envelope surfaces
We construct a class of envelope surfaces in R d , more precisely envelopes of balls. An envelope surface is a closed C 1 (tangent continuous) manifold wrapping tightly around the union of a set of balls. Such a manifold is useful in modeling since the union of a finite set of balls can approximate any closed smooth manifold arbitrarily close.The theory of envelope surfaces generalizes the theoretical framework of skin surfaces [5] developed by Edelsbrunner for molecular modeling. However, envelope surfaces are more flexible: where a skin surface is controlled by a single parameter, envelope surfaces can be adapted locally.We show that a special subset of envelope surfaces is piecewise quadratic and derive conditions under which the envelope surface is C 1 . These conditions can be verified automatically. We give examples of envelope surfaces to demonstrate their flexibility in surface design.
legendre-fenchel transform smooth surfaces piecewise quadratic surfaces envelopes of spheres