Author(s)

Mohamed Abdel-Latif Soliman, Nassar Hassan Abdel-All, Soad Ali Hassan, Sayed Abdel-Naeim Badr

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We present algorithms for computing the differential geometry properties of Frenet apparatus {t,n,b,κ,τ} and higher-order derivatives of intersection curves of implicit and parametric surfaces in R³ for transversal and tangential intersection. This work is considered as a continuation to Ye and Maekawa [1]. We obtain a classification of the singularities on the intersection curve. Some examples are given and plotted.

Geometric Properties, Frenet Frame, Frenet Apparatus, Frenet-Serret Formulas, Surface-Surface Intersection, Transversal Intersection, Tangential Intersection, Dupin Indicatrices

M. Soliman, N. Abdel-All, S. Hassan and S. Badr, "Intersection Curves of Implicit and Parametric Surfaces in R³," Applied Mathematics, Vol. 2 No. 8, 2011, pp. 1019-1026. doi: 10.4236/am.2011.28141.