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  A locally optimal triangulation of the hyperbolic paraboloid (1995)

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by Olivier Devillers
Technical Report, INRIA, Sophia Antipolis
http://www-sop.inria.fr/prisme/publis/dd-lothp-95.ps.gz
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Abstract:

and corresponding data values for a specic non-convex surface, the unit hyperbolic paraboloid, we consider the problem of nding a locally optimal triangulation of S for the linear approximation of this surface. The chosen optimality criterion will be the L 2 norm: it means that we will try to nd directly a triangulation that minimizes the L 2 error made when approximating locally the surface with triangles.

Citations

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67 Voronoi diagrams and arrangements – Edelsbrunner, Seidel - 1986
63 Software for C Surface Interpolation – Lawson - 1977
15 Algorithms for the construction of Data dependent triangulations – Dyn, Levin, et al. - 1990
10 Vertex based data dependent triangulations – Brown - 1991
2 l p optimal d dimensional triangulations for piecewise linear interpolation: A new result on data dependent triangulations – Melissaratos - 1993