PDE blending surfaces with C continuity

In this paper, we propose to use a general sixth-order partial differential equation (PDE) to solve the problem of C² continuous surface blending. Good accuracy and high efficiency are obtained by constructing a compound solution function, which is able to both satisfy the boundary conditions exactly and minimise the error of the PDE. This method can cope with much more complex surface-blending problems than other published analytical PDE methods. Comparison with the existing methods indicates that our method is capable of generating blending surfaces almost as fast and accurately as the closed-form method and it is more efficient and accurate than other extant PDE-based methods.