# Developable surface patches bounded by NURBS curves

## TL;DR

This paper presents a method to construct developable surface patches bounded by NURBS curves through reparameterization, enabling the creation of developable surfaces that are not necessarily NURBS, with solutions involving algebraic equations.

## Contribution

It introduces a novel reparameterization approach for NURBS boundary curves to generate developable surface patches, expanding the design possibilities beyond traditional NURBS surfaces.

## Key findings

- Reparameterization involves solving algebraic equations, often quadratic or quartic.
- Applicable to cubic, spline, and Bezier curves on parallel planes.
- Method enables construction of developable patches not limited to NURBS surfaces.

## Abstract

In this paper we construct developable surface patches which are bounded by two rational or NURBS curves, though the resulting patch is not a rational or NURBS surface in general. This is accomplished by reparameterizing one of the boundary curves. The reparameterization function is the solution of an algebraic equation. For the relevant case of cubic or cubic spline curves, this equation is quartic at most, quadratic if the curves are Bezier or splines and lie on parallel planes, and hence it may be solved either by standard analytical or numerical methods.