TY - BOOK
AU - Loera,Jesús A.De
AU - Rambau,Jörg
AU - Santos,Francisco
ED - SpringerLink (Online service)
TI - Triangulations: Structures for Algorithms and Applications
T2 - Algorithms and Computation in Mathematics,
SN - 9783642129711
AV - QA564-609
U1 - 516.35 23
PY - 2010///
CY - Berlin, Heidelberg
PB - Springer Berlin Heidelberg
KW - Mathematics
KW - Computers
KW - Computer science
KW - Algebraic geometry
KW - Computer mathematics
KW - Convex geometry
KW - Discrete geometry
KW - Discrete mathematics
KW - Algebraic Geometry
KW - Discrete Mathematics
KW - Theory of Computation
KW - Convex and Discrete Geometry
KW - Mathematics of Computing
KW - Computational Mathematics and Numerical Analysis
N1 - 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
N2 - 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
UR - http://dx.doi.org/10.1007/978-3-642-12971-1
ER -