Envelope surfaces

We construct a class of envelope surfaces in Rd , more precisely envelopes of balls. An envelope surface is a closed C1 (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 C1 . These conditions can be verified automatically. We give examples of envelope surfaces to demonstrate their flexibility in surface design. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]:...

• Type: Conference
• Year: 2006
• Where: COMPGEOM
• Authors: Nico Kruithof, Gert Vegter
• Keywords: COMPGEOM 2006, Envelope Surfaces, Piecewise Quadratic Surfaces, Skin Surface