ISSN : 1796-2048
Volume : 2    Issue : 6    Date : November 2007

Shape Morphing of Complex Geometries Using Partial Differential Equations
Gabriela González Castro and Hassan Ugail
Page(s): 15-25
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An alternative technique for shape morphing using a surface generating method using partial
differential equations is outlined throughout this work. The boundaryvalue nature that is inherent to
this surface generation technique together with its mathematical properties are hereby exploited for
creating intermediate shapes between an initial shape and a final one. Four alternative shape
morphing techniques are proposed here. The first one is based on the use of a linear combination
of the boundary conditions associated with the initial and final surfaces, 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. The fourth of these alternatives is based on the manipulation of the spine of the
surfaces, which is computed as a by-product of the solution. Results of morphing sequences
between two topologically nonequivalent surfaces are presented. Thus, it is shown that the PDE
based approach for morphing is capable of obtaining smooth intermediate surfaces automatically
in most of the methodologies presented in this work and the spine has been revealed as a powerful
tool for morphing surfaces arising from the method proposed here.

Index Terms
Morphing, PDE surfaces, Geometric modelling, PDE method, geometric algorithms, boundary