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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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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
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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. –  lhf May 11 '12 at 22:24
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