Isosurfaces: geometry, topology, and algorithms

Description

"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. This book presents the basic algorithms for isosurface construction and gives a rigorous mathematical perspective to some of the algorithms and results. It offers a solid introduction to research in this area as well as an organized overview of the various algorithms associated with isosurfaces"-- Read more... Content: 1. Introduction -- 2. Marching cubes and variants -- 3. Dual contouring -- 4. Multilinear interpolation -- 5. Isosurface patch construction -- 6. Isosurface generation in 4D -- 7. Interval volumes -- 8. Data structures -- 9. Multiresolution tetrahedral meshes -- 10. Multiresolution polyhedral meshes -- 11. Isovalues -- 12. Contour trees -- A. Geometry -- B. Topology -- C. Graph theory -- D. Notation. Abstract: "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. This book presents the basic algorithms for isosurface construction and gives a rigorous mathematical perspective to some of the algorithms and results. It offers a solid introduction to research in this area as well as an organized overview of the various algorithms associated with isosurfaces"