Triangulations: structures for algorithms and applications

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 treatmentof 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 establishconnections 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. First comprehensive treatment of the theory of regular triangulations, secondary polytopes and related topics appearing in book form Discusses the geometric structure behind the algorithms and shows new emerging applications Theory discusses high-dimensional situations, an area that is not always covered in computational geometry Step-by-step introduction assuming very little background Hundreds of illustrations, examples, and exercises INDICE: 1 Triangulations in Mathematics.- 2 Configurations, Triangulations, Subdivisions, and Flips.- 3 Life in two Dimensions.- 4 A Tool Box.- 5 Regular Triangulations and Secondary Polytopes.- 6 Some Interesting Configurations.-7 Some Interesting Triangulations.- 8 Algorithmic Issues.- 9 Further Topics.-Bibliography.- Index

• ISBN: 978-3-642-12970-4
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 539
• Fecha Publicación: 01/08/2010
• Nº Volúmenes: 1
• Idioma: Inglés