page 208 A.6 Comparison......Page 209 Bibliography......Page 215 Index......Page 238 "Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes."--Publisher's website