Explicit Inversion of Planar NURBS Curves
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913104071229440 |
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| author | Marsala, Michelangelo Mazón, Pablo |
| author_facet | Marsala, Michelangelo Mazón, Pablo |
| contents | We prove that a general planar NURBS curve parametrization $ϕ: [u_0,u_m] \xrightarrow{} C \subset \mathbb{R}^2$ admits an inverse map $ϕ^{-1}: C \xrightarrow{} [u_0,u_m]$ defined by rational splines. More specifically, we construct a family of rational spline functions on the curve $C$, present explicit formulas for their computation, and prove that the inverse parametrization admits a representation as a linear combination of these functions. Several examples are provided to illustrate the effectiveness of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08087 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit Inversion of Planar NURBS Curves Marsala, Michelangelo Mazón, Pablo Graphics We prove that a general planar NURBS curve parametrization $ϕ: [u_0,u_m] \xrightarrow{} C \subset \mathbb{R}^2$ admits an inverse map $ϕ^{-1}: C \xrightarrow{} [u_0,u_m]$ defined by rational splines. More specifically, we construct a family of rational spline functions on the curve $C$, present explicit formulas for their computation, and prove that the inverse parametrization admits a representation as a linear combination of these functions. Several examples are provided to illustrate the effectiveness of the proposed approach. |
| title | Explicit Inversion of Planar NURBS Curves |
| topic | Graphics |
| url | https://arxiv.org/abs/2605.08087 |