Isosurfaces: Geometry, Topology, and Algorithms

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.

Table of Contents

Chapter 1 Introduction
Chapter 2 Marching Cubes And Variants
Chapter 3 Dual Contouring
Chapter 4 Multilinear Interpolation
Chapter 5 Isosurface Patch Construction
Chapter 6 Isosurface Generation In 4D
Chapter 7 Interval Volumes
Chapter 8 Data Structures For Faster Isosurface Construction
Chapter 9 Multiresolution Tetrahedal Meshes
Chapter 10 Multiresolution Polyhedral Meshes
Chapter 11 Isovalues
Chapter 12 Contour Trees
Appendix A Geometry
Appendix B Topology
Appendix C Graph Theory
Appendix D Notation