Tech Report WUCSE-2004-9: Improved Curvature Estimation on Triangular Meshes

This paper takes a systematic look at calculating the curvature of surfaces represented by triangular meshes. We have developed a suite of test cases for assessing the sensitivity of curvature calculations, to noise, mesh resolution, and mesh regularity. These tests are applied to existing discrete curvature approximation techniques and three common surface fitting methods (polynomials, radial basis functions and conics). We also introduce a modification to the standard parameterization technique. Finally, we examine the behaviour of the curvature calculation techniques in the context of segmentation.