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The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications (Classic Reprint) - Hardcover
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Inhaltsangabe
Excerpt from The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications
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.
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.
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Excerpt from The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications
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.
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.
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- VerlagForgotten Books
- Erscheinungsdatum2018
- ISBN 10 0267960271
- ISBN 13 9780267960279
- EinbandTapa dura
- SpracheEnglisch
- Anzahl der Seiten34
- Kontakt zum HerstellerNicht verfügbar
(Keine Angebote verfügbar)
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