Isosurfaces —— Geometry, Topology, and Algorithms

----- 等值面：几何、拓扑结构和算法

ISBN: 9781466570979 出版年：2013 页码：484 Wenger, Rephael CRC Press

Introduction What Are Isosurfaces? Applications of Isosurfaces Isosurface Properties Isosurface Construction Limitations of Isosurfaces Multi-Valued Functions and Vector Fields Definitions and Basic Techniques Marching Cubes and Variants Definitions Marching Squares Marching Cubes Marching Tetrahedra Dual Contouring Definitions Surface Nets Dual Marching Cubes Comparison with Marching Cubes Multilinear Interpolation Bilinear Interpolation: 2D The Asymptotic Decider: 3D Trilinear Interpolation Isosurface Patch Construction Definitions and Notation Isosurface Patch Construction Isosurface Table Construction Marching Polyhedra Algorithm Isohull Isosurface Generation in 4D Definitions and Notation Isosurface Table Generation in 4D Marching Hypercubes Marching Simplices Marching Polytopes 4D Isohull 4D Surface Nets Interval Volumes Definitions and Notation MCVol Automatic Table Generation MCVol Interval Volume Properties Tetrahedral Meshes Convex Polyhedral Meshes Data Structures Uniform Grid Partitions Octrees Span Space Priority Trees Seed Sets Multiresolution Tetrahedral Meshes Bisection of Tetrahedra Multiresolution Isosurfaces Multiresolution Polyhedral Meshes Multiresolution Convex Polyhedral Mesh Multiresolution Surface Nets Multiresolution in 4D Isovalues Counting Grid Vertices Counting Grid Edges and Grid Cubes Measuring Gradients Contour Trees Examples of Contour Trees Definition of Contour Tree Join, Split and Merge Trees Constructing Join, Split and Merge Trees Constructing Contour Trees Theory and Proofs Simplification of Contour Trees Applications Appendix A: Geometry Appendix B: Topology Appendix C: Graph Theory Appendix D: Notation Bibliography Index Notes and Comments appear at the end of each chapter.