Improved Curvature Estimation on Triangular Meshes

This paper takes a systematic look at several techniques for calculating curvature of a surface that is represented by a triangular mesh. Both discrete curvature approximation techniques and surface fitting methods are considered. We develop new methods based on a surface fit using a natural surface parameterization, and by fitting a general equation for a conic as an implicit function. Another key contribution is development of a suite of test cases for assessing the sensitivity of these, and existing methods, to noise, mesh resolution, and mesh regularity. Finally, assesment of the new and existing curvature calculation techniques is applied to the problem of segmenting complex surfaces.