Curvatures at the singular points of algebraic curves and surfaces
  In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which have intersections with the original curves and surfaces at the singular points. Three algorithms are presented for three cases of plane curves, space curves and surfaces. 
Chong-Jun Li, Ren-Hong Wang
math.DG math.AG math.NA