Shape Morphing using PDE Surfaces

G. González Castro, H. Ugail, P. Willis, and I.J. Palmer (UK)


Geometric modelling, geometric algorithms, bound ary representations, morphing.


A methodology for shape morphing using partial dif ferential equation (PDE) surfaces is presented in this work. The use of the PDE formulation shows how shape morph ing can be based on a boundary-value approach by which intermediate shapes can be created. Furthermore, the mathematical properties of the method give rise to several alternatives in which morphing one shape into another can be achieved. Three of these alternatives are presented here. The first one is based on the gradual variation of the weighted sum of the boundary conditions for each surface, the second one consists of varying the Fourier mode for which the PDE is solved whilst the third results from a combination of the first two. Examples showing the efficiency of these methodologies are presented. Thus, it is shown that the PDE based approach for morphing, when combined with a parametric variation of the boundary conditions, is capable of obtaining smooth intermediate surfaces automatically.

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