With prescribed (free) boundary curves you can plot the surface satisfying the PDE . For , this is a biharmonic surface. You can choose the height () of any boundary control point. You can modify the prescribed boundary curves and the parameter to see the change in the surface.
In the authors' preprint "Bézier PDE Surfaces for Interactive Design", submitted to the Journal of Computer Aided Geometric Design, they give an explicit formula for the Bézier control points of the PDE surface that fulfills the modified biharmonic equation for a prescribed boundary.
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