-Interpolation and Blending on Surfaces

Erich Hartmann

Abstract:
A method for curvature continuous (-) interpolation of an arbitrary sequence of points on a surface (implicit or parametric) with prescribed tangent and geodesic curvature at every point is introduced. The method can also be used for -blending of curves on surfaces. The interpolation/blending curve is the intersection curve of the given surface with a functional spline (implicit) surface. For the construction of blending curves the necessary formulas for the curvature of surface curves are derived. Intermediate results are -interpolation/blending methods in .

Keywords: interpolation, blending, -continuity.

 
Figure 1: -blending curves on a torus