Surface representation using second, fourth and mixed order partial differential equations

Partial differential equations (PDEs) are powerful tools for the generation of free-form surfaces. In this paper, techniques of surface representation using PDEs of different orders are investigated. In order to investigate the real-time performance and capacity of surface generation based on the PDE method, the forms of three types of partial differential equations are put forward, which are the second, mixed and fourth order PDEs. The closed form solutions of these PDEs are derived. The advantages and disadvantages of each of them are discussed. A number of examples are given to demonstrate the use and effectiveness of the techniques.