Convolution Surfaces based on Polygonal Curve Skeletons An Application of Symbolic Integration to Graphics

This paper reviews and generalizes Convolution Surfaces, a technique used in Com-puter Graphics to generate smooth 3D models around polygonal line serving as skeletons. Convolution surfaces are defined as level set of a function obtained by integrating a kernel function along this skeleton. To allow interactive modeling, the technique has relied on closed form formulae for integration obtained through symbolic computation software. This paper provides new qualitative results and generalizations on the topic. It is also an opportunity for us to introduce the field of convolution surfaces to the sym-bolic computation community, hoping that researchers well versed into integration techniques can bring additional contribution to this appealing shape representation