This reminds me of a related question I've long had about measuring curvature of a given physical object. In the University of Goettingen's math museum, there's a sculpture of Apollo with lines inked on the surface to separate regions of positive curvature from regions of negative curvature. The book Geometry and the Imagination by Hilbert and Cohn-Vossen shows this object as Fig. 204 and says Felix Klein had the lines drawn on it to test his theory of facial beauty based on curvature. I'm curious what his theory was, but what I'm mainly wondering is how were the lines drawn? What technique or physical device does one apply to a given physical surface to locate the "parabolic lines" that separate areas of positive and negative curvature?
Given that Klein died in 1925, I suspect it was doen by hand by an artist who felt the surface for the poins of zero curvature. What I would think would be interesting would be to get a three-dimensional digital representation of the statue; apply some more formal technique; and see how well the two agree. Whit