On the derivatives of rational Bézier curves
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911981007536128 |
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| author | Shi, Mao |
| author_facet | Shi, Mao |
| contents | 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 $k$th degree derivative of a $n$th 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16156 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the derivatives of rational Bézier curves Shi, Mao Graphics 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 $k$th degree derivative of a $n$th 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. |
| title | On the derivatives of rational Bézier curves |
| topic | Graphics |
| url | https://arxiv.org/abs/2303.16156 |