We present algorithms for computing the differential geometry properties of Frenet apparatus and higher-order derivatives of intersection curves of implicit and parametric surfaces in 3 for transversal and tangential intersection. This work is considered as a continuation to Ye and Maekawa . We obtain a classification of the singularities on the intersection curve. Some examples are given and plotted. t, n, b, κ, τ
a b s t r a c tThe aim of this paper is to compute all the Frenet apparatus of non-transversal intersection curves (hyper-curves) of three implicit hypersurfaces in Euclidean 4-space. The tangential direction at a transversal intersection point can be computed easily, but at a nontransversal intersection point, it is difficult to calculate even the tangent vector. If three normal vectors are parallel at a point, the intersection is ''tangential intersection''; and if three normal vectors are not parallel but are linearly dependent at a point, we have ''almost tangential'' intersection at the intersection point. We give algorithms for each case to find the Frenet vectors (t, n, b 1 , b 2 ) and the curvatures (k 1 , k 2 , k 3 ) of the non-transversal intersection curve.
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