Interactive control of mesh topology in quadrilateral mesh generation based on 2D tensor fields

Generating quadrilateral meshes is very important in many industrial applications such as finite element analysis and B-spline surface fitting. However, it is still a challenging task to design appropriate vertex connectivity in the quadrilateral meshes by respecting the shapes of the target object and its boundary. This paper presents an approach for interactively editing such mesh topology in quadrilateral meshes by introducing a 2D diffusion tensor field to the interior of the target object. The primary idea is to track the two principal directions of the tensor field first and then construct the dual graph of the quadrilateral mesh, so that we can control the mesh topology through the design of the underlying 2D diffusion tensor field. Our method provides interactive control of such mesh topology through editing the orientations of the tensor samples on the boundary of the target object. Furthermore, it also allows us to intentionally embed degeneracy inside the object to introduce extraordinary (i.e., non-degree-four) vertices according to user requirements.