In this paper, we introduce a 3D local operator that automatically combines typical simpler operators as removal of vertices, collapse of edges or swap of faces and edges. This operator is inherited from incremental methods where the mesh k is modified iteratively through sequences of insertion of a point P: Hk+1=Hk−CP+BP, where CP is the cavity of P and BP the ball of P. We derive two algorithms to compute Cp . The first algorithm is tuned to be a fast point reprojection to the geometry even in the presence of a boundary layer mesh. The second one is tuned to generate boundary layer meshes for complex geometries. We show how quasi-structured elements can be enforced. In addition, enhancements as multi-normals can be incorporated in the process. Both operators can be used with surface and volume point while preserving a given geometry. They rely on the use on an existing initial volume mesh and always produce a valid 3D mesh on output.