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This paper* discusses the problem of how to approximate the length of a parametric curve γ : [0; T] → IRn from points qi = γ(ti), where the parameters ti are not given. Of course, it is necessary to make some assumptions about the distribution of the ti: in the present paper Ɛ-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 Ɛ-uniformity is needed. This work may be of interest in computer graphics, approximation and complexity theory, digital and computational geometry, and digital image processing.