Remeshing by Curvature Driven Diffusion
We present a method to regularize an arbitrary topology mesh M, which defines a piecewise linear approximation of a surface \(\mathcal{M}\) , with the purpose of having an accurate representation of \(\mathcal{M}\) : the density of the nodes should correl
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Remeshing by Curvature Driven Diffusion Serena Morigi and Marco Rucci
Abstract We present a method to regularize an arbitrary topology mesh M , which defines a piecewise linear approximation of a surface M , with the purpose of having an accurate representation of M : the density of the nodes should correlate with the regularity of M . We use the mean curvature as an intrinsic measure of regularity. Unlike sophisticated parameterization-dependent techniques, our parameterizationfree method directly redistributes the vertices on the surface mesh to obtain a good quality sampling with edges on element stars approximately of the same size, and areas proportional to the curvature surface features. First, an appropriate area distribution function is computed by solving a partial differential equation (PDE) model on the surface mesh, using discrete differential geometry operators suitably weighted to preserve surface curvatures. Then, an iterative relaxation scheme incrementally redistributes the vertices according to the computed area distribution, to adapt the size of the elements to the underlying surface features, while obtaining a good mesh quality. Several examples demonstrate that the proposed approach is simple, efficient and gives very desirable results especially for curved surface models with sharp creases and corners.
11.1 Introduction The 3D geometry commonly used for shape representation in geometric modeling, physical simulation and scientific visualization is mainly based on meshes. The 3D scanning devices, medical equipments and computer vision systems often perform a uniform acquisition without any a priori knowledge of the surface properties. This may lead to raw meshes with a sampling quality usually far away from the desired sampling distribution needed for subsequent processing. Algorithms S. Morigi () M. Rucci Department of Mathematics-CIRAM, University of Bologna, Bologna, Italy e-mail: [email protected]; [email protected] M. Breuß et al. (eds.), Innovations for Shape Analysis, Mathematics and Visualization, DOI 10.1007/978-3-642-34141-0 11, © Springer-Verlag Berlin Heidelberg 2013
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for mesh simplification, denoising (fairing), decimation and remeshing represent fundamental preliminary steps in mesh processing. In particular, remeshing refers to the improvement process of the mesh quality in terms of redistribution of the sampling, connectivity of the geometry, and triangle quality, in order to satisfy mesh property requirements while maintaining surface features. The reader is referred to [1] and the references therein for a survey on remeshing techniques. Some remeshing techniques are parameterization-dependent, i.e. they associate the mesh with a planar parameterization, and apply the algorithms on this plane. For arbitrary genus objects, this involves also the creation of an atlas of parametrization, a well known complex process that inevitably introduces some metric distortion and may lead to the loss of important feature information [2, 4, 9].
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