Before revision:  This approach is based on a new computational characterisation of the singular points of the curve and on how this curve is located with respect to the projection of the considered quadrics (whose boundaries are the so called silhouette curves).
After revision:  This approach is based on a new computational characterisation of the singular points of the cutcurve and on how this curve is located with respect to the projection of the considered quadrics (whose boundaries are the so called silhouette curves).