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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 10 > No. 1


Convergence Orders in Length Estimation with Exponential Parameterization and e -Uniformly Sampled Reduced Data

PP: 107-115
Ryszard Kozera, Lyle Noakes, Piotr Szmielew,
We investigate the length approximation of the unknown regular curve in arbitrary Euclidean space upon applying a piecewise-quadratic interpolation based on e -uniformly sampled reduced data in combination with the exponential parameterization. As proved in this paper, similarly to the trajectory estimation, there is a discontinuity in the quality of length estimation with exponential parameterization performing no better than a blind uniform guess for the unknown knots, except for the case of cumulative chords. The theoretical asymptotic estimates established here for length approximation are also experimentally confirmed to be nearly sharp.

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