Robotics Research Technical Report: Linear Time Algorithms for Visibility and Shortest Path, Problems Inside Simple Polygons (Classic Reprint) - Hardcover

L. Guibas

Hardcover

ISBN 10: 0332164586 ISBN 13: 9780332164588

Publisher: Forgotten Books, 2018

Synopsis

Unlock fast solutions for visibility and shortest paths inside simple polygons.

This work presents new linear-time algorithms that build on a triangulation of the polygon to solve key geometric problems. It offers practical methods and data structures that enable fast queries and preprocessing for complex polygon scenes.

The book shows how to compute a shortest path tree from a fixed point, determine which parts of the polygon are visible from a given edge or point, and perform fast shooting queries that find where a ray first hits the boundary. It also covers hierarchical decompositions, hourglass structures, and convex rope calculations, all designed to run in linear time with careful data organization. The results extend the state of the art in linear-time polygon processing and connect visibility with shortest-path problems through concrete algorithms and proofs.

• Learn how to build a shortest-path tree inside a simple polygon in linear time
• See how to preprocess a polygon for logarithmic-time visibility and shooting queries
• Explore hierarchical decompositions and hourglass structures used in fast computations
• Discover the convex rope approach to reachability and related geometric problems

Ideal for readers of computational geometry seeking practical, fast algorithms for visibility, shortest paths, and related polygon problems.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0332164586
• ISBN 13: 9780332164588
• Binding: Hardcover
• Number of pages: 59