After a discussion of some of the problem issues and the state of the art in three-dimensional mesh generation and the demands in the fields of CAD and TCAD in Chapter 2, a brief overview of the concept and the means of mesh generation is given in Chapter 3. Such a ``theory'' of mesh generation includes topics as mesh quality, the discretization scheme, the generation of a surface mesh, and mesh adaptation. The notion of control space which defines a control function to guide a mesh generator in making more problem-dependent than geometry-dependent meshes is introduced.

Chapter 4 provides a concise summary of common meshing techniques. Most existing meshing methods can be distinguished in such a manner. Hybrid methods combine some of the given techniques. The text further concentrates on Delaunay methods. These are among the unstructured approaches the one with the strongest mathematical background. All aspects related to the theory of Delaunay are discussed in Chapter 5. This includes the definition of the Delaunay properties, some combinatorial facts, an overview of Delaunay algorithms, and the concept of Steiner Triangulations. The basic characteristics of a Delaunay Triangulation which is defined for a given point set are the duality to the Voronoi graph and the empty circumsphere property. If the reader is not at all familiar with that, he is advised to browse through Chapter 5 beforehand. Previous chapters which include the review of research and methodologies refer to Delaunay techniques frequently.

The design and architecture of the developed mesh generator are presented in Chapter 6. Finally, several examples of CAD and TCAD structures are given in Chapter 7 and an Outlook in Chapter 8.

2000-01-20