Despite recent advances in geometric modeling, 3D mesh modeling still involves a considerable amount of manual labor by experts. In this paper, we introduce Mesh Draping: a neural method for transferring existing mesh structure from one shape to another. The method drapes the source mesh over the target geometry and at the same time seeks to preserve the carefully designed characteristics of the source mesh. At its core, our method deforms the source mesh using progressive positional encoding. We show that by leveraging gradually increasing frequencies to guide the neural optimization, we are able to achieve stable and high quality mesh transfer. Our approach is simple and requires little user guidance, compared to contemporary surface mapping techniques which rely on parametrization or careful manual tuning. Most importantly, Mesh Draping is a parameterization-free method, and thus applicable to a variety of target shape representations, including point clouds, polygon soups, and non-manifold meshes. We demonstrate that the transferred meshing remains faithful to the source mesh design characteristics, and at the same time fits the target geometry well.
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