Reference software for finding Chebyshev best-fit geometric elements

G. T. Anthony, H. M. Anthony, B. Bittner, B. P. Butler, M. G. Cox, R. Drieschner, R. Elligsen, A. B. Forbes, H. Gross, S. A. Hannaby, P. M. Harris, J. Kok

Research output: Contribution to journalArticlepeer-review

57 Citations (Scopus)

Abstract

This paper summarizes work carried out in a project supported by the European Communities' Bureau of Reference (BCR) to develop reference software for finding best-fit geometric elements, under specified criteria, to coordinate data. The geometric elements considered are the line, plane, circle, sphere, cylinder, and cone. The criteria for determining the elements are, generally, minimum zone (MZ) and, where appropriate, minimum circumscribed (MC) and maximum inscribed (MI). The software developed implements methods founded on optimization theory. Two approaches are described: the first implements mathematical programming methods that exploit the particular structure of the problems considered and provide a unified approach to their solution; the second, applicable to the MZ and, where appropriate, MC problems for the line [in two-dimensions (2-D)], plane, circle (in 2-D) and sphere, implements a combinatorial method that returns all global solutions.

Original languageEnglish
Pages (from-to)28-36
Number of pages9
JournalPrecision Engineering
Volume19
Issue number1
DOIs
Publication statusPublished - Jul 1996
Externally publishedYes

Keywords

  • Best fit
  • Chebyshev approximation
  • Combinatorics
  • Coordinate measuring machines
  • Geometric elements
  • Geometric form
  • Global solutions
  • Reference software
  • Substitute elements

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