Computational Geometry on Surfaces

1. Front Matter

   Pages i-xv

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2. Preliminaries

   • Clara I. Grima, Alberto Márquez

   Pages 1-17

3. Euclidean Position

   • Clara I. Grima, Alberto Márquez

   Pages 19-29

4. Convex Hull

   • Clara I. Grima, Alberto Márquez

   Pages 31-59

5. Voronoi Diagrams

   • Clara I. Grima, Alberto Márquez

   Pages 61-83

6. Radii

   • Clara I. Grima, Alberto Márquez

   Pages 85-105

7. Visibility

   • Clara I. Grima, Alberto Márquez

   Pages 107-125

8. Triangulations

   • Clara I. Grima, Alberto Márquez

   Pages 127-172

9. Back Matter

   Pages 173-191

   PDF

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.

• Triangulation
• algorithms
• calculus
• combinatorics
• complexity
• computational geometry
• computer
• computer graphics
• convex hull
• geometry
• graph theory
• robotics

• Department of Applied Mathematics (E.U.I.T.A.), University of Seville, Seville, Spain

  Clara I. Grima

• Department of Applied Mathematics (F.I.E..), University of Seville, Seville, Spain

  Alberto Márquez

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