A friend of mine sent me a Wofram Alpha link to a parametric curve that creates a detailed drawing of a game character.
The parametric equation that draws it is about ~9 screens tall on my computer; and appears to consist of thousands of sine's added together; unlike simpler examples like the Batman Curve, this would have taken an enormous amount of effort to construct by hand; leaving me wondering how exactly is something like this created?
My guess for this case:
The drawing was recorded as a sequence of $(x,y)$ couples, using a graphical editor. The coordinates were considered as functions of an independent parameter $t$, defining $x(t)$ and $y(t)$. (The simplest rule is to assign $t=\frac in$ to the $i^{th}$ point).
Then the Fourier series mechanism allows to express these functions as sums of sinusoids of higher and higher frequencies, with computed phases and amplitudes, allowing to interpolate the curve for any $t$.
In addition, the Heaviside function was used to introduce discontinuities. How the two techniques were combined should be deeper scrutinized.
