Geometry, Imaging and Computing

Volume 3 (2016)

Number 3-4

A new approach towards transversal intersection curves of two surfaces in $\mathbb{R}^3$

Pages: 81 – 99

DOI: http://dx.doi.org/10.4310/GIC.2016.v3.n3.a2

Authors

Mohamd Saleem Lone (Central University of Jammu, Jammu and Kashmir, India)

Mohammad Hasan Shahid (Jamia Millia Islamia, New Delhi, India)

S. D. Sharma (Department of Mathematics, Central University of Jammu, Jammu and Kashmir, India)

Abstract

In this paper, we formulate new algorithms to obtain the differential geometric properties of surface-surface intersection curves in $\mathbb{R}^3$. We also show its applicability to obtain geodesic curvature and geodesic torsion of two regular implicit surfaces in $\mathbb{R}^3$. Our new method will be distinguished from the older ones in the sense that we will use Rodrigues’ rotation formula and using a new operator $T$.

Full Text (PDF format)

Received 31 December 2016

Published 19 April 2018