Part I: Discrete or Continuous Shortest PathsEuclidean Shortest PathsDeltas and EpsilonsRubberband AlgorithmsPart II: Paths in the PlaneConvex Hulls in the PlanePartitioning a Polygon or the PlaneApproximate ESP AlgorithmsPart III: Paths in Three-Dimensional SpacePaths on SurfacesPaths in Simple PolyhedronsPaths in Cube CurvesPart IV: Art GalleriesTouring PolygonsWatchman RouteSafari and Zookeeper Problems
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.
Reviews algorithms for the exact or approximate solution of Euclidean shortest-path problems, with a specific focus on rubberband algorithmsProvides theoretical and programming exercises at the end of each chapterDiscusses each concept and algorithm in depth, including mathematical proofs for many of the given statements