Synopsis
Excerpt from Separating Two Simple Polygons, by a Sequence of Translations
Let P and Q be two disjoint simple polygons having m and n sides respectively. We present an algorithm which determines whether Q can be moved by a sequence of translations to a position sufficiently far from P without colliding with P, and which produces such a motion if it exists. Our algorithm runs in time O(mn a(mn) log m log n) where a(k) is the extremely slowly growing inverse Ackermann's function. Since. In the worst ease O(mn) translations may be necessary to separate Q from P, our algorithm is close to optimal.
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Separating Two Simple Polygons, by a Sequence of Translations (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book presents an innovative algorithm to determine whether two disjoint simple polygons can be moved by a sequence of translations to a position sufficiently far from each other without colliding, and if so, produces such a motion. The algorithm can also determine whether a given polygon can be separated from another using a specified number of translations, and if so, produces a motion using the smallest number of translations or a motion with the shortest total translational distance. The problem that this book addresses is a special instance of the motion planning problem that seeks a purely translational collision-free motion of a polygonal object amidst a collection of polygonal obstacles. The author has shown that the existence of a motion of this type can be determined in time that is close to optimal. 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 # 9781332194605_0
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Separating Two Simple Polygons, by a Sequence of Translations Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332194605
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Separating Two Simple Polygons, by a Sequence of Translations Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332194605
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