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Partial differential equations for function based geometry modelling within visual cyberworlds

Ugail, Hassan
; 
Sourin, A.
Publication Date
2008
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Keywords
Partial differential equations (PDEs), Shape modelling, Visual cyberworlds, Biharmonic equation
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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.
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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: 224-231.
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Link to Version of Record
https://doi.org/10.1109/CW.2008.42
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Conference paper
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