The Total Squared Curvature of Curves and Approximation by Piecewise Circular Curves |
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| Authors: | Kazuyuki Enomoto Mio Okura |
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| Affiliation: | 1. Faculty of Industrial Science and Technology, Tokyo University of Science, Oshamambe, Hokkaido, 049–3514, Japan
2. 59–6, Aza Horizoe, Arai, Wakabayashi-ku, Sendai, Miyagi, 984–0032, Japan
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| Abstract: | For a smooth curve in the Euclidean spaces, the total squared curvature is defined as the integral of the square of the curvature. If one takes three points on the curve which are close to one another, the reciprocal of the radius of the circle passing through those points approximates the curvature. We use this to approximate the total squared curvature and study its convergence rate. |
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