Discrete Costa Surface

Inspired by Stefan Sechelmann's presentation at the recent AAG, I've been having a go at using Kangaroo to optimize for quasiisothermic meshes. This is a discrete Costa Minimal Surface. All the quads are planar with tangent incircles.

  • Behnood Eghbali

    How?!

  • Daniel Piker

    The optimization is done with a combination of equalization, planarization and bending forces.

    I'll post a definition soon.

  • Michael Pryor

    "The optimization is done with a combination of equalization, planarization and bending forces." you forgot to add skills ;)

    well done

  • Behnood Eghbali

    thank u so much for sharing :)

  • David Stasiuk

    wow!

  • Daniel Piker

    Here's the model if anyone is interested:

    http://dl.dropbox.com/u/26034251/discrete_costa.3dm

  • Daniel Piker

  • Behnood Eghbali

    so you can create all types of minimal surfaces... this is really awesome ;)

  • Daniel Piker

    Yes, in theory this approach should work with many types of surface. The tricky part is initializing it with the right singularities though.

  • Woong Ki Sung

    Wow, this is awesome. Could you let me know where can I find references to understand the algorithm?

  • Vangel Kukov

    Thanks for sharing!

  • Dedackelzucht

    Yeah! Awesome! Thanks for sharing!

  • Daniel Piker

    For further reading :

    http://page.math.tu-berlin.de/~sechel/DiplomaThesis.pdf

    http://page.math.tu-berlin.de/~bobenko/MinimalCircle/minsurftalk.pdf

    and 

    S. Sechelmann, T. Roerig, and A. I. Bobenko. Quasiisothermic Mesh Layout. In Hesselgren, L.; Sharma, S.; Wallner, J.; Baldassini, N.; Bompas, P.; Raynaud, J. (Eds.). Advances in Architectural Geometry 2012. 2012, 344 p. 285 illus. in color. ISBN 978-3-7091-1250-2

     

    I use a slightly different energy (which I'll write a post about soon), but to optimize towards the same condition.

  • Roig

    awesome¡¡ thanks4sharing

  • Behnood Eghbali

    thx for sharing! very helpful!

  • first1

    HI, Daniel, I can't open the quasiisothermic. gh file, why? my version is rhino5 ,gh 0.9.0006

  • PEPE ALGECIRAS

    Hi, Daniel, I'm unable to open it too, although my version is gh 0.9.0006 but in Rhino 4

  • GuangYang

    thank you very much!!!!

  • Xavier Tellier

    Hi Daniel,

    I would really like to see how you implemented this surface. However, it looks like you deleted the gh file from your dropbox. Would you mind sharing it again ? I am particularly interested in how you implemented the formula given by Mr. Bobenko to compute the radii of the circles.

  • Abderrahman Taha

    Very nice work! Thanks for sharing

  • Angel Antequera

    the files are no longer available, can somebody send me the files please...
    thanks in advance.

  • jasonroc

    the link of the gh&3dm file was lost~ could plz attach them again? thank you very much