ABSTRACT
This chapter is devoted to describing some basic planar grid-generation algorithms. It begins with a statement of the basic planar grid-generation problem. Although the transfinite interpolation method is a solution to the basic problem, it has significant limitations. Thus other approaches to the basic problem are often preferred. The other approaches in the chapter are divided between nonelliptic generators and elliptic generators. This division reflects the authors’ bias toward elliptic generators; considerably more space is devoted to the discussion of elliptic grid generation in this book. The transfinite interpolation map discussed is an example of a map that solves the basic planar grid-generation problem. Algebraic grid generation methods have been extensively developed to take advantage of their two main strengths: rapid computation of the grids compared to partial differential equation methods and direct control over grid point locations. An important fact about conformal mappings is summarized in the Riemann Mapping Theorem.
