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    Partial differential equations for function based geometry modelling within visual cyberworlds

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    UgailSourinPartial2008.pdf (684.9Kb)
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    Publication date
    2008
    Author
    Ugail, Hassan
    Sourin, A.
    Keyword
    Partial differential equations (PDEs)
    Shape modelling
    Visual cyberworlds
    Biharmonic equation
    Rights
    Copyright © [2008] IEEE. Reprinted from International Conference on Cyberworlds, 2008. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Bradford's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubspermissions@ ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
    Peer-Reviewed
    Yes
    
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    Abstract
    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 problems. Here we show how the PDE based on the Biharmonic 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 geometry whereby the resulting geometry can be visualised efficiently at arbitrary levels of shape resolutions. In particular, we discuss how function based PDE surfaces can be readily integrated within VRML and X3D environments
    URI
    http://hdl.handle.net/10454/2612
    Version
    Accepted Manuscript
    Citation
    Ugail, H. and Sourin, A. (2008). Partial differential equations for function based geometry modelling within visual cyberworlds. In: International Conference on Cyberworlds. IEEE Computer Society. pp.224-231.
    Link to publisher’s version
    http://ieeexplore.ieee.org/document/4741304/
    Type
    Conference paper
    Collections
    Engineering and Informatics Publications

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