Mesh fairing based on an intrinsic PDE approach

Abstract In this paper, we propose to create fair surfaces satisfying prescribed G 1 boundary constraints, based on solving a partial differential equation (PDE) that is intrinsic. The PDE is simple and leads to surfaces that have no local mean curvature extrema in the interior. It enables the reproduction of the important class of surfaces with constant mean curvature, containing spheres, cylinders and minimal surfaces. As an application, we present an algorithm that creates fair meshes with a semi-regular structure. The construction scheme is designed to produce meshes that are partitioned into regular domains. Using this domain knowledge in advance, we can develop a fast iterative algorithm that produces surfaces of high aesthetic quality.

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