Curly-Cue: Geometric Methods for Highly Coiled Hair

We present geometric methods for generating shapes that are characteristic of highly coiled hair. Different features become visually relevant when hairs are well-approximated by high-frequency helices instead of low-frequency curves, so we present algorithms for three such phenomena. First, a Fourier-based method for phase locking, the process by which disparate helices near the scalp coalesce into a single curl. Second, a method for period skipping which models individual helices deviating from the coalesced curl. Third, a non-linear optimization that directly generates the shapes of switchbacks, a.k.a.~helical perversions, which heretofore could only be produced through direct physical simulation. By applying all three methods in tandem, we show that we can achieve richly detailed depictions of highly coiled hair.