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Arrangements of Curves in the Plane Topology, Combinatorics, and Algorithms (Classic Reprint) - Brossura
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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.
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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.
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- EditoreForgotten Books
- Data di pubblicazione2018
- ISBN 10 1334013810
- ISBN 13 9781334013812
- RilegaturaCopertina flessibile
- Numero di pagine28
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Arrangements of Curves in the Plane Topology, Combinatorics, and Algorithms
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Paperback. Condizione: New. Print on Demand. This book presents a study of arrangements of curves in the plane. These arrangements are fundamental to many problems in computational and combinatorial geometry, such as motion planning, algebraic cell decomposition, and geometric optimization. The author develops basic tools for the construction, manipulation, and analysis of these arrangements, and provides a generalization of the zone theorem of Chazelle, Edelsbrunner, and Guibas. This theorem states that the combinatorial complexity of the zone of a curve is nearly linear in the number of curves, and the author shows that this result can be applied to obtain a nearly quadratic incremental algorithm for the construction of such arrangements. The book also includes a discussion of the topological and combinatorial properties of these arrangements, and provides new insights into the combinatorial complexity of a single component in an arrangement of triangles in three-dimensional space. The work presented in this book has important implications for a wide range of problems in computational geometry, and provides a valuable resource for researchers and practitioners in this field. Forgotten Books publishes hundreds of thousands of rare and classic books. 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. The digital edition of all books may be viewed on our website before purchase. print-on-demand item. Codice articolo 9781334013812_0
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Arrangements of Curves in the Plane Topology, Combinatorics, and Algorithms Classic Reprint
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LX-9781334013812
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Arrangements of Curves in the Plane Topology, Combinatorics, and Algorithms Classic Reprint
Da: PBShop.store UK, Fairford, GLOS, Regno Unito
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LX-9781334013812
Quantità: 15 disponibili