Robotics Research Technical Report: Computing the Geodesic Center of a Simple Polygon (Classic Reprint) - Softcover
Synopsis
Find the geodesic center of a simple polygon with a clear, step-by-step algorithm that runs in near‑linear time.
This book presents the problem of locating the geodesic center inside a polygonal region and explains how it differs from the standard Euclidean facility location problem. It outlines the key ideas behind triangulation, a specialized search through diagonals, and a sequence of techniques that turn a geometric question into a tractable optimization task. The authors describe how to build shortest-path trees, use tangent lines to constrain the search, and apply Megiddo’s linear-time ideas to narrow the region where the center lies. The result is a practical method with concrete time bounds for computing the geodesic center.
What you’ll experience- A guided overview of the geodesic center concept and its geometric underpinnings.
- Step-by-step description of the main algorithm, including RELCEN and GEOCEN.
- Insight into how to reduce a geometric problem to a min‑max optimization over a family of distance functions.
- Discussion of related problems in polygon geometry and the best known approaches at the time.
- A concise path from triangulation to a final, verifiable center, with attention to computational efficiency and implementation considerations.
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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 introduces an algorithm designed to locate the geodesic center of a simple polygon, which is a point inside the polygon with the minimal maximum distance to any point within the polygon. This geodesic center problem is an expansion of the classic Euclidean facility location problem, where the objective is to find the point that minimizes the distance between the facility and the furthest point in a given set. The algorithm provided by the author calculates the geodesic center of a simple polygon in time O(n log2n), where n is the number of vertices in the polygon. This is an improvement over the existing algorithm by Asano and Toussaint, which achieves O(n4log n) time complexity. The book explores the geometric definitions of geodesic diameter and geodesic center, and explains how to compute the geodesic diameter of a given polygon using a method by Suri. It also discusses topics such as the link diameter and link center, P-convex sets, and shortest path trees within a polygon. The author presents a linear-time technique by Megiddo for linear programming in R2, which is utilized within the algorithm. By decomposing the problem into smaller subproblems and employing fast parallel algorithms, the author achieves efficient sequential optimization. Overall, this book provides a valuable contribution to the field of computational geometry, offering a practical algorithm for a complex problem and advancing the understanding of geodesic center computation. 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 # 9781332115457_0
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Robotics Research Technical Report Computing the Geodesic Center of a Simple Polygon Classic Reprint
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332115457
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Robotics Research Technical Report Computing the Geodesic Center of a Simple Polygon Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332115457
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