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Laplacian surface editing

: Sorkine, O.; Cohen-Or, D.; Alexa, M.; Rössl, C.; Seidel, H.-P.

Scopigno, R. ; European Association for Computer Graphics -EUROGRAPHICS-; Association for Computing Machinery -ACM-, Special Interest Group on Graphics -SIGGRAPH-:
SGP 2004, Symposium on Geometry Processing. Proceedings
Aire-la-Ville: Eurographics Association, 2004
ISBN: 3-905673-13-4
Symposium on Geometry Processing (SGP) <2, 2004, Nice>
Conference Paper
Fraunhofer IGD ()
computational geometry; surface representation; mesh

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.