Isosurfaces : Geometry, Topology, and Algorithms book cover
1st Edition

Geometry, Topology, and Algorithms

ISBN 9780429101861
Published June 24, 2013 by A K Peters/CRC Press
488 Pages

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Book 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. 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

Introduction. Marching Cubes and Variants. Dual Contouring. Multilinear Interpolation. Isosurface Patch Construction. Isosurface Generation in 4D. Interval Volumes. Data Structures. Multiresolution Tetrahedral Meshes. Multiresolution Polyhedral Meshes. Isovalues. Contour Trees. Appendices. Bibliography. Index.

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Rephael Wenger is an associate professor in the Department of Computer Science and Engineering at the Ohio State University. He earned a Ph.D. from McGill University. He has published over fifty papers in computational geometry, computational topology, combinatorics, geometric modeling, and visualization.


"Visualization has long needed a solid, standard and detailed text on the algorithmic aspects of isosurface construction and use. This text will become the standard entry point into this vast literature for at least the next decade, even for researchers already accustomed to working with isosurfaces. It belongs on every professional’s shelf."
—Hamish Carr, University of Leeds

"Isosurfaces are one of the most prevalent ways to visualize three-dimensional data. This wonderful book is the first that nicely summarizes the foundations as well as the state of the art on isosurfaces. Everyone, from the novice to the expert, will find something new and interesting in this book. This book's treatment of isosurfaces goes way beyond the surface, deep into the heart and soul of this rich topic situated in between the fields of graphics, visualization, and computational geometry."
—Torsten Möller, University of Vienna (Universität Wien)

"…well written, well illustrated, and extensively referenced."
—Lyuba S. Alboul, Mathematical Reviews Clippings, January 2015