Partial differential equations for function based geometry modeling within visual cyberworlds

We propose the use of Partial Differential Equations (PDEs) for shape modelling within visual cyberworlds. PDEs, especially those that are elliptic in nature, enable surface modelling to be defined as boundary-value prob-lems. Here we show how the PDE based on the Bihar-monic equation subject to suitable boundary conditions can be used for shape modelling within visual cyberworlds. We discuss an analytic solution formulation for the Biharmonic equation which allows us to define a function based geom-etry whereby the resulting geometry can be visualised effi-ciently at arbitrary levels of shape resolutions. In partic-ular, we discuss how function based PDE surfaces can be readily integrated within VRML and X3D environments. 1