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arXiv · 1701.03058

Efficient modified Jacobi-Bernstein basis transformations

Przemysław Gospodarczyk·Paweł Woźny
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Abstract

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 B\'ezier 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.

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Przemysław Gospodarczyk, Paweł Woźny. 2017-01-11. Efficient modified Jacobi-Bernstein basis transformations. https://arxiv.org/abs/1701.03058

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