Reproduce “Explicit Inversion of Planar NURBS Curves” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Michelangelo Marsala, Pablo Mazón
Researchers at the University of Florence and CUNEF University developed an explicit rational spline representation for the inverse map of planar Non-Uniform Rational B-Spline (NURBS) curves, replacing traditional numerical root-finding with direct function evaluations. The work introduces "physical rational splines" defined directly on the curve, allowing for a structured and globally defined inverse, which is shown to be C-infinity smooth for injective parametrizations.
Key insights
- A general planar NURBS curve parametrization admits an inverse map that can be represented as rational splines defined directly on the curve in the physical domain, moving beyond purely numerical approaches.
- Local inverse maps for NURBS curve segments can be explicitly derived as ratios of minors of Sylvester matrices, providing a constructive algebraic technique.
- The newly introduced "physical rational splines" act as pullbacks of parametric B-splines via the inverse map, retaining properties like nonnegativity, local support, and partition of unity.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.