Finding direction of intersection curve in critical cases of surface-surface intersection

Determining the topology of intersection curves is one of the important issues of surface-surface intersection problem used in Computer Aided Geometric Design and Computer Graphics. To compute the intersection curves, we first need to determine the topology of the curves. Thomas A. Grandine[Gr97] presented an algorithm to determine topology using partial derivatives of surface intersection equations. When the two surfaces meet tangentially, the differential values of the parameters of the surfaces are not determined in the intersection equations. These cases are called critical cases. In [Ye99] a method of finding the values of the differentials is presented for the case of the contact of order 1. We present general methods for the case of the contact of higher order ≥ 1 using perturbation method. With these results, we can decide starting or ending of the critical boundary point