Details of talk
|Title||Approximation of the Curvature and the Torsion of Curves by the Discrete Curvature and the Discrete Torsion|
|Presenter||Yuta 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.