Triangulations: Structures for Algorithms and Applications

✍ Scribed by Jesús A. De Loera, Jörg Rambau, Francisco Santos (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2010
• Tongue: English
• Leaves: 550
• Series: Algorithms and Computation in Mathematics 25
• Edition: 1
• Category: Library

✦ Synopsis

Triangulations appear everywhere, from volume computations and meshing to algebra and topology. This book 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. A central theme of the book is the use of the rich structure of the space of triangulations to solve computational problems (e.g., counting the number of triangulations or finding optimal triangulations with respect to various criteria), and to establish connections to applications in algebra, computer science, combinatorics, and optimization. With many examples and exercises, and with nearly five hundred illustrations, the book gently guides readers through the properties of the spaces of triangulations of "structured" (e.g., cubes, cyclic polytopes, lattice polytopes) and "pathological" (e.g., disconnected spaces of triangulations) situations using only elementary principles.

✦ Table of Contents

Front Matter....Pages i-xiii
Triangulations in Mathematics....Pages 1-41
Configurations, Triangulations, Subdivisions, and Flips....Pages 43-92
Life in Two Dimensions....Pages 93-148
A Tool Box....Pages 149-208
Regular Triangulations and Secondary Polytopes....Pages 209-274
Some Interesting Configurations....Pages 275-336
Some Interesting Triangulations....Pages 337-376
Algorithmic Issues....Pages 377-432
Further Topics....Pages 433-511
Back Matter....Pages 513-535

✦ Subjects

Convex and Discrete Geometry; Mathematics of Computing; Computational Mathematics and Numerical Analysis; Combinatorics; Algorithms