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I am doing some numerical computations searching for an optimal shape for a certain functional. In my particular case, the shape $\Omega$ is a 2 dimensional star shaped domain by the origin, which means that its boundary can be completely characterized by the radial function $r(\theta)$. Developing $r$ into a Fourier series $r(\theta)=a_0/2+\sum a_n \cos(n\theta)+\sum b_n \sin (n\theta)$ and truncating to the first $M$ sin and cos coefficients we can get a pretty good approximation of the actual shape using only a finite number of parameters ($2M+1$).

Do you know any similar ways to characterize a general shape using only a finite number of parameters?

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