Finite difference surface representation considering effect of boundary curvature

摘要

Surface representation using the solution to a partial differential equation (PDE) is an important topic of computer graphics and computer aided design. In existing references, various free-from surfaces were created with a fourth order PDE which is only able to meet the tangential conditions at the surface boundaries. The need for a sixth order PDE in surface modeling arises in two situations: one is to generate surfaces with curvature continuity; and the other is to use curvature values as a user handle for surface shape manipulation. In this paper, we introduce such a sixth order PDE for free-form surface generation and develop a finite difference method to solve this PDE. We also investigate the effects of boundary curvature and the vector-valued shape parameters on the surface shape. It is found that their variation has strong influence on the shape of the surfaces, therefore, can be used as flexible user handles.