Download or read book Arrangements of Curves in the Plane written by University of Illinois at Urbana-Champaign. Department of Computer Science and published by . This book was released on 1988 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arrangements of curves in the plane are fundamental to many problems in computational and combinatorial geometry (e.g. motion planning, algebraic cell decomposition, etc.). In this paper we study various topological and combinatorial properties of such arrangements under some mild assumptions on the shape of the curves, and develop basic tools for the construction, manipulation, and analysis of these arrangements. Our main results include a generalization of the zone theorem of [EOS], [CGL] to arrangements of curves (in which we show that the combinatorial complexity of the zone of a curve is nearly linear in the number of curves), and an application of that theorem to obtain a nearly quadratic incremental algorithm for the construction of such arrangements.
Download or read book Arrangements of Curves in the Plane Topology Combinatorics and Algorithms Classic Reprint written by Herbert Edelsbrunner and published by Forgotten Books. This book was released on 2018-02-11 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Arrangements of Curves in the Plane Topology, Combinatorics, and Algorithms Theorem. Let A be an arrangement of 11 lines and let I be another line. Then the total number of edges bounding the faces of A that intersect I is O(u). We refer to the collection of all these edges as the zone of I in A. One useful application of this theorem is that it facilitates the construction of the arrangement ahi of u+1 lines from the arrangement An of the first 71 lines in linear time as follows. Assume without loss of generality that I =in+1 is the z - axis. First find the leftmost unbounded face of A crossed by I. Next process the faces of An crossed by I from left to right. At each such face I find the rightmost point of 10 f this will determine the next face I of An crossed by I and the process is then repeated for f'. The crossing points of I with the boundaries of the faces in An are found by traversing all edges in the zone of I; the number of such edges is O(u) by the Zone Theorem. For each of these faces f the algorithm also splits f into two new faces in Au, and updates (also in linear time) the planar map representation of the arrangement. The resulting sequence of incremental updates yields an overall optimal C(uz) algorithm for the calculation of arrangements of 11 lines. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book ARRANGEMENTS OF CURVES IN THE PLANE TOPOLOGY COMBINATORICS AND ALGORITHMS written by HERBERT. EDELSBRUNNER and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Arrangement of the Real Branches of Plane Algebraic Curves written by Virginia Ragsdale and published by . This book was released on 1906 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Arrangements of Curves in the Plane Topology Combinatorics and Algorithms Primary Source Edition written by Herbert Edelsbrunner and published by Nabu Press. This book was released on 2013-09 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
Download or read book Intersection and Decomposition Algorithms for Arrangements of Curves in the Plane written by Pankaj K. Agarwal and published by . This book was released on 1989 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Plane Algebraic Curves written by Gerd Fischer and published by American Mathematical Soc.. This book was released on 2001 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an excellent introduction to algebraic geometry, which assumes only standard undergraduate mathematical topics: complex analysis, rings and fields, and topology. Reading this book will help establish the geometric intuition that lies behind the more advanced ideas and techniques used in the study of higher-dimensional varieties.
Download or read book On The Arrangement Of The Real Branches Of Plane Algebraic Curves written by Virginia Ragsdale and published by Legare Street Press. This book was released on 2023-07-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A foundational work in the study of plane algebraic curves and their real branches, including solutions to complex equations and geometric constructions. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book Topological Invariants of the Complement to Arrangements of Rational Plane Curves written by José Ignacio Cogolludo-Agustín and published by American Mathematical Soc.. This book was released on 2002 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors analyse two topological invariants of an embedding of an arrangement of rational plane curves in the projective complex plane, namely, the cohomology ring of the complement and the characteristic varieties. Their main result states that the cohomology ring of the complement to a rational arrangement is generated by logarithmic 1 and 2-forms and its structure depends on a finite number of invariants of the curve (its combinatorial type).
Download or read book Lectures on the Theory of Plane Curves written by Surendramohan Ganguli and published by . This book was released on 1919 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Arrangements and Spreads written by Branko Grnbaum and published by American Mathematical Soc.. This book was released on 1972-12-31 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Treatise on Algebraic Plane Curves written by Julian Lowell Coolidge and published by Courier Corporation. This book was released on 2004-01-01 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are much employed, however, especially those involving the projective geometry of hyperspace. 1931 edition. 17 illustrations.
Download or read book CGAL Arrangements and Their Applications written by Efi Fogel and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arrangements of curves constitute fundamental structures that have been intensively studied in computational geometry. Arrangements have numerous applications in a wide range of areas – examples include geographic information systems, robot motion planning, statistics, computer-assisted surgery and molecular biology. Implementing robust algorithms for arrangements is a notoriously difficult task, and the CGAL arrangements package is the first robust, comprehensive, generic and efficient implementation of data structures and algorithms for arrangements of curves. This book is about how to use CGAL two-dimensional arrangements to solve problems. The authors first demonstrate the features of the arrangement package and related packages using small example programs. They then describe applications, i.e., complete standalone programs written on top of CGAL arrangements used to solve meaningful problems – for example, finding the minimum-area triangle defined by a set of points, planning the motion of a polygon translating among polygons in the plane, computing the offset polygon, finding the largest common point sets under approximate congruence, constructing the farthest-point Voronoi diagram, coordinating the motion of two discs moving among obstacles in the plane, and performing Boolean operations on curved polygons. The book contains comprehensive explanations of the solution programs, many illustrations, and detailed notes on further reading, and it is supported by a website that contains downloadable software and exercises. It will be suitable for graduate students and researchers involved in applied research in computational geometry, and for professionals who require worked-out solutions to real-life geometric problems. It is assumed that the reader is familiar with the C++ programming-language and with the basics of the generic-programming paradigm.
Download or read book Singular Points of Plane Curves written by C. T. C. Wall and published by Cambridge University Press. This book was released on 2004-11-15 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Download or read book Constructive Geometry of Plane Curves written by Thomas Henry Eagles and published by . This book was released on 1885 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Links and Complements of Arrangements of Complex Projective Plane Algebraic Curves written by Angelo Di Pasquale and published by . This book was released on 1999 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Plane Curves of the Third Order written by Henry Seely White and published by . This book was released on 1925 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
