Geodesic
On Piecewise Linear Approximation of Quadratic Functions
Journal for geometry and graphics, Tome 4 (2000) no. 1, pp. 031-054 
H. Pottmann; R. Krasauskas; B. Hamann; K. Joy; W. Seibold. On Piecewise Linear Approximation of Quadratic Functions. Journal for geometry and graphics, Tome 4 (2000) no. 1, pp. 031-054. http://geodesic.mathdoc.fr/item/JGG_2000_4_1_a2/
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     author = {H. Pottmann and R. Krasauskas and B. Hamann and K. Joy and W. Seibold},
     title = {On {Piecewise} {Linear} {Approximation} of {Quadratic} {Functions}},
     journal = {Journal for geometry and graphics},
     pages = {031--054},
     year = {2000},
     volume = {4},
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     url = {http://geodesic.mathdoc.fr/item/JGG_2000_4_1_a2/}
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Voir la notice de l'article provenant de la source Heldermann Verlag

We study piecewise linear approximation of quadratic functions defined on Rn. Invariance properties and canonical Cayley/Klein metrics that help in understanding this problem can be handled in arbitrary dimensions. However, the problem of optimal approximants in the sense that their linear pieces are of maximal size by keeping a given error tolerance, is a difficult one. We present a detailled discussion of the case n = 2, where we can partially use results from convex geometry and discrete geometry. The case n = 3 is considerably harder, and thus just a few results can be formulated so far.