Synopsis
Unraveling closed planar curves, constructively.
This book presents a practical take on Hopf’s theorem for polygons. It shows how to move from abstract results to a concrete, step-by-step method you can implement.
In clear, accessible terms, you’ll learn how polygons can be transformed into a standard form and how a linear-time algorithm finds those steps. The approach builds a unique normal form for each class and demonstrates why a quadratic number of moves suffices to reach it.- How to model closed curves as polygons and define equivalent transformations
- How to reduce any polygon to a canonical “star” form on a circle
- A linear-time algorithm to compute a sequence of transformations
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About the Author
Prof. Kurt Mehlhorn was appointed a Fellow of the ACM (1999) "for important contributions in complexity theory and in the design, analysis, and practice of combinatorial and geometric algorithms." A Professor of Computer Science at Saarland University since 1975, and a director of the Max-Plack-Institut fA1/4r Informatik in SaarbrA1/4cken, he has coauthored over 250 refereed papers/articles, in collaboration with 200 researchers. Other awards include the Leibniz Award of the German Research Foundation in 1986 and the Konrad Zuse Medal of the German Society for Informatics in 1995.
Prof. Peter Sanders is a Professor of Computer Science at the University of Karlsruhe. A leading researcher in the area of theoretical and experimental algorithm analysis, in particular related to efficient algorithms for parallel processing and communication in networks, his responsibilities include organizing the European Symposium on Algorithms in Karlsruhe in 2008.
The authors have considerable experience teaching on the topic of algorithms and working on related industrial projects.
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Constructive Hopf's Theorem, or How to Untangle Closed Planar Curves
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Paperback. Condition: New. Print on Demand. This book presents a constructive proof of Hopf's theorem, providing a groundbreaking algorithmic approach to untangling closed planar curves. The author's direct proof offers quantitative and complexity information implicit in the result. The text delves into the classication of polygons, utilizing a unique approach that involves transformations such as insertion, deletion, and translation. This work advances the field of computational geometry, providing valuable insights into the behavior of closed curves and their classification. 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 # 9781332870813_0
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