The details of the math are beyond me (if anyone could explain it, that’d be awesome), but I believe it basically uses Fourier series-based formulas to reduce the curves of text into equations.

I don’t see any real Fourier here, just a parametric breakdown of x (first 9 lines) and y (next three lines) as a function of t (usually time). If it were a result of Fourier analysis, each term would have a linear increment of the multiplier for t.

Though I am reminded of the original “Duck Dodgers in the 24-1/2 Century” cartoon [Daffy Duck cast as Duck Dodgers, Porky Pig as Space Cadet].