Laplacian Surface Editing
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Surface editing operations commonly require geometric
details of the surface to be preserved as much as possible. We argue
that geometric detail is an intrinsic property of a surface and that,
consequently, surface editing is best performed by operating over an
intrinsic surface representation. We provide such a representation of
a surface, based on the Laplacian of the mesh, by encoding each vertex
relative to its neighborhood. The Laplacian of the mesh is enhanced to
be invariant to locally linearized rigid transformations and scaling.
Based on this Laplacian representation, we develop useful editing
operations: interactive free-form deformation in a region of interest
based on the transformation of a handle, transfer and mixing of
geometric details between two surfaces, and transplanting of a partial
surface mesh onto another surface. The main computation involved in
all operations is the solution of a sparse linear system, which can be
done at interactive rates. We demonstrate the effectiveness of our
approach in several examples, showing that the editing operations
change the shape while respecting the structural geometric detail.
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