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Algorithms in Combinatorial Geometry

Algorithms in Combinatorial Geometry

Author: Herbert Edelsbrunner

Publisher: Springer Science & Business Media

ISBN: 9783642615689

Category: Computers

Page: 423

View: 768

Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.
Algorithms in Combinatorial Geometry
Language: en
Pages: 423

Algorithms in Combinatorial Geometry

Authors: Herbert Edelsbrunner
Categories: Computers
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of
Combinatorial Geometry and Its Algorithmic Applications
Language: en
Pages: 235

Combinatorial Geometry and Its Algorithmic Applications

Authors: János Pach, Micha Sharir, Mîkā Šārîr
Categories: Mathematics
Type: BOOK - Published: 2009 - Publisher: American Mathematical Soc.

This book, based on the authors' lecture series at a 2006 satellite meeting of the International Congress of Mathematicians, offers a comprehensive survey of core areas of combinatorial geometry. These lecture notes aptly describe both the history and the state of the art of these topics. These combinatorial techniques have
Visibility Algorithms in the Plane
Language: en
Pages:

Visibility Algorithms in the Plane

Authors: Subir Kumar Ghosh
Categories: Computers
Type: BOOK - Published: 2007-03-29 - Publisher: Cambridge University Press

A human observer can effortlessly identify visible portions of geometric objects present in the environment. However, computations of visible portions of objects from a viewpoint involving thousands of objects is a time consuming task even for high speed computers. To solve such visibility problems, efficient algorithms have been designed. This
Advances in Discrete and Computational Geometry
Language: en
Pages: 463

Advances in Discrete and Computational Geometry

Authors: Bernard Chazelle, Jacob E. Goodman, Richard Pollack
Categories: Mathematics
Type: BOOK - Published: 1999 - Publisher: American Mathematical Soc.

This volume is a collection of refereed expository and research articles in discrete and computational geometry written by leaders in the field. Articles are based on invited talks presented at the AMS-IMS-SIAM Summer Research Conference, ``Discrete and Computational Geometry: Ten Years Later'', held in 1996 at Mt. Holyoke College (So.
Automated Deduction in Geometry
Language: en
Pages: 193

Automated Deduction in Geometry

Authors: Tetsuo Ida, Jacques Fleuriot
Categories: Computers
Type: BOOK - Published: 2013-09-02 - Publisher: Springer

This book constitutes the thoroughly refereed post-workshop proceedings of the 9th International Workshop on Automated Deduction in Geometry, ADG 2012, held in Edinburgh, UK, in September 2012. The 10 revised full papers presented together with 2 invited papers were carefully selected during two rounds of reviewing and improvement from the

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