Triangulation and display of rational parametric surfaces

We present a comprehensive algorithm to construct a topologically correct triangulation of the real affine part of a rational parametric surface with few restrictions on the defining rational functions. The rational functions are allowed to be undefined on domain curves (pole curves) and at certain special points (base points), and the surface is allowed to have nodal or cuspidal self-intersections. We also recognize that for a complete display, some real points on the parametric surface may be generated only by complex parameter values, and that some finite points on the surface may be generated only by infinite parameter values; we show how to compensate for these conditions. Our techniques for handling these problems have applications in scientific visualization, rendering non-standard NURBS, and in finite-element mesh generation