Numerical Parameterization of Curves and Surfaces

Erich Hartmann

(Comp. Aided Geom. Des. 17(2000), 251-266)

Abstract:
A method for parameterizing nearly arbitrary implicit plane/space curves and surfaces is introduced. The parameterizations are of class tex2html_wrap_inline54 if the given curves/surfaces are of class tex2html_wrap_inline56. The computation of points and derivatives is performed numerically. These parameterizations can be used for controlled determination of points on curves and surfaces and for the application of developed techniques for parametric curves and surfaces (mesh generation, texture mapping, curve integrals, surface integerals ...) to implicit curves and surfaces. The idea of the normalform of a curve/surface introduced in recent papers makes it possible to apply the numerical parameterization to nearly arbitrary curves and surfaces.

Keywords: parameterization, implicit curve, normalform, mesh generation, curvature, foot point, intersection curve

 figure35
Figure 1: Curves on an implicit surface


Erich Hartmann
Tue Feb 2 13:12:29 MET 1999