Robotics Research Technical Report: The Complexity of Many Cells in Arrangements of Planes and Related Problems (Classic Reprint) - Softcover
Synopsis
Understand how complex shapes form when many planes intersect
Learn how researchers bound the number of faces in multi-plane arrangements and design efficient algorithms to compute them. This edition presents core ideas, from three-dimensional arrangements to higher dimensions, with accessible explanations of the techniques used to tame combinatorial complexity.
In this work, the authors analyze the complexity of many cells formed by n planes in 3D space and extend the results to higher dimensions. They introduce a constructive approach that combines divide-and-conquer with random sampling to split problems into smaller pieces, then recombine the results. The methods yield sharp upper bounds on the number of facets bounding cells and on incidences between points and planes, while also offering randomized algorithms that run efficiently in practice.
- How to model and measure the complexity of cell boundaries in plane arrangements
- Techniques for decomposing problems into smaller subproblems using random samples
- Recurrence-driven analysis that leads to near-tight upper bounds in multiple dimensions
- Output-sensitive algorithms for computing cells and incidences in arrangements
Ideal for readers of computational geometry, discrete mathematics, and advanced algorithm design who want a rigorous yet practical view of these classic problems.
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Robotics Research Technical Report (Classic Reprint)
Print on DemandSeller: Forgotten Books, London, United Kingdom
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Paperback. Condition: New. Print on Demand. This book explores the intricate relationships between points and planes, particularly in three-dimensional space and to a lesser extent in higher dimensions. The text begins by defining what is meant by an arrangement of planes and then goes on to consider the complexity of such arrangements, or, in other words, how complicated they can be. The author establishes both upper and lower bounds on this complexity, providing a precise understanding of the possible configurations of points and planes. The book also investigates the problem of counting the number of incidences between points and planes, with the author obtaining sharp bounds on the maximum number of such incidences. These results have important implications for various fields, including computational geometry, which deals with problems related to the representation and manipulation of geometric objects. 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. Seller Inventory # 9781332115365_0
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Robotics Research Technical Report The Complexity of Many Cells in Arrangements of Planes and Related Problems Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332115365
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Robotics Research Technical Report The Complexity of Many Cells in Arrangements of Planes and Related Problems Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332115365
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