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arXiv · 2605.08087

Explicit Inversion of Planar NURBS Curves

Michelangelo Marsala·Pablo Mazón
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Abstract

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.

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Michelangelo Marsala, Pablo Mazón. 2026-01-26. Explicit Inversion of Planar NURBS Curves. https://arxiv.org/abs/2605.08087

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