Abstract
In this paper we derive the matrix of transformation of the Jacobi polynomial basis form into the Bernstein polynomial basis of the same degree n and vice versa. This enables us to combine the superior least-squares performance of the Jacobi polynomials with the geometrical insight of the Bernstein form. Application to the inversion of the Bézier curves is given.
| Original language | English |
|---|---|
| Pages (from-to) | 206-214 |
| Number of pages | 9 |
| Journal | Computational Methods in Applied Mathematics |
| Volume | 4 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2004 |
| Externally published | Yes |
Keywords
- Bernstein polynomials
- Jacobi polynomials
- basis transformation
- computer aided geometric design
- inversion of Bézier curves
- least-squares approximation
- orthogonal polynomials
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics
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