Author : Herbert Edelsbrunner
Publisher : Forgotten Books
ISBN 13 : 9781334013812
Total Pages : 26 pages
Book Rating : 4.0/5 (138 download)
Book Synopsis Arrangements of Curves in the Plane Topology, Combinatorics, and Algorithms (Classic Reprint) by : Herbert Edelsbrunner
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 2016-10-20 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 n lines and let I be another line. Then the total number of edges bounding the faces of A that intersect I is 0(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 n]1 lines from the arrangement An of the first n lines in linear time as follows. Assume without loss of generality that I =ln+1 is the r - 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 (d 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 A, are found by traversing all edges in the zone of I; the number of such edges is 0(u) by the Zone Theorem. For each of these faces f, the algorithm also splits into two new faces in An, and updates (also in linear time) the planar map representation of the arrangement. The resulting sequence of incremental updates yields an overall optimal 0(uz) algorithm for the calculation of arrangements of 12 lines. The zone theorem has found other applications, some of which are described in [ed]. 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.
