Differential Geometry, Lie Theory and Low-Dimensional Topology, Melbourne, Australia, 2016

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Details of talk

TitleApproximation of the Curvature and the Torsion of Curves by the Discrete Curvature and the Discrete Torsion
PresenterYuta Hatakeyama (Kyushu University)
Author(s)Mr Yuta Hatakeyama

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The shape of a smooth curve in R^3 is determined uniquely by the curvature and
the torsion. On practical applications, very often we can get information only
about discrete points on a given curve. Hence, it is important to approximate
the curvature and the torsion by data of only discrete points and to evaluate
the errors. In this talk, we discretize a smooth curve by choosing discrete
points on the original curve and define the discrete curvature and the discrete
torsion at these points. We evaluate the errors between the curvature and the
discrete curvature, and the torsion and the discrete torsion when we increase
the number of discrete points on the smooth curve. We also apply our results to
some explicit examples.