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Sinopsis
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.
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- EditorialForgotten Books
- Año de publicación2018
- ISBN 10 1334264155
- ISBN 13 9781334264153
- EncuadernaciónTapa blanda
- IdiomaInglés
- Número de páginas36
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The Upper Envelope of Piecewise Linear Functions Algorithms and Applications Classic Reprint
Librería: PBShop.store US, Wood Dale, IL, Estados Unidos de America
Calificación del vendedor: 5 de 5 estrellas
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LX-9781334264153
Cantidad disponible: 15 disponibles
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The Upper Envelope of Piecewise Linear Functions Algorithms and Applications Classic Reprint
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
Calificación del vendedor: 4 de 5 estrellas
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LX-9781334264153
Cantidad disponible: 15 disponibles
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The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications
Impresión bajo demandaLibrería: Forgotten Books, London, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
Paperback. Condición: New. 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. print-on-demand item. Nº de ref. del artículo: 9781334264153_0
Cantidad disponible: Más de 20 disponibles