This paper presents an interactive 3D mesh smoothing method, which is useful for intuitive, efficient geometric modeling of freeform polygonal models. With our method, users can remove unwanted bumps and cavities, or smooth creases by drawing two strokes to map out the smoothing area. Discrete fairing is applied on the surrounded area to minimize its membrane energy and its thin plate energy. During the process of fairing, an umbrella operator smoothes the vertices in the surrounded area one by one; and a remeshing scheme is used to optimize the topology structure of the mesh inside the surrounded area during smoothing. Compare to other well-known approaches, our method will not be influenced by the topology structure of the smoothing mesh. Thus, it can be applied to any triangular mesh surface. At the end of this paper, examples of our mesh smoothing implementation are shown to demonstrate its functionality.

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