A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames

Rida T. Farouki, Graziano Gentili, Carlotta Giannelli +2

A rotation-minimizing frame $({\mathbf{f}}_1,{\mathbf{f}}_2,{\mathbf{f}}_3)$ on a space curve $\mathbf{r}(\xi )$ defines an orthonormal basis for ${\mathbb{R}}^3$ in which ${\mathbf{f}}_1={\mathbf{r}}^{\prime }/|{\mathbf{r}}^{\prime }|$…