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Recent works in geometric modeling show the advantage of local differential in various surface processing applications. In this paper we review methods that advocate surface representation via differential as a basis to interactive mesh editing. One of the main challenges editing a mesh is to retain the visual appearance of the surface after various modifications. The differential coordinates capture the local details and therefore are a natural surface representation for applications. The coordinates are obtained by applying a linear to the mesh geometry. Given suitable deformation constraints, the mesh is reconstructed from the differential representation by solving a linear system. The differential coordinates are not rotation-invariant thus their rotation must be explicitly handled in order to retain the orientation of the surface details. We review two methods for computing local rotations: the first estimates them heuristically using a deformation only preserves the underlying smooth surface, and the second estimates rotations implicitly through a variational representation of the problem. show that the linear reconstruction system can be solved fast enough to interactive response time thanks to a precomputed factorization of coefficient matrix. We demonstrate that this approach enables to edit meshes while retaining the shape of the details in their natural.
Lipman et al. (Wed,) studied this question.