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

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Piecewise Linear Approximation of Quadratic Functions

Helmut Pottmann, Rimvydas Krasauskas, Bernd Hamann, Kenneth Joy, Wolfgang Seibold

Institute of Geometry, Vienna University of Technology,
Wiedner Hauptstr. 8-10/113, A-1040 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, data-dependent triangulation, Voronoi tessellation, power diagram, Delone triangulation, convex geometry, discrete geometry, Cayley-Klein geometry

Classification (MSC2000): 65D15; 65D18

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Electronic fulltext finalized on: 14 Mar 2002. This page was last modified: 10 May 2013.

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