Article citationsMore>>

M. P. do Carmo, “Differential Geometry of Curves and Surface,” Prentice Hall, Englewood Cliffs, NJ, 1976.

has been cited by the following article:

• 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.