Computing Curvatures Based on Template Sampling and MLS Energy Function

Most conventional curvature computational algorithms run in a k-ring neighborhood(k=1,2,3),which is inevitably subject to meshing quality and resolution.To overcome the disadvantage,this paper proposes a novel algorithm for curvature computation based on template sampling and MLS energy functions.First,local discrete exponential maps centered at each vertex are computed as a preprocessing step.Second,the actual point set contributing to curvature computation is extracted by mapping a given 2D sampling template onto the curved surface.Finally,we directly compute curvatures based on MLS energy functions,without a surface fitting operation.Theoretically speaking,this algorithm avoids the inconsistence from triangulation.Experimental results show that the new approach is able to extract curvatures stably,robust to meshing quality and resolution,and insensitive to noises.