A curvature-sensitive parameterization-independent triangulation algorithm
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2008-09
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Triangulations of a connected subset F of parametric surfaces S(u,v) (with continuity C2 or higher) are required because a C0 approximation of such F(called a FACE) is widely required for finite element analysis, rendering, manufacturing, design, reverse engineering, etc -- The triangulation T is such an approximation, when its piecewise linear subsets are triangles (which, on the other hand, is not a compulsory condition for being C0) -- A serious obstacle for algorithms which triangulate in the parametric space u−v is that such a space may be extremely warped, and the distances in parametric space be dramatically different of the distances in R3 -- Recent publications have reported parameter -independent triangulations, which triangulate in R3 space -- However, such triangulations are not sensitive to the curvature of the S(u,v) -- The present article presents an algorithm to obtain parameter-independent, curvature-sensitive triangulations -- The invariant of the algorithm is that a vertex v of the triangulation if identified, and a quasiequilateral triangulation around v is performed on the plane P tangent to S(u,v) at v -- The size of the triangles incident to v is a function of K(v), the curvature of S(u,v) at v -- The algorithm was extensively and successfully tested, rendering short running times, with very demanding boundary representations
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@inproceedings{2008_Ruiz_Curvature,
title={A Curvature-Sensitive Parameterization-Independent Triangulation Algorithm},
author={Ruiz, O. and Congote, J. and Cadavid, C. and Lalinde, J.G.},
booktitle={5th Annual International Symposium on Voronoi Diagrams in Science and Engineering. 4th International Kyiv Conference on Analytic Number Theory and Spatial Tessellations.},
volume={2},
isbn={967-966-02-4892-2},
address={Kiev, Ukraine},
year={2008},
}