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