Numerical Implicitation for Intersection and -continuous Blending of Surfaces

Erich Hartmann

(Comp. Aided Geom. Des. 15, 377-397)

Abstract:
The idea of numerical implicitation allows to treat not only parametric surfaces but also a lot of surfaces of practical use which have per definition no standard (parametric or implicit) representations in a uniform way as implicit surfaces. So it suffices to have a surface/surface intersection algorithm for implicit surfaces. Further more the simple -blending techniques for implicit surfaces are applicable. The intersection of a space curve and a surface is just a specialization of a suitable surface/surface intersetion problem.

Keywords: implicitation, surface/surface intersection, curve/surface intersection, blending, -continuity, functional spline, parametric surface, implicit surface, offset surface, Voronoi surface, rolling ball, envelope, developable surface.

 
Figure 1: -blending surface between a quartic cylinder and a tensorproduct Bézier surface with rolling ball contact curves and the intersection curve with a cylinder