Estimation of the principle curvatures of approximated surfaces

This paper presents a method for estimating curvature values of a surface, which is given only approximatively, e.g., by measured data. The presented method requires estimates of the curvature of curves. These lead, along with the theorems from Euler and Meusnier, to the values of surface curvature. Methods are presented, which converge with the different error order of O(h2) and O(h2n). For the first of them explicit formulae are given. It is proved that the error order remains the same through all further calculations until the final estimation of surface curvature is found.  2000 Published by Elsevier Science B.V. All rights reserved.