Convolution Surfaces based on Polygonal Curve Skeletons

Evelyne Hubert 1, * Marie-Paule Cani 2
* Corresponding author
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
2 IMAGINE - Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
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 formulae for integration obtained through symbolic computation software.
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Evelyne Hubert, Marie-Paule Cani. Convolution Surfaces based on Polygonal Curve Skeletons. Journal of Symbolic Computation, Elsevier, 2012, Advances in Mathematics Mechanization, 47 (6), pp.680-699. ⟨10.1016/j.jsc.2011.12.026⟩. ⟨inria-00429358v3⟩

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