Download Free On The Zone Theorem For Hyperplane Arrangements Book in PDF and EPUB Free Download. You can read online On The Zone Theorem For Hyperplane Arrangements and write the review.

Abstract: "The zone theorem for an arrangement of n hyperplanes in d-dimensional real space says that the total number of faces bounding the cells intersected by another hyperplane is O(n[superscript d-1]). This result is the basis of a time-optimal incremental algorithm that constructs a hyperplane arrangement and has a host of other algorithmic and combinatorial applications. Unfortunately, the original proof of the zone theorem, for d[greater than or equal to]3, turned out to contain a serious and irreparable error. This paper presents a new proof of the theorem. Our proof is based on an inductive argument, which also applies in the case of pseudo-hyperplane arrangements. We also briefly discuss the fallacies of the old proof along with some ways of partially saving that approach."
Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.
This volume presents the proceedings of the Second Workshop on Algorithms and Data Structures (WADS '91), held at Carleton University in Ottawa. The workshop was organized by the School of Computer Science at Carleton University. The workshop alternates with the Scandinavian Workshop on Algorithm Theory (SWAT), continuing the tradition of SWAT '88 (LNCS, Vol. 318), WADS '89 (LNCS, Vol. 382), and SWAT '90 (LNCS, Vol. 447). From 107 papers submitted, 37 were selected for presentation at the workshop. In addition, there were 5 invited presentations.
"Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks. "Combinatorial Geometry and Its Algorithmic Applications" is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography."--BOOK JACKET.
A comprehensive treatment of a fundamental tool for solving problems in computational and combinatorial geometry.
Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic in formation systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self-study.
The design and analysis of geometric algorithms have seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD. The goals of this book are twofold: first to provide a coherent and systematic treatment of the foundations; secondly to present algorithmic solutions that are amenable to rigorous analysis and are efficient in practical situations. When possible, the algorithms are presented in their most general d-dimensional setting. Specific developments are given for the 2- or 3-dimensional cases when this results in significant improvements. The presentation is confined to Euclidean affine geometry, though the authors indicate whenever the treatment can be extended to curves and surfaces. The prerequisites for using the book are few, which will make it ideal for teaching advanced undergraduate or beginning graduate courses in computational geometry.
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.
This volume contains selected papers from the symposium "New Results and NewTrends in Computer Science" held in Graz, Austria, June 20-21, 1991. The symposium was organized to give a wide-ranging overview of new work in the field on the occasion of the fiftieth birthday of the editor of the volume. Topics covered include: information on neural nets, ideas on a new paradigm for informatics, hypermedia systems and applications, axioms for concurrent processes, techniques for image generation and compression, the role of data visualization, object-oriented programming andgraphics, algorithms for layout compaction, new methods in database systems, the future of data networks, object-oriented artificial intelligence, problems in data structures and sorting, aspects of user interfaces, a theory of structures, applications of cryptography, evaluation of Ada, results in algorithmic geometry, remarks on the history of computers, and a novel interpretation of machine learning. In total, the 26 high-level contributions authored by prominent experts from all over the world give an up-to-date survey of almost all subfields of computer science. The book is written in a style which is easy to follow, and it is of interest for any computer scientist, be it in research, teaching or practice.