# Fitting of Closed Curve in the Polar Coordinate.

I know how to fit a curve when given some data points in the cartesian coordinate. Recently, I encountered a model that needs to fit a closed curve in the polar coordinate. I'm thinking of deducing a similar formula using Maximum Likelyhood, but the problem is I don't know what kind of hypothesis to choose.

In Cartesian coordinate, we can use the hypothesis of Polynomials $y=a_nx^n+...+a_0$, but this cannot be extended to my model because the "polynomial" in the polar coordinate $r=a_n\theta^n+...+a_0$ may not be closed.

What can I do?

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Possibly I'm crazy, but why don't you try expasion in $\sin(n~\theta)$ and $cos(n~\theta)$? –  H. Kabayakawa Jun 6 '12 at 19:31