Convolution surfaces based on polygonal curve skeletons

Abstract

This paper reviews and generalizes convolution surfaces, a technique used in computer graphics to generate smooth 3D volumes around skeletons that are lower dimensional or simpler geometric models of the shape to be created. Convolution surfaces are defined as level sets of a function obtained by integrating a kernel function along this skeleton. To allow interactive modeling, the technique has relied on closed form formulas for integration obtained through symbolic computation software.This paper provides new qualitative results and generalizations on the topic when the skeleton is a polygonal line. It is also an opportunity for us to introduce the field of convolution surfaces to the symbolic computation community, hoping that researchers well versed into integration techniques can bring additional contributions to this appealing shape representation.