Blending solids with approximate analytical solution to PDE

Blending is an interesting subject in computer graphics and CAD. Although surface blending has been well studied, to our knowledge, solid blending remains a blank research area. In this paper, we develop a partial differential equation (PDE) based solid blending method where a vector-valued fourth order PDE together with some surface boundary conditions are involved. In order to solve the partial differential equation, we propose an approximate analytical method which satisfies all the boundary conditions exactly. Unlike surface blending which only gives the information on the blending surface, solid blending represents properly not only the external surface, but also the interior of the solid. Three examples are given in the paper to demonstrate the applications of the proposed method in solid blending.