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[資源]
曲面重構(gòu)的數(shù)值分析算法（英文版）
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英文書：Curve and surface reconstruction: Algorithms with mathematical analysis Many applications in science and engineering require a digital model of a real physical object. Advanced scanning technology has made it possible to scan such objects and generate point samples on their boundaries. This book shows how to compute a digital model from this point sample. After developing the basics of sampling theory and its connections to various geometric and topological properties, the author describes a suite of algorithms that have been designed for the reconstruction problem, including algorithms for surface reconstruction from dense samples, from samples that are not adequately dense and from noisy samples. Voronoi and Delaunay based techniques, implicit surface based methods and Morse theory based methods are covered. Scientists and engineers working in drug design, medical imaging, CAD, GIS, and many other areas will benefit from this first book on the subject. 目錄： Preface page xi 1 Basics 1 1.1 Shapes 2 1.1.1 Spaces and Maps 3 1.1.2 Manifolds 6 1.1.3 Complexes 7 1.2 Feature Size and Sampling 8 1.2.1 Medial Axis 10 1.2.2 Local Feature Size 14 1.2.3 Sampling 16 1.3 Voronoi Diagram and Delaunay Triangulation 18 1.3.1 Two Dimensions 19 1.3.2 Three Dimensions 22 1.4 Notes and Exercises 23 Exercises 24 2 Curve Reconstruction 26 2.1 Consequences of ε-Sampling 27 2.2 Crust 30 2.2.1 Algorithm 30 2.2.2 Correctness 32 2.3 NN-Crust 35 2.3.1 Algorithm 35 2.3.2 Correctness 36 2.4 Notes and Exercises 38 Exercises 39 3 Surface Samples 41 3.1 Normals 43 3.1.1 Approximation of Normals 43 3.1.2 Normal Variation 45 3.1.3 Edge and Triangle Normals 47 3.2 Topology 50 3.2.1 Topological Ball Property 50 3.2.2 Voronoi Faces 53 3.3 Notes and Exercises 57 Exercises 57 4 Surface Reconstruction 59 4.1 Algorithm 59 4.1.1 Poles and Cocones 59 4.1.2 Cocone Triangles 62 4.1.3 Pruning 64 4.1.4 Manifold Extraction 66 4.2 Geometric Guarantees 70 4.2.1 Additional Properties 72 4.3 Topological Guarantee 73 4.3.1 The Map ν 73 4.3.2 Homeomorphism Proof 75 4.4 Notes and Exercises 76 Exercises 78 5 Undersampling 80 5.1 Samples and Boundaries 80 5.1.1 Boundary Sample Points 81 5.1.2 Flat Sample Points 82 5.2 Flatness Analysis 83 5.3 Boundary Detection 87 5.3.1 Justification 88 5.3.2 Reconstruction 89 5.4 Notes and Exercises 90 Exercises 91 6 Watertight Reconstructions 93 6.1 Power Crust 93 6.1.1 Definition 94 6.1.2 Proximity 97 6.1.3 Homeomorphism and Isotopy 99 6.1.4 Algorithm 101 6.2 Tight Cocone 104 6.2.1 Marking 105 6.2.2 Peeling 107 6.3 Experimental Results 109 6.4 Notes and Exercises 111 Exercises 111 7 Noisy Samples 113 7.1 Noise Model 113 7.2 Empty Balls 115 7.3 Normal Approximation 119 7.3.1 Analysis 119 7.3.2 Algorithm 122 7.4 Feature Approximation 124 7.4.1 Analysis 126 7.4.2 Algorithm 130 7.5 Notes and Exercises 131 Exercises 132 8 Noise and Reconstruction 133 8.1 Preliminaries 133 8.2 Union of Balls 136 8.3 Proximity 142 8.4 Topological Equivalence 144 8.4.1 Labeling 145 8.4.2 Algorithm 147 8.5 Notes and Exercises 149 Exercises 150 9 Implicit Surface-Based Reconstructions 152 9.1 Generic Approach 152 9.1.1 Implicit Function Properties 153 9.1.2 Homeomorphism Proof 154 9.2 MLS Surfaces 155 9.2.1 Adaptive MLS Surfaces 156 9.3 Sampling Assumptions and Consequences 159 9.3.1 Influence of Samples 162 9.4 Surface Properties 166 9.4.1 Hausdorff Property 167 9.4.2 Gradient Property 170 9.5 Algorithm and Implementation 172 9.5.1 Normal and Feature Approximation 172 9.5.2 Projection 173 9.6 Other MLS Surfaces 175 9.6.1 Projection MLS 175 9.6.2 Variation 176 9.6.3 Computational Issues 176 9.7 Voronoi-Based Implicit Surface 179 9.8 Notes and Exercises 180 Exercises 181 10 Morse Theoretic Reconstructions 182 10.1 Morse Functions and Flows 182 10.2 Discretization 185 10.2.1 Vector Field 185 10.2.2 Discrete Flow 187 10.2.3 Relations to Voronoi/Delaunay Diagrams 190 10.3 Reconstruction with Flow Complex 192 10.3.1 Flow Complex Construction 192 10.3.2 Merging 193 10.3.3 Critical Point Separation 194 10.4 Reconstruction with a Delaunay Subcomplex 196 10.4.1 Distance from Delaunay Balls 196 10.4.2 Classifying and Ordering Simplices 198 10.4.3 Reconstruction 201 10.4.4 Algorithm 202 10.5 Notes and Exercises 205 Exercises 205 Bibliography 207 Index 213 |
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