Creating a parametric representation of a curve

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I have to do a project for my high school calculus class. I am interested in figuring out how to create equations for simple outlined shapes like this bird if I were to plot it on a coordinate plane. I have investigated the Fourier Series, but I am not quite sure how to implement it (where to start, I guess). I assume I should start by taking coordinates from the curve once at certain intervals, but I'm not sure where to go from there.