Intersection Curves of Implicit and Parametric Surfaces in R^{3}

Author(s)
Mohamed Abdel-Latif Soliman,
Nassar Hassan Abdel-All,
Soad Ali Hassan,
Sayed Abdel-Naeim Badr

Abstract

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**R**^{3} 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.

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

Keywords

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

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

Cite this paper

nullM. Soliman, N. Abdel-All, S. Hassan and S. Badr, "Intersection Curves of Implicit and Parametric Surfaces in R^{3}," *Applied Mathematics*, Vol. 2 No. 8, 2011, pp. 1019-1026. doi: 10.4236/am.2011.28141.

nullM. Soliman, N. Abdel-All, S. Hassan and S. Badr, "Intersection Curves of Implicit and Parametric Surfaces in R

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