Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow (1999) [275 citations — 20 self]
http://www.multires.caltech.edu/pubs/ImplicitFairi
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author = {Mathieu Desbrun and Mark Meyer and Peter Schröder and Alan H. Barr},
title = {Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow},
year = {1999}
}
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Abstract:
In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high-fidelity computer graphics objects using imperfectly-measured data from the real world. Our approach contains three novel features: an implicit integration method to achieve efficiency, stability, and large time-steps; a scale-dependent Laplacian operator to improve the diffusion process; and finally, a robust curvature flow operator that achieves a smoothing of the shape itself, distinct from any parameterization. Additional features of the algorithm include automatic exact volume preservation, and hard and soft constraints on the positions of the points in the mesh. We compare our method to previous operators and related algorithms, and prove that our curvature and Laplacian operators have sev...
