Schramm circle pattern

A Schramm circle pattern, as described by Oded Schramm in his paper 'Circle patterns with the combinatorics of the square grid' generated using Kangaroo

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  • Dedackelzucht

    Hey Daniel,

    yes, thats exactly how I did it. Funny! Like in the script explained I started with the "DUPIN CYCLIDES" and then connected them together to "CYCLIDIC NETS" based on four circles.

    Where do you have all so cool pdfs from? :-)

    Best Regards

    DeDackel

  • Daniel Piker

    DeDackel,

    This could be something really interesting to try on a circular quad mesh.

    (there are already some examples up of how equalization forces in Kangaroo can be used to generate such a mesh, where the vertices of each quad lie on a circle. I'll try and post some more examples soon though).

    Then you could fit a cyclide patch like you show below to each quad/circle of the mesh.

    For a given circular mesh, you still have a choice of how you orient the corner frames - though once you fix one, that determines all the others through mirroring operations.

    I think it should also be possible to use Kangaroo to generate and transform cyclidic nets directly, based on the 'cyclidic cube' construction in that first paper.

    Lots of fun things to try!

  • Dedackelzucht

    Hey,

    2 out of 3 orientations of the frames (corners where 4 circles touch) are fixed. If you see it as a strict rectengular grid the x and y direction have alternate positive and negative the same angle. this angel you can change it has a impact on the radius of the edge-arcs of each patch.

    Right now I have too much to do . I cannot spent some more time now in it... :-(

    Thanks again

    DeDackel