３角形分割：アルゴリズムと応用の構造 Triangulations : Structures for Algorithms and Applications (Algorithms and Computation in Mathematics) 〈Vol. 25〉

Loera, Jesus A./ Rambau, Joerg/ Santos Leal, Francisco

Springer（2010/09発売）

• 製本 Hardcover:ハードカバー版／ページ数 539 p.／サイズ 430 illus., 215 in color
• 商品コード 9783642129704

基本説明

Studies the subdivisions and triangulations of polyhedral regions and point sets and presents the first comprehensive treatment of the theory of secondary polytopes and related topics.

Full Description

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.