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I have $n$ points (in this example $11$) and I need to interpolate them in such a way that I have a function $f(t) \rightarrow (R, R)$ where $t \in [0; 2\pi]$. It can be parametric curve, but I need to have a function.

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    @RahulNarain I want to parameterize points belong to convex hull (but function should return points between them).2012-05-12

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Order the points according to polar coordinates centered at the barycenter. Join consecutive points by a line segment. This gives you a piecewise linear curve using the angle as parameter.

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    See also [Graham scan](http://en.wikipedia.org/wiki/Graham_scan).2012-05-11