PDE Surface Generation with Combined Closed and Non-Closed Form Solutions

Partial differential equations (PDEs) combined with suitably chosen boundary conditions are effective in creating free form surfaces. In this paper, a fourth order partial differential equation and boundary conditions up to tangential continuity are introduced. The general solution is divided into a closed form solution and a non-closed form one leading to a mixed solution to the PDE. The obtained solution is applied to a number of surface modelling examples including glass shape design, vase surface creation and arbitrary surface representation.