Tubular parametric volume objects: Thickening a piecewise smooth 3D stick figure

In this paper, a volume parametric model is computed from a piecewise smooth skeleton. Generating a volume model from a stick figure S defined in 3D is an intuitive process: given S whose topology is a pseudo-graph and whose edges are embedded as Bézier curves in R3, we propose a method for creating a thick volume parametric model “around” S. The volume model we generate is based on semi-simploidal sets, which guarantees a proper topology and provides a 3D parametric domain for Bézier spaces. This volume is a continuous piecewise Bézier representation which boundary corresponds to a B-Rep made of tensor product Bézier patches.