Triangular surface mesh fairing via Gaussian curvature flow

Authors:
Huanxi Zhao;Guoliang Xu
Affiliations:
Department of Mathematics, Central South University, Changsha, China and LSEC, ICMSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China;LSEC, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, China
Venue:
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Year:
2006

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Abstract

Surface mesh fairing by the mean curvature flow and its various modifications have become a popular topic. However, very few researches have been attempted on using the Gaussian curvature flow in surface fairing. The aim of this paper is to investigate such a problem. We find that Gaussian curvature flow can only be used to smooth convex meshes. Hence, it cannot be used to smooth noisy surface meshes because a noisy surface mesh is not convex. To overcome this difficulty, we design a new diffusion equation whose evolution direction depends on the mean curvature normal and the magnitude is a properly defined function of the Gaussian curvature. Experimental results show that the designed fairing scheme can effectively remove the noise and simultaneously preserve the sharp features, such as corners and edges.