Triangulations : structures for algorithms and applications
QA197 .D45 2010
- Unknown QA197 .D45 2010
- Includes bibliographical references (p. -530) and index.
- Triangulations in Mathematics.- Configurations, Triangulations, Subdivisions, and Flips.- Life in Two Dimensions.- A Tool Box.- Regular Triangulations and Secondary Polytopes.- Some Interesting Configurations.- Some Interesting Triangulations.- Algorithmic Issues.- Further Topics.
- (source: Nielsen Book Data)
- Publisher's Summary
- Triangulations appear in many different parts of mathematics and computer science since they are the natural way to decompose a region of space into smaller, easy-to-handle pieces. From volume computations and meshing to algebra and topology, there are many natural situations in which one has a ?xed set of points that can be used as vertices for the triangulation. Typically one wants to ?nd an optimal triangulation of those points or to explore the set of their all triangulations. The given points may represent the "sites" for a Delaunay triangulation computation, d thetest pointsfora surfacereconstruction, ora set ofmonomials, representedaslattice pointsinZ , inanalgebra- geometric meaning. A central theme of this book is to use the rich geometric structure of the space of triangulations of a given set of points to solve computational problems (e.g., counting the number of triangulations or ?nding optimal triangulations with respect to various criteria), and for setting up connections to novel applications in algebra, computer science, combinatorics, and optimization. Thus at the heart of the book is a comprehensive treatment of the theory of regular subdivisions, secondary polytopes, ?ips, chambers, and their interactions. Again, we ?rmly believe that understandingthe fundamentsof geometry and combinatoricspays up for algorithmsand applications.
(source: Nielsen Book Data)
- Supplemental links
Table of contents
Table of contents
- Publication date
- Jesús A. De Loera, Jörg Rambau, Francisco Santos.
- Algorithms and computation in mathematics, 1431-1550 ; v. 25
- "With 550 figures and 14 tables"--T.p.