Surface modeling with boundary constraints and partial differential equations

In this paper, we present a method to create and manipulate free form surfaces. A surface is generated from boundary constraints through a vector-valued fourth order partial differential equation involving an externally applied force. In addition to this function, the boundary constraints and the externally applied force also serve as shape manipulation tools. The proposed approach is applied in surface creation, surface manipulation, surface rebuilding and surface animation. It can tackle the problems of tangential continuity in patch modeling and is cheap to compute. The examples given in this paper indicate that our proposed method can create and manipulate free from surfaces easily and quickly.