Uniformly interleaved decorative knots

Knots created by combinations of sines and cosines are common and generalise to produce curves which can be quite complex. Loop crossings can be interleaved in simple knots with carefully chosen sin/cosine functions but these are only approximations and often need large amplitudes to ensure crossing don't intersect..

In these designs, the interleaving is done by computing the crossing points and then using a segmented cosine function in which each half-wavelength is equal to the 'length'