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In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth sur- face. 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 integra- tion method to achieve efficiency, stability, and large time-steps; a scale-dependent Laplacian operator to improve the diffusion pro- cess; 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 vol- ume preservation, and hard and soft constraints on the positions of the points in the mesh. We compare our method to previous operators and related algo- rithms, and prove that our curvature and Laplacian operators have several mathematically-desirable qualities that improve the appear- ance of the resulting surface. In consequence, the user can easily select the appropriate operator according to the desired type of fair- ing. Finally, we provide a series of examples to graphically and numerically demonstrate the quality of our results.

Implicit fairing of irregular meshes using diffusion and curvature flow