Inhaltsangabe
Excerpt from Triangles in Space or Building (and Analyzing) Castles in the Air
At various points in our analysis we will have to consider planar arrangements of segments which are similar to the 3-dimensional case, partitions of a plane into faces, edges, and vertices induced by a collection of segments in that plane. As a bounded face of such an arrangement need not be simply connected, its boundary will in general consist of a single outer component that encloses the entire face and zero or more islands each enclosing a portion of the plane that does not belong to the face. An unbounded face has a similar structure, except its boundary does not have anouter component.
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Triangles in Space or Building (and Analyzing) Castles in the Air
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Paperback. Zustand: New. Print on Demand. This book delves into the fascinating world of three-dimensional arrangements of triangles, exploring their combinatorial complexity and offering insights into the broader field of computational geometry. The book begins by laying a solid foundation in the basics of arrangements and their properties, providing readers with a comprehensive understanding of this complex subject. It then delves into the intricate problem of analyzing the combinatorial structure of individual cells within such arrangements, presenting novel techniques to determine their exact complexity. The author also delves into the complexities of obtaining both worst-case and average-case bounds on the combinatorial complexities, showcasing both theoretical and practical applications of these concepts. Throughout the book, the author draws connections between this specialized topic and its wider implications in motion planning, robotics, and other related fields. By providing a comprehensive exploration of the subject and its broader significance, this book establishes itself as an invaluable resource for researchers and practitioners working in computational geometry and related disciplines. 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. Bestandsnummer des Verkäufers 9781334013997_0
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