TITLE:
Intersection Curves of Implicit and Parametric Surfaces in R3
AUTHORS:
Mohamed Abdel-Latif Soliman, Nassar Hassan Abdel-All, Soad Ali Hassan, Sayed Abdel-Naeim Badr
KEYWORDS:
Geometric Properties, Frenet Frame, Frenet Apparatus, Frenet-Serret Formulas, Surface-Surface Intersection, Transversal Intersection, Tangential Intersection, Dupin Indicatrices
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.8,
August
24,
2011
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 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.