The torsion, the local conical constants and their application in corneal topography

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.