Rockwood,A: Feature based, transfinite interpolation with applications to industrial design and terrain modeling

KAUST, Saudi Arabia


A method is developed that simultaneously interpolates scattered points and parametric curves in space.  The curves do not have an obvious topological structure; the curves might be disconnected, self intersecting and randomly distributed.  The method involves minimizing an energy functional based on distance to simple curve and point pre-images in parameter space.   The minimization yields an analytic surface definition, which can be shown to generalize Shepard's formula to vector-valued parametric curves.  The method also allows derivative information to be included; thus slopes and curvatures along the curves could be part of the input .