Computational Geometry on Surfaces: Performing Computational Geometry on the Cylinder, the Sphere, the Torus, and the Cone / Edition 1

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This book demonstrates that classical problems of computational geomet ry can be solved when the input and output data are on surfaces other than the plane, but that planar techniques cannot always be adapted su ccessfully, and new techniques must be considered. Well-known problems from computational geometry are adapted to cases where the objects ar e on surfaces, and an attempt is made to answer questions that arise i n the growing list of areas in which the results of computational geom etry are applicable. These areas are, among others, engineering, compu ter aided design, manufacturing, geographic information systems, opera tions research, robotics, computer graphics, and solid modelling. Audi ence: This volume will be of interest to postgraduate students and res earchers whose work involves computational geometry, algorithms, combi natorics, and graph theory.

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Product Details

  • ISBN-13: 9781402002021
  • Publisher: Springer Netherlands
  • Publication date: 11/30/2001
  • Edition description: 2002
  • Edition number: 1
  • Pages: 192
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.50 (d)

Table of Contents

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.

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