Generalized Barycentric Coordinates Based Mesh Editing

Mesh editing can be widely applied in computer animation, geometric modeling, 3D game and virtual simulation. The performance of mesh editing approaches closely depends on time efficiency, degree of freedom for control and detail preservation. With advance in barycentric coordinates and GPU, mesh editing based on generalized barycentric coordinates recently gains more and more attention.The pipeline of this kind of editing is as follows: firstly, a coarse closed mesh, known as cage, should be created to bound the source mesh; Secondly, generalized barycentric coordinates of each vertex of the source mesh are computed with respect to the cage so that each vertex of the source mesh can be expressed as a unique linear combination of the vertices of the cage; Finally, instead of directly manipulating the source mesh, we edit the cage and pass the deformations of the cage onto the source mesh by the coordinates. As the generalized barycentric coordinates can be precomputed, the deformation transfer is completed by blending the vertices of the cage using the coordinates, mesh editing based on generalized barycentric coordinates is usually very efficient. Morever, as the barycentric coordinates only depend on the topology of the cage, and has nothing to do with the source mesh, this makes it possible editing any kind of geometries, even point clouds.This paper studies generalized barycentric coordinates based mesh editing. The main contributions include:Four kinds of typical generalized barycentric coordinates are compared in terms of properties such as time efficiency, interior locality, non-negative, smoothness, Lagrange interpolation and detail preserving. This can guide the selection of generalized barycentric coordinates in mesh editing.Equidistance cage generation is investigated. Given a triangular mesh to be edited, we firstly decimate it by the QEM simplification method. A distance field is then built with respect to the simplified model and an offset mesh is subsequently extracted according to a specified distance value. Finally mesh simplification is performed again on the offset mesh to create a simple cage. Cages created by our method look good and can be successfully applied in mesh editing and deformation based on barycentric coordinates.