A Symbolic-Numeric Approach for Parametrizing Ruled Surfaces

This paper presents symbolic algorithms to determine whether a given surface (implicitly or parametrically defined) is a rational ruled surface and find a proper parametrization of the ruled surface. However, in practical applications, one has to deal with numerical objects that are given approximately, probably because they proceed from an exact data that has been perturbed under some previous measuring process or manipulation. For these numerical objects, the authors adapt the symbolic algorithms presented by means of the use of numerical techniques. The authors develop numeric algorithms that allow to determine ruled surfaces “close” to an input (not necessarily ruled) surface, and the distance between the input and the output surface is computed.