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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.

enter image description here

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Do you need smooth function, or just piecewise linear will fit? – Norbert May 11 '12 at 21:48
I think that linear will be enough. – jcubic May 11 '12 at 21:55
The convex hull does not necessarily include all the points. So do you want to interpolate the $n$ points or do you want to parameterize the convex hull? – Rahul May 11 '12 at 23:15
@RahulNarain I want to parameterize points belong to convex hull (but function should return points between them). – jcubic May 12 '12 at 4:28

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. – lhf May 11 '12 at 22:24

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