Characterization of Rational Ruled Surfaces

TL;DR

This paper develops algorithms to identify and convert implicit and parametric surfaces into standard rational ruled surface forms, aiding geometric modeling in computer-aided design.

Contribution

It introduces methods to determine if a surface is rational ruled and provides algorithms for reparameterization to standard form.

Findings

Algorithms successfully identify rational ruled surfaces

Reparameterization to standard form is achieved

Enhances geometric modeling capabilities

Abstract

The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to determine and find the standard form. In this paper, we present algorithms to determine whether a given implicit surface is a rational ruled surface. A parametrization of the surface is computed for the affirmative case. We also consider the parametric situation. More precisely, after a given rational parametric surface is determined as a ruled one, we reparameterize it to the standard form.