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Partial differential equations for function based geometry modelling within visual cyberworlds

By Hassan Ugail and A. Sourin

Abstract

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

Topics: Partial differential equations (PDEs), Shape modelling, Visual cyberworlds, Biharmonic equation
Publisher: IEEE Computer Society
Year: 2008
OAI identifier: oai:bradscholars.brad.ac.uk:10454/2612
Provided by: Bradford Scholars

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