Weierstrass-type approximation theorems with Pythagorean hodograph curves

Hyeong In Choi, Hwan Pyo Moon

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We prove the Weierstrass-type approximation theorem that states every C1 curve in the 2-dimensional or 3-dimensional Euclidean space or in the 3-dimensional Minkowski space can be uniformly approximated by Pythagorean hodograph curves in the corresponding space. This abundance of PH curves is another theoretical confirmation of the usefulness and the versatility of the PH curves. We also address some algorithmic aspects of proposed PH approximation schemes and their convergence rates.

Original languageEnglish
Pages (from-to)305-319
Number of pages15
JournalComputer Aided Geometric Design
Volume25
Issue number4-5
DOIs
StatePublished - May 2008

Keywords

  • Bernstein approximation
  • Chebyshev approximation
  • Minkowski Pythagorean hodograph
  • Pythagorean hodograph
  • Weierstrass approximation

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