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
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/2612 |
| Date | January 2008 |
| Creators | Ugail, Hassan, Sourin, A. |
| Publisher | IEEE Computer Society |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Conference paper, Accepted manuscript |
| 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. |
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