A simple matrix form for degree reduction of Bézier curves using Chebyshev-Bernstein basis transformations

Abedallah Rababah, Byung Gook Lee, Jaechil Yoo

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)

Abstract

We use the matrices of transformations between Chebyshev and Bernstein basis and the matrices of degree elevation and reduction of Chebyshev polynomials to present a simple and efficient method for r times degree elevation and optimal r times degree reduction of Bézier curves with respect to the weighted L2-norm for the interval [0, 1], using the weight function w (x) = 1 / sqrt(4 x - 4 x2). The error of the degree reduction scheme is given, and the degree reduction with continuity conditions is also considered.

Original languageEnglish
Pages (from-to)310-318
Number of pages9
JournalApplied Mathematics and Computation
Volume181
Issue number1
DOIs
Publication statusPublished - Oct 1 2006
Externally publishedYes

Keywords

  • Basis transformations
  • Bézier curves
  • Chebyshev polynomials
  • Continuity conditions
  • Degree elevation
  • Degree reduction

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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