On the approximation order of tangent estimators

G. Albrecht, J. P. Bécar, G. Farin, D. Hansford

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A classic problem in geometric modelling is curve interpolation to data points. Some of the existing interpolation schemes only require point data, whereas others, require higher order information, such as tangents or curvature values, in the data points. Since measured data usually lack this information, estimation of these quantities becomes necessary. Several tangent estimation methods for planar data points exist, usually yielding different results for the same given point data. The present paper thoroughly analyses some of these methods with respect to their approximation order. Among the considered methods are the classical schemes FMILL, Bessel, and Akima as well as a recently presented conic precision tangent estimator. The approximation order for each of the methods is theoretically derived by distinguishing purely convex point configurations and configurations with inflections. The approximation orders vary between one and four for the different methods. Numerical examples illustrate the theoretical results.

Original languageEnglish (US)
Pages (from-to)80-95
Number of pages16
JournalComputer Aided Geometric Design
Volume25
Issue number2
DOIs
StatePublished - Feb 2008

Fingerprint

Order of Approximation
Tangent line
Interpolation
Estimator
Approximation Order
Interpolate
Configuration
Geometric Modeling
Friedrich Wilhelm Bessel
Curvature
Vary
Higher Order
Numerical Examples
Curve
Necessary

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Geometry and Topology
  • Modeling and Simulation

Cite this

Albrecht, G., Bécar, J. P., Farin, G., & Hansford, D. (2008). On the approximation order of tangent estimators. Computer Aided Geometric Design, 25(2), 80-95. https://doi.org/10.1016/j.cagd.2007.05.005

On the approximation order of tangent estimators. / Albrecht, G.; Bécar, J. P.; Farin, G.; Hansford, D.

In: Computer Aided Geometric Design, Vol. 25, No. 2, 02.2008, p. 80-95.

Research output: Contribution to journalArticle

Albrecht, G, Bécar, JP, Farin, G & Hansford, D 2008, 'On the approximation order of tangent estimators', Computer Aided Geometric Design, vol. 25, no. 2, pp. 80-95. https://doi.org/10.1016/j.cagd.2007.05.005
Albrecht, G. ; Bécar, J. P. ; Farin, G. ; Hansford, D. / On the approximation order of tangent estimators. In: Computer Aided Geometric Design. 2008 ; Vol. 25, No. 2. pp. 80-95.
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