Numerical Computation with General Two-Dimensional Domains
John R. Rice · ACM Transactions on Mathematical Software · 1984
Consider a bounded two-dimensional domain R with boundary OR.Applications that involve processing R include approximation, numerical integration, and the numerical solution of partial differential equations.In each case the geometric information of R and OR must be put into a data structure (either implicitly or explicitly) as an initial phase of the problem solution.This paper presents one approach to this problem based on overlaying R by a rectangular grid.R is assumed to be defined by parameterization of pieces of OR plus an orientation.Specific representations of this information are given, and a data structure that is convenient for using the geometric information in various applications is presented.An algorithm to produce this information is given in a companion paper, "Algorithm xxx: A Two-Dimensional Domain Processor"; various special techniques of the algorithm are described.The application to numerical integration is discussed in some detail.