Triangulations

Structures for Algorithms and Applications

  • Jesús A. De Loera
  • Jörg Rambau
  • Francisco Santos

Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 25)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Jesús A. De Loera, Jörg Rambau, Francisco Santos
    Pages 1-41
  3. Jesús A. De Loera, Jörg Rambau, Francisco Santos
    Pages 43-92
  4. Jesús A. De Loera, Jörg Rambau, Francisco Santos
    Pages 93-148
  5. Jesús A. De Loera, Jörg Rambau, Francisco Santos
    Pages 149-208
  6. Jesús A. De Loera, Jörg Rambau, Francisco Santos
    Pages 209-274
  7. Jesús A. De Loera, Jörg Rambau, Francisco Santos
    Pages 275-336
  8. Jesús A. De Loera, Jörg Rambau, Francisco Santos
    Pages 337-376
  9. Jesús A. De Loera, Jörg Rambau, Francisco Santos
    Pages 377-432
  10. Jesús A. De Loera, Jörg Rambau, Francisco Santos
    Pages 433-511
  11. Back Matter
    Pages 513-535

About this book

Introduction

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.

Keywords

Graph algorithms computational geometry convex geometry polyhedral subdivisions polytopes triangulations

Authors and affiliations

  • Jesús A. De Loera
    • 1
  • Jörg Rambau
    • 2
  • Francisco Santos
    • 3
  1. 1.Department of MathematicsUniversity of California, DavisDavisUSA
  2. 2.Lehrstuhl für WirtschaftsmathematikUniversität BayreuthBayreuthGermany
  3. 3.Depto. Matemáticas Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-12971-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-12970-4
  • Online ISBN 978-3-642-12971-1
  • Series Print ISSN 1431-1550
  • About this book