Multiple degree reduction and elevation of bzier curves using Jacobi-Bernstein basis transformations

Abedallah Rababah, Byung Gook Lee, Jaechil Yoo

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

In this article, we find the optimal r times degree reduction of Bzier curves with respect to the Jacobi-weighted L2-norm on the interval [0, 1]. This method describes a simple and efficient algorithm based on matrix computations. Also, our method includes many previous results for the best approximation with L1, L2, and L-norms. We give some examples and figures to demonstrate these methods.

Original languageEnglish
Pages (from-to)1179-1196
Number of pages18
JournalNumerical Functional Analysis and Optimization
Volume28
Issue number9-10
DOIs
Publication statusPublished - Sep 2007
Externally publishedYes

Keywords

  • Basis transformation
  • Bernstein polynomials
  • Bzier curves
  • Degree reduction
  • Jacobi polynomials
  • Least-squares approximation
  • Orthogonal polynomials

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

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