Euclidean Shortest Paths

This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Topics and features: provides theoretical and programming exercises at the end of each chapter; presents a thorough introduction to shortest paths in Euclidean geometry, and the class of algorithms called rubberband algorithms; discusses algorithms for calculating exact or approximate ESPs in the plane; examines the shortest paths on 3D surfaces, in simple polyhedrons and in cube-curves; describes the application of rubberband algorithms for solving art gallery problems, including the safari, zookeeper, watchman, and touring polygons route problems; includes lists of symbols and abbreviations, in addition to other appendices.

Part I: Discrete or Continuous Shortest Paths.-Euclidean Shortest Paths.- Deltas and Epsilons.- Rubberband Algorithms.-Part II: Paths in the Plane.-Convex Hulls in the Plane.- Partitioning a Polygon or the Plane.- Approximate ESP Algorithms.-Part III: Paths in Three-Dimensional Space.-Paths on Surfaces.- Paths in Simple Polyhedrons.- Paths in Cube Curves.-Part IV: Art Galleries.-Touring Polygons.- Watchman Route.- Safari and Zookeeper Problems.