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Convolution Surfaces based on Polygons for Infinite and Compact Support Kernels

Evelyne Hubert 1 
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We provide formulae to create 3D smooth shapes fleshing out a skeleton made of line segments and planar polygons. The boundary of the shape is a level set of the convolution function obtained by integration along the skeleton. The convolution function for a complex skeleton is thus the sum of the convolution functions for the basic elements of the skeleton. Providing formulae for the convolutionof a polygon is the main contribution of the present paper. We improve on previous results in several ways. First we do not require the prior triangulation of the polygon. Then, we obtain formulae for families of kernels, either with infinite or compact supports. Last, but not least, in the case of compact support kernels, the geometric computations needed are restricted to intersections of spheres with line segments.
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Submitted on : Wednesday, November 17, 2010 - 3:20:52 AM
Last modification on : Thursday, August 4, 2022 - 4:52:37 PM
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Evelyne Hubert. Convolution Surfaces based on Polygons for Infinite and Compact Support Kernels. Graphical Models, 2012, 74 (1), pp.1-13. ⟨10.1016/j.gmod.2011.07.001⟩. ⟨inria-00536840⟩



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