Elevation topography equipment measures freeform surfaces by representing the surface with elevation maps, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature. From a geodetic point of view, every regular point on a parametric surface can be described as a function of the principal curvatures and the local torsion concerning a reference path at each point. Here, we present some fundamentals required to create these density maps to represent the absolute torsion and the local conic constant of all points on a regular freeform surface.
Valencia-Estrada et al. (Wed,) studied this question.