Robotics Research Technical Report: On the Geodesic Voronoi Diagram of Point Sites in a Simple Polygon (Classic Reprint) - Hardcover

Boris Aronov

9780332802152: Robotics Research Technical Report: On the Geodesic Voronoi Diagram of Point Sites in a Simple Polygon (Classic Reprint)

Hardcover

ISBN 10: 0332802159 ISBN 13: 9780332802152

Publisher: Forgotten Books, 2018

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Extend the classic Voronoi idea to a polygon world with geodesic distance.

This work develops and analyzes an algorithm to compute the geodesic Voronoi diagram for a set of point sites inside a simple polygon. Distance is measured by the length of the shortest internal paths, making this a new kind of metric geometry with practical algorithmic insights.

The author shows how to build the diagram efficiently, avoiding the heavy cost of computing full shortest-path trees. The approach combines divide-and-conquer, a careful extension step through the polygon, and a merging process that yields a diagram with linear size relative to the polygon and sites. The result is a concrete, step-by-step method that highlights both the structure of geodesic Voronoi diagrams and the challenges of working inside a polygonal world.

Understand how geodesic distance changes Voronoi cells inside a polygon
Learn how to extend partial diagrams and merge them in linear time
See how the algorithm achieves near-linear performance for this complex problem
Explore potential applications like closest-pair and all-nearest-neighbors in a polygonal environment

Ideal for readers who want a solid, implementable approach to proximity queries under interior geodesic metrics, and for researchers exploring new metric generalizations of Voronoi diagrams.

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