On piecewise linear approximation of quadratic functions

  • Pottmann H
  • Krasauskas R
  • Hamann B
 et al. 
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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.

Author-supplied keywords

  • Cayley-Klein geometry
  • Convex geometry
  • Data--dependent triangulation
  • Delone triangulation
  • Discrete geometry
  • Optimal polygon meshes
  • Piecewise linear approximation
  • Power diagram
  • Voronoi tessellation

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  • SCOPUS: 2-s2.0-84976899674
  • SGR: 84976899674
  • PUI: 620737300
  • ISSN: 14338157

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