Intersection Curves of Implicit and Parametric Surfaces in R3

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Applied Mathematics·Volume 02 (2011)·Pages 1019–1026·Published 3 August 2011·DOI10.4236/am.2011.28141

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.

KeywordsGeometric PropertiesFrenet FrameFrenet ApparatusFrenet-Serret FormulasSurface-Surface IntersectionTransversal IntersectionTangential IntersectionDupin Indicatrices

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Intersection Curves of Implicit and Parametric Surfaces in R<sup>3</sup>

Abstract

References (13)