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.
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There may be a better way, but one very time-consuming method is to try to parametrize each part individually and use the Heaviside function to switch the functions on and off at each boundary. See the Batman curve for an example of this type of parametrization. Here's a detailed discussion of each part courtesy of a math.SE user. – Sep 20 '16 at 00:50
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I actually did a project similar to this some years ago in a class teaching about parametric functions. The most efficient way to go about this is to use Bézier curves, which can be easily manipulated (i.e. they don't need exquisite manipulation like the Batman curve's components) and are very versatile. And they make up My Little Ponies. – Parcly Taxel Sep 20 '16 at 01:15