Explicit Inversion of Planar NURBS Curves

Fuente: arXiv
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Autori principali: Marsala, Michelangelo, Mazón, Pablo
Natura: Preprint
Pubblicazione: 2026
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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