Surveys on Discrete and Computational Geometry PDF Download

Author: Jacob E. Goodman
Publisher: American Mathematical Soc.
ISBN: 0821842390
Category : Combinatorial geometry
Languages : en
Pages : 568

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Book Description
This volume contains nineteen survey papers describing the state of current research in discrete and computational geometry as well as a set of open problems presented at the 2006 AMS-IMS-SIAM Summer Research Conference Discrete and Computational Geometry--Twenty Years Later, held in Snowbird, Utah, in June 2006. Topics surveyed include metric graph theory, lattice polytopes, the combinatorial complexity of unions of geometric objects, line and pseudoline arrangements, algorithmic semialgebraic geometry, persistent homology, unfolding polyhedra, pseudo-triangulations, nonlinear computational geometry, $k$-sets, and the computational complexity of convex bodies.

Author: Janos Pach
Publisher: Springer Science & Business Media
ISBN: 3642580432
Category : Mathematics
Languages : en
Pages : 342

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Book Description
Discrete and computational geometry are two fields which in recent years have benefitted from the interaction between mathematics and computer science. The results are applicable in areas such as motion planning, robotics, scene analysis, and computer aided design. The book consists of twelve chapters summarizing the most recent results and methods in discrete and computational geometry. All authors are well-known experts in these fields. They give concise and self-contained surveys of the most efficient combinatorical, probabilistic and topological methods that can be used to design effective geometric algorithms for the applications mentioned above. Most of the methods and results discussed in the book have not appeared in any previously published monograph. In particular, this book contains the first systematic treatment of epsilon-nets, geometric tranversal theory, partitions of Euclidean spaces and a general method for the analysis of randomized geometric algorithms. Apart from mathematicians working in discrete and computational geometry this book will also be of great use to computer scientists and engineers, who would like to learn about the most recent results.

Author: Jiri Matousek
Publisher: Springer Science & Business Media
ISBN: 1461300398
Category : Mathematics
Languages : en
Pages : 491

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Book Description
The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.

Author: Jacob E. Goodman
Publisher: American Mathematical Soc.
ISBN: 9780821865958
Category : Mathematics
Languages : en
Pages : 378

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Book Description
The first DIMACS special year, held during 1989-1990, was devoted to discrete and computational geometry. The workshops addressed the following topics: geometric complexity, probabilistic methods in discrete and computational geometry, polytopes and convex sets, arrangements, and algebraic and practical issues in geometric computation. This volume presents results of the workshops and the special year activities. Containing both survey articles and research papers, this collection presents an excellent overview of discrete and computational geometry. The diversity of these papers demonstrate how geometry continues to provide a vital source of ideas in theoretical computer science and discrete mathematics as well as fertile ground for interaction and stimulation between the two disciplines.

Author: Jacob E. Goodman
Publisher: Cambridge University Press
ISBN: 9780521848626
Category : Computers
Languages : en
Pages : 640

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Book Description
This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.

Author: Peter Brass
Publisher: Springer Science & Business Media
ISBN: 0387238158
Category : Mathematics
Languages : en
Pages : 507

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Book Description
This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.

Author: Bernard Chazelle
Publisher: American Mathematical Soc.
ISBN: 0821806742
Category : Mathematics
Languages : en
Pages : 463

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Book Description
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. Hadley, MA). Topics addressed range from tilings, polyhedra, and arrangements to computational topology and visibility problems. Included are papers on the interaction between real algebraic geometry and discrete and computational geometry, as well as on linear programming and geometric discrepancy theory.

Author: Jin Akiyama
Publisher: Springer Nature
ISBN: 3030900487
Category : Computers
Languages : en
Pages : 196

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Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the 21st Japanese Conference on Discrete and Computational Geometry and Graphs, JCDCGGG 2018, held in Quezon City, Philippines, in September 2018. The total of 14 papers included in this volume was carefully reviewed and selected from 25 submissions. The papers feature advances made in the field of computational geometry and focus on emerging technologies, new methodology and applications, graph theory and dynamics.

Author: Satyan L. Devadoss
Publisher: Princeton University Press
ISBN: 1400838983
Category : Mathematics
Languages : en
Pages : 270

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Book Description
An essential introduction to discrete and computational geometry Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only).

Author: Boris Aronov
Publisher: Springer Science & Business Media
ISBN: 3642555667
Category : Mathematics
Languages : en
Pages : 853

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Book Description
An impressive collection of original research papers in discrete and computational geometry, contributed by many leading researchers in these fields, as a tribute to Jacob E. Goodman and Richard Pollack, two of the ‘founding fathers’ of the area, on the occasion of their 2/3 x 100 birthdays. The topics covered by the 41 papers provide professionals and graduate students with a comprehensive presentation of the state of the art in most aspects of discrete and computational geometry, including geometric algorithms, study of arrangements, geometric graph theory, quantitative and algorithmic real algebraic geometry, with important connections to algebraic geometry, convexity, polyhedral combinatorics, the theory of packing, covering, and tiling. The book serves as an invaluable source of reference in this discipline.