On piecewise linear approximation of quadratic functions

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We study piecewise linear approximation of quadratic functions defined on Rn. Invariance properties and canonical Caley/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 di±cult 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.

Original languageEnglish (US)
Pages (from-to)31-53
Number of pages23
JournalJournal for Geometry and Graphics
Volume4
Issue number1
StatePublished - 2000

Keywords

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

ASJC Scopus subject areas

  • Applied Psychology
  • Geometry and Topology
  • Applied Mathematics

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