Mesh Editing Based on Discrete Laplace and Poisson Models

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. This intrinsic representation could be derived from differential properties of the mesh, i.e. its Laplacian. The modeling process poses nonzero boundary constraints so that this idea results in a Poisson model. Different ways of representing the intrinsic geometry and the boundary constraints result in alternatives for the properties of the modeling system. In particular, the Laplacian is not invariant to scaling and rotations. Either the intrinsic representation is enhanced to be invariant to (linearized) transformations, or scaling and rotation are computed in a preprocess and are modeled as boundary constraints. Based on this representation, useful editing operations can be developed: Interactive free-form deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric detail between two surfaces, and transplanting of a partial surface mesh into 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 this approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.