Numerical parameterization of curves and surfaces Original Research Article

A method for parameterizing nearly arbitrary implicit plane/space curves and surfaces is introduced. The parameterizations are of class Cn−1 if the given curves/surfaces are of class Cn. 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 integrals …) 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.