Rockwood,A: Feature based, transfinite interpolation with applications to industrial design and terrain modeling
KAUST, Saudi Arabia
Abstract
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 .
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