Robotics Research Technical Report: Common Tangents and Common Transversals (Classic Reprint) - Softcover
Synopsis
This book explores the topological structure of common tangent hyperplanes to separated convex sets in Rd, demonstrating that under certain conditions the space of such hyperplanes is homeomorphic to a sphere of dimension d – k. The author, a leading expert in computational geometry, then exploits this result to derive sharp bounds on the complexity of the space of all common transversal hyperplanes to a given family of separated convex sets in Rd. The book provides a unique and in-depth analysis of the combinatorial structure of the space of common transversals, extending previous results known in lower-dimensional cases. It also presents an efficient algorithm for determining the space of common transversals if the convex sets are polytopal or have sufficiently simple boundaries. The insights provided in this book are significant for understanding the geometric relationships between convex sets and have applications in areas such as motion planning, robotics, and computational geometry. The author's clear and concise presentation makes this book accessible to researchers and graduate students in mathematics, computer science, and related fields.
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Robotics Research Technical Report: Common Tangents and Common Transversals
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Paperback. Condition: New. Print on Demand. This book explores the topological structure of common tangent hyperplanes to separated convex sets in Rd, demonstrating that under certain conditions the space of such hyperplanes is homeomorphic to a sphere of dimension d â" k. The author, a leading expert in computational geometry, then exploits this result to derive sharp bounds on the complexity of the space of all common transversal hyperplanes to a given family of separated convex sets in Rd. The book provides a unique and in-depth analysis of the combinatorial structure of the space of common transversals, extending previous results known in lower-dimensional cases. It also presents an efficient algorithm for determining the space of common transversals if the convex sets are polytopal or have sufficiently simple boundaries. The insights provided in this book are significant for understanding the geometric relationships between convex sets and have applications in areas such as motion planning, robotics, and computational geometry. The author's clear and concise presentation makes this book accessible to researchers and graduate students in mathematics, computer science, and related fields. 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 # 9781332087990_0
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Robotics Research Technical Report Common Tangents and Common Transversals Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332087990
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Robotics Research Technical Report Common Tangents and Common Transversals Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332087990
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ROBOTICS RESEARCH TECHNICAL RE
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Condition: New. KlappentextrnrnExcerpt from Robotics Research Technical Report: Common Tangents and Common TransversalsProof: Enlarging each K, slightly if necessary, we may assume that the sets K, are strictly convex and have non-empty interior. Seller Inventory # 2147923007
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