On the computation of singularities of parametrized ruled surfaces

Abstract

Given a ruled surface V defined in the standard parametric form P(t 1 , t 2 ), we present an algorithm that determines the singularities (and their multiplicities) of V from the parametrization P. More precisely, from P we construct an auxiliary parametric curve and we show how the problem can be simplified to determine the singularities of this auxiliary curve. Only one univariate resultant has to be computed and no elimination theory techniques are necessary. These results improve some previous algorithms for detecting singularities for the special case of parametric ruled surfaces.

B-Lift curves and its ruled surfaces

“…If all points of a curve on a surface are singular, this curve is called a singular curve [1]. Recently, many studies have been done on the singularity of curves [11][12][13][14][15][16].…”