The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications
Language: English
Published by Forgotten Books, 2024
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
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Condition: New
£ 13.26
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Print on Demand. This book delves into the fascinating realm of piecewise linear functions and their envelopes, exploring their applications in computational geometry. The author skillfully navigates through topics such as hidden line/surface elimination, motion planning, transversals of polytopes, and Voronoi diagrams, providing both combinatorial and computational insights. Building upon established combinatorial bounds, the book presents efficient algorithms for calculating envelopes of piecewise linear functions. It delves into special cases and extensions, addressing scenarios where functions intersect or where they are represented by half-hyperplanes or disjoint simplices. The thematic depth of this book lies in its exploration of the intricate relationship between piecewise linear functions and geometric problems. It reveals how envelopes provide a powerful framework for understanding and solving problems in diverse areas of computational geometry. From visualizing complex objects to planning collision-free paths for robots, the book showcases the versatility and practical significance of these mathematical concepts. By bridging the gap between theory and application, this book offers valuable insights into the power of piecewise linear functions as a tool for geometric analysis and algorithm design. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781334264153_0
- Title
- The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications
- Author
- Herbert Edelsbrunner, L. Guibus
- Publisher
- Forgotten Books
- Publication year
- 2024
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1334264155
- ISBN 13
- 9781334264153
- Seller catalogs
- Geometry
This section presents an algorithm for constructing the upper envelope of a set of n triangles in three dimensions. The algorithm follows the outline of the proof in [ps] that shows that the combinatorial complexity of this envelope is At several points we have to introduce intricate algorithmic tools in order to get a worst - case optimal algorithm. For some of these tools the complexity goes up more than desired when we generalize them to four and higher dimensions. This explains why we do not have an optimal (or even near-optimal) method for computing envelopes in four or higher dimensions yet. After presenting and analyzing the algo rithm, we study a few extensions of envelope constructions. These will lead to several computational and combinatorial results used in later sections of this paper.
We next present the algorithm that constructs the upper envelope of a set, S, of n triangles in three dimensions. Whenever convenient in the discussion we will make implicit assumptions about the triangles being in general position. The main reason isthat we hope to get the point across if we leave out tedious complications. We see the general method, called the simulation of simplicity, described in [bm] (see also Elf), as a justification of this sloppy attitude.
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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.
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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.
This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.
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