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Controllable C1 continuous blending of time-dependent parametric surfaces

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Abstract

This paper proposes the concept of blending time-dependent varying surfaces, and develops a new method to create a controllable C1 continuous blending surface between primary parametric surfaces whose position and shape change with time. We treat it as a boundary-valued problem defined by the mathematical model of a vectored dynamic fourth-order partial differential equation subjected to time-dependent C1 continuous blending boundary constraints. High performance blending surface generation is achieved through the development of an approximate analytical solution of the mathematical model. We investigate the accuracy and efficiency of the solution, study the effective shape control of the blending surfaces, and apply the obtained solution to tackle surface blending problems. The applications demonstrate that our proposed approach is very effective and efficient in dealing with controllable C1 continuous surface blending between time-dependent varying parametric surfaces.

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Acknowledgements

This research is supported by the grant of UK Royal Society International Joint Projects/NSFC 2010.

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Authors and Affiliations

  1. National Center for Computer Animation, Bournemouth University, Bournemouth, UK

    L. H. You & Jian J. Zhang

  2. Center for Visual Computing, University of Bradford, Bradford, UK

    H. Ugail

Authors
  1. L. H. You
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  2. H. Ugail
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  3. Jian J. Zhang
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Correspondence to L. H. You.

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You, L.H., Ugail, H. & Zhang, J.J. Controllable C1 continuous blending of time-dependent parametric surfaces. Vis Comput 28, 573–583 (2012). https://doi.org/10.1007/s00371-012-0693-0

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  • DOI: https://doi.org/10.1007/s00371-012-0693-0

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