Documentation API of the 'vmm3d.surface.parametric.ChenGackstatter' Java class

Class ChenGackstatter

  • All Implemented Interfaces:
    EventListener, ChangeListener, Decorateable, Parameterizable

    public class ChenGackstatterextends WeierstrassMinimalSurface
    The Chen-Gackstatter surface posed surprising numerical difficulties, which increased with exponent. 1.) One cannot integrate the Weierstrass Data close enough into the three saddles to close gaping holes, starting at exponent = 5. 2.) For putting the pieces together one has to find the intersection of the symmetry planes. Only after experimentation did I find points on these symmetry lines that allowed to compute the intersection with sufficient accuracy. This then worked also in the Lopez-Ros morph. 3.) Finally, the period-closing Lopez-Ros value had to be found. One only has to solve a linear equation with coefficients depending on the minimal surface. For reasons that I could not find this worked only for symmetry parameters 2,3,4,5 and then developed visible inaccuracies. These went away after repeating the determination of the Lopez-Ros parameter three times. This indicates that the linear equation has inaccurately defined coefficients, but I do not see a reason for that. 4.) For esthetic reasons the big holes had to be closed. For the top and bottom symmetry points this worked satisfactorily. The middle symmetry point still has gaps for exponent > 5. H. Karcher

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