Sampling points on regular parametric curves with control of their distribution

We propose an iterative algorithm to generate a sequence of a prescribed number of points on a parametric curve with control of their distribution. Our algorithm depends on a free parameter which controls the achievement of a final distribution of points lying between two extreme cases: uniform arc length distribution and bending energy dependent distribution. This is obtained by computing a reparametrization function that interpolates the inverse of the arc length function at equidistant arguments. The proposed reparametrization function is a C1 rational linear spline, therefore if the original curve is a NURBS then the reparametrized curve is also a NURBS of the same degree, but with an enlarged set of knots.

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