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

In the last thirty years Computational Geometry has emerged as a new discipline from the field of design and analysis of algorithms. That dis­ cipline studies geometric problems from a computational point of view, and it has attracted enormous research interest. But that interest is mostly concerned with Euclidean Geometry (mainly the plane or Eu­ clidean 3-dimensional space). Of course, there are some important rea­ sons for this occurrence since the first applieations and the bases of all developments are in the plane or in 3-dimensional space. But, we can find also some exceptions, and so Voronoi diagrams on the sphere, cylin­ der, the cone, and the torus have been considered previously, and there are manY works on triangulations on the sphere and other surfaces. The exceptions mentioned in the last paragraph have appeared to try to answer some quest ions which arise in the growing list of areas in which the results of Computational Geometry are applicable, since, in practiee, many situations in those areas lead to problems of Com­ putational Geometry on surfaces (probably the sphere and the cylinder are the most common examples). We can mention here some specific areas in which these situations happen as engineering, computer aided design, manufacturing, geographie information systems, operations re­ search, roboties, computer graphics, solid modeling, etc.

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This book demonstrates that classical problems of computational geometry can be solved when the input and output data are on surfaces other than the plane, but that planar techniques cannot always be adapted successfully, and new techniques must be considered.
Well-known problems from computational geometry are adapted to cases where the objects are on surfaces, and an attempt is made to answer questions that arise in the growing list of areas in which the results of computational geometry are applicable. These areas are, among others, engineering, computer aided design, manufacturing, geographic information systems, operations research, robotics, computer graphics, and solid modelling.
Audience: This volume will be of interest to postgraduate students and researchers whose work involves computational geometry, algorithms, combinatorics, and graph theory.

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This book demonstrates that classical problems of computational geometry can be solved when the input and output data are on surfaces other than the plane, but that planar techniques cannot always be adapted successfully, and new techniques must be considered.
Well-known problems from computational geometry are adapted to cases where the objects are on surfaces, and an attempt is made to answer questions that arise in the growing list of areas in which the results of computational geometry are applicable. These areas are, among others, engineering, computer aided design, manufacturing, geographic information systems, operations research, robotics, computer graphics, and solid modelling.
Audience: This volume will be of interest to postgraduate students and researchers whose work involves computational geometry, algorithms, combinatorics, and graph theory.
Content:
Front Matter....Pages i-xv
Preliminaries....Pages 1-17
Euclidean Position....Pages 19-29
Convex Hull....Pages 31-59
Voronoi Diagrams....Pages 61-83
Radii....Pages 85-105
Visibility....Pages 107-125
Triangulations....Pages 127-172
Back Matter....Pages 173-191

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This book demonstrates that classical problems of computational geometry can be solved when the input and output data are on surfaces other than the plane, but that planar techniques cannot always be adapted successfully, and new techniques must be considered.
Well-known problems from computational geometry are adapted to cases where the objects are on surfaces, and an attempt is made to answer questions that arise in the growing list of areas in which the results of computational geometry are applicable. These areas are, among others, engineering, computer aided design, manufacturing, geographic information systems, operations research, robotics, computer graphics, and solid modelling.
Audience: This volume will be of interest to postgraduate students and researchers whose work involves computational geometry, algorithms, combinatorics, and graph theory.
Content:
Front Matter....Pages i-xv
Preliminaries....Pages 1-17
Euclidean Position....Pages 19-29
Convex Hull....Pages 31-59
Voronoi Diagrams....Pages 61-83
Radii....Pages 85-105
Visibility....Pages 107-125
Triangulations....Pages 127-172
Back Matter....Pages 173-191
....