Efficient modified Jacobi-Bernstein basis transformations
For researchers in computer-aided geometric design, this provides a more efficient algorithm for degree reduction of Bézier curves.
The paper presents O(n^2) transformations between modified Jacobi and Bernstein bases, improving the O(n^3) complexity of prior work, and demonstrates faster practical running times.
In the paper, we show that the transformations between modified Jacobi and Bernstein bases of the constrained space of polynomials of degree at most $n$ can be performed with the complexity $O(n^2)$. As a result, the algorithm of degree reduction of Bézier curves that was first presented in (Bhrawy et al., J. Comput. Appl. Math. 302 (2016), 369--384), and then corrected in (Lu and Xiang, J. Comput. Appl. Math. 315 (2017), 65--69), can be significantly improved, since the necessary transformations are done in those papers with the complexity $O(n^3)$. The comparison of running times shows that our transformations are also faster in practice.