On The Approximation Of The Normal Vector Field Of A Smooth Surface

Jean-Marie Morvan 1 Boris Thibert
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this paper, we compare the normal vector field of a compact (oriented) smooth surface S with the normals of a triangulated mesh T whose vertices belong to S. As a corollary, we deduce an approximation of the area of S by the area of T. We apply this result to the restricted Delaunay triangulation obtained with a sample of S. Using Chew's algorithm, we build sequences of triangulations inscribed on S, whose curvature measures tend to the curvature measures of S.
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Jean-Marie Morvan, Boris Thibert. On The Approximation Of The Normal Vector Field Of A Smooth Surface. RR-4476, INRIA. 2002. ⟨inria-00072112⟩

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