Computational Geometry on Surfaces: Performing Computational Geometry on the Cylinder, the Sphere, the Torus, and the Cone

Preface. Acknowledgments. 1: Preliminaries. 1. Introduction. 2. Notations and Terminology. 3. Orbifolds. 4. Point Location and Range Searching. 5. Notes and comments. 2: Euclidean Position. 1. Introduction. 2. Euclidean Position. 3. Cylindrical position in the Torus. 4. Euclidean position in Orbifolds and in General Surfaces. 5. Notes and comments. 3: Convex Hull. 1. Introduction. 2. Hyperconvex Hull. 3. Metrically Convex Hull. 4. Analysis of complexity. 5. Minimum enclosing polygon. 6. Notes and comments. 4: Voronoi Diagrams. 1. Introduction. 2. Voronoi diagrams. 3. Proximity problems and Voronoi diagrams. 4. Furthest point Voronoi diagram. 5. Generalized Voronoi diagrams. 6. Notes and Comments. 5: RADII. 1. Introduction. 2. The Width of a Convex Set on the Sphere. 3. Circumradius. 4. Diameter. 5. Maximum and minimum distances. 6. Notes and remarks. 6: Visibility. 1. Introduction. 2. Stabbing line segments. 3. Visibility in the presence of obstacles. 4. Notes and comments. 7: Triangulations. 1. Introduction. 2. Triangulations on the cylinder. 3. Triangulations on the sphere and on the torus. 4. The graph of triangulations on non-planar surfaces. 5. Notes and Comments. References. Topic Index. Author Index.