Weighted polynomial approximation of rational Bézier curves
This work provides a computational tool for geometric modeling, but it is an incremental improvement over existing approximation methods.
The paper presents an efficient algorithm for constrained least squares approximation of rational Bézier curves by Bézier curves using dual constrained Bernstein basis polynomials with recursive properties, demonstrating effectiveness through examples.
We present an efficient method to solve the problem of the constrained least squares approximation of the rational Bézier curve by the Bézier curve. The presented algorithm uses the dual constrained Bernstein basis polynomials, associated with the Jacobi scalar product, and exploits their recursive properties. Examples are given, showing the effectiveness of the algorithm.