a) (b) (c) (d) Figure 1. Generating fair triangle meshes with discrete elastica. (a) An initial mesh outlined a complex tubular object. (b) A discrete elastica surface (mesh) obtained from the initial mesh. (c) The Stanford bunny model with a large part of the mesh removed and then triangulated. (d) The modified part of the bunny is restored as a discrete elastica. Coloring by the mean curvature is used to demonstrate a high quality of the generated meshes. Abstract Surface fairing, generating

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... ree-form surfaces satisfying aesthetic requirements, is important for many computer graphics and geometric modeling applications. A common approach for fair surface design consists of minimization of fairness measures penalizing large curvature values and curvature oscillations. The paper develops a numerical approach for fair surface modeling via curvature-driven evolutions of triangle meshes. Consider a smooth surface each point of which moves in the normal direction with speed equal to a function of curvature and curvature derivatives. Chosen the speed function properly, the evolving surface converges to a desired shape minimizing a given fairness measure. Smooth surface evolutions are approximated by evolutions of triangle meshes. A tangent speed component is used to improve the quality of the evolving mesh and to increase computational stability. Contributions of the paper include also an improved method for estimating the mean curvature.