Formulas for second curvature, third curvature, normal curvature, first geodesic curvature and first geodesic torsion of implicit curve in n-dimensions

Authors:
Osmar Aléssio
Affiliations:
UFTM - Triíngulo Mineiro Federal University, Institute of Exact Sciences, Natural and Education - ICENE, Uberaba, MG, Brazil
Venue:
Computer Aided Geometric Design
Year:
2012

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Abstract

We present closed formulas for computing the differential geometry properties of the intersection curve of n-1 implicit hypersurfaces in R^n. These closed formulas include second curvature, third curvature, normal curvature, first geodesic curvature and first geodesic torsion for implicit curves in n-dimensions.