# parametric cartoon curve

is there a algorithm that turns a drawing into parametric curves?

Ok. I think i know. The general simplest non-trivial case is to draw 2 arbitrarily shaped ovals, as 2 loops. We can focus on drawing one loop first. It'll have the form {f,g} with sine in both, basically a deformed circle. To draw 2nd or more loops, find the t range for the loops, e.g. Range1=[t1Min,t1Max], range2=[t2Min,t2Max], shift them so that t1Max == t2Min. This solves the drawing multiple loops problem. Unit step function (aka Heaviside step function) can be used if needed for lifting pen. [ Heaviside step function ] [ 2021-02-08 https://en.wikipedia.org/wiki/Heaviside_step_function ]

Now, how do you find the parametric equation for a cartoon loop? Basically, you use curve fitting methods. The loop is a sequence of {x,y} data points. Decompose the loop's x and y axis movements. Lets focus on the x-axis first. You get a sequence of values. You just find a function for it. It can be a polynomial function. This is easy as there are established algorithms. But creating a sine function shouldn't be difficult, either directly from data or turning the polynomial into sine.

[Making Formulas… for Everything—From Pi to the Pink Panther to Sir Isaac Newton By Michael Trott. At https://blog.wolfram.com/2013/05/17/making-formulas-for-everything-from-pi-to-the-pink-panther-to-sir-isaac-newton/ ]