Abstract
This paper discusses the problem of how to approximate the length of a parametric curve γ: [0, T] → ℝn from points q i =γ(t i), where the parameters t i are not given. Of course, it is necessary to make some assumptions about the distribution of the t i: in the present paper ε-uniformity. Our theoretical result concerns an algorithm which uses piecewise-quadratic interpolants. Experiments are conducted to show that our theoretical estimates are sharp, and that the assumption of ε-uniformity is needed. This work may be of interest in computer graphics, approximation and complexity theory, digital and computational geometry, and digital image processing.
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Noakes, L., Kozera, R., Klette, R. (2001). Length Estimation for Curves with ε-Uniform Sampling. In: Skarbek, W. (eds) Computer Analysis of Images and Patterns. CAIP 2001. Lecture Notes in Computer Science, vol 2124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44692-3_63
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DOI: https://doi.org/10.1007/3-540-44692-3_63
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