Surface design with minimum energy networks
Henry Moreton, Carlo H. Séquin · 1991
We describe a method for free form surface design that uses a mesh formed by networks of curves of minimum energy to define surfaces satisfying position, normal, and curvature constraints.The work addresses difficult problems arising in solid modeling, specifically at difficult blending problems, e.g. a blend at a high order vertex with simultaneous convex and concave blends incident to it.The techniques that we describe here may also be applied to general free form surface design.Previous methods for scattered data interpolation use linearized strain energy to produce a G1 network of curves which are subsequently blended.In this work we globall minii mize one of two nonlinear curvature funci.ionals,~(s)2ds J (strain energy) or ~'(s)2ds (curvature variation) produce a G2 network of c rves.The two functional are compared and both are shown to result in a high degree of fairness.