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 language | English |
---|---|
Pages (from-to) | 310-318 |
Number of pages | 9 |
Journal | Applied Mathematics and Computation |
Volume | 181 |
Issue number | 1 |
DOIs | |
Publication status | Published - Oct 1 2006 |
Externally published | Yes |
Keywords
- Basis transformations
- Bézier curves
- Chebyshev polynomials
- Continuity conditions
- Degree elevation
- Degree reduction
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics