Journal for Geometry and Graphics Vol. 4, No. 1, pp. 31–53 (2000) 

Piecewise Linear Approximation of Quadratic FunctionsHelmut Pottmann, Rimvydas Krasauskas, Bernd Hamann, Kenneth Joy, Wolfgang SeiboldInstitute of Geometry, Vienna University of Technology,Wiedner Hauptstr. 810/113, A1040 Wien, Austria, emails: pottmann@geometrie.tuwien.ac.at, Rimvydas.Krasauskas@maf.vtu.lt, hamann(joy)@cs.ucdavis.edu Abstract: We study piecewise linear approximation of quadratic functions defined on R^n. 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. Keywords: optimal polygon meshes, piecewise linear approximation, datadependent triangulation, Voronoi tessellation, power diagram, Delone triangulation, convex geometry, discrete geometry, CayleyKlein geometry Classification (MSC2000): 65D15; 65D18 Full text of the article: (for faster download, first choose a mirror)
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