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    Towards a definition of virtual objects with Partial Differential Equations

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    Publication date
    2009
    Author
    Ugail, Hassan
    Sourin, A.
    Sourina, O.
    Gonzalez Castro, Gabriela
    Keyword
    PDE
    Shape modelling
    Shared virtual spaces
    X3D
    VRML
    Peer-Reviewed
    Yes
    
    Metadata
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    Abstract
    We propose an efficient alternative to commonly used parametric surfaces such as NURBS surfaces for definition of complex geometry in shared virtual spaces. Our mathematical model allows to define objects by only providing coordinates of the section curves in 3-space. The resulting parametric functions allow fast calculation of the coordinates of the points on the surface of the objects. We devise an algorithm which evaluates the coefficients of these functions in real time. Given the small size of the resulting formulas and interactive rates for their calculation, we are able to efficiently use such PDE-based models for making virtual objects in shared virtual spaces. We describe the modeling framework and illustrate the proposed theoretical concepts with our function-based extension of VRML and X3D.
    URI
    http://hdl.handle.net/10454/4967
    Version
    No full-text available in the repository
    Citation
    Ugail H., Gonzalez Castro, G., Sourin, A. and Sourina, O. (2009). Towards a definition of virtual objects with Partial Differential Equations. In: Proceedings of International Conference on Cyberworlds, Bradford, 7-11 Sept, 2009. pp. 138-145.
    Type
    Conference paper
    Collections
    Engineering and Digital Technology Publications

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