Isosurfaces : geometry, topology, and algorithms
- Rephael Wenger.
- Boca Raton : CRC Press, 2013.
- Physical description
- xiii, 474 pages : illustrations (chiefly color) ; 25 cm
Math & Statistics Library
|QA573 .W46 2013||Unknown|
- Wenger, Rephael.
- Includes bibliographical references (pages 453-467) and index.
- 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.
- (source: Nielsen Book Data)9781466570979 20160612
- Publisher's Summary
- Ever since Lorensen and Cline published their paper on the Marching Cubes algorithm, isosurfaces have been a standard technique for the visualization of 3D volumetric data. Yet there is no book exclusively devoted to isosurfaces. Isosurfaces: Geometry, Topology, and Algorithms represents the first book to focus on basic algorithms for isosurface construction. It also gives a rigorous mathematical perspective on some of the algorithms and results. In color throughout, the book covers the Marching Cubes algorithm and variants, dual contouring algorithms, multilinear interpolation, multiresolution isosurface extraction, isosurfaces in four dimensions, interval volumes, and contour trees. It also describes data structures for faster isosurface extraction as well as methods for selecting significant isovalues. For designers of visualization software, the book presents an organized overview of the various algorithms associated with isosurfaces. For graduate students, it provides a solid introduction to research in this area. For visualization researchers, the book serves as a reference to the vast literature on isosurfaces.
(source: Nielsen Book Data)9781466570979 20160612
- Publication date
- "An AK Peters Book."
- 9781466570979 (hardback)
- 1466570970 (hardback)
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