On the derivatives of rational Bézier curves

2023/03/27 by Mao Shi, Shi, Mao
Engineering · #Advanced Numerical Analysis Techniques #FOS: Computer and information sciences #Graphics (cs.GR)

paper · pdf · doi:10.48550/arxiv.2303.16156

openalex publication_date 2023/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By studying the existing higher order derivation formulas of rational Bézier curves, we find that they fail when the order of the derivative exceeds the degree of the curves. In this paper, we present a new derivation formula for rational Bézier curves that overcomes this drawback and show that the kth degree derivative of a nth degree rational Bézier curve can be written in terms of a (2^kn)th degree rational Bézier curve.we also consider the properties of the endpoints and the bounds of the derivatives.

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