High order approximation method for curves

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26 Citations (Scopus)


In this paper, an approximation procedure for space curves is described, which significantly improves the standard approximation rate via parametric Taylor's approximations. The method takes advantages of the freedom in the choice of the parametrization and yields the order (m + 1) + [ (m + 1) (2d - 1)] for a curve in Rd, where m is the degree of the approximating polynomial parametrization. Moreover, the optimal rate (m + 1)+[ (m - 1) (d - 1)], for a curve in Rd, is also achieved for a particular set of curves. The cubic case is studied with examples which shows that our approximation method is an interesting quantity as well as quality improvement over standard methods.

Original languageEnglish
Pages (from-to)89-102
Number of pages14
JournalComputer Aided Geometric Design
Issue number1
Publication statusPublished - Feb 1995
Externally publishedYes


  • Approximation order
  • Computer aided geometric design
  • High accuracy
  • Space curves
  • Taylor polynomial

ASJC Scopus subject areas

  • Modelling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design


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