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.
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.
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.
Behnood Eghbali
How?!
Oct 4, 2012
Daniel Piker
The optimization is done with a combination of equalization, planarization and bending forces.
I'll post a definition soon.
Oct 4, 2012
Michael Pryor
"The optimization is done with a combination of equalization, planarization and bending forces." you forgot to add skills ;)
well done
Oct 4, 2012
Behnood Eghbali
thank u so much for sharing :)
Oct 4, 2012
David Stasiuk
wow!
Oct 4, 2012
Daniel Piker
Here's the model if anyone is interested:
http://dl.dropbox.com/u/26034251/discrete_costa.3dm
Oct 4, 2012
Daniel Piker
and here's the definition:
http://dl.dropbox.com/u/26034251/quasiisothermic.gh
Oct 4, 2012
Behnood Eghbali
so you can create all types of minimal surfaces... this is really awesome ;)
Oct 4, 2012
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.
Oct 4, 2012
Woong Ki Sung
Wow, this is awesome. Could you let me know where can I find references to understand the algorithm?
Oct 4, 2012
Vangel Kukov
Thanks for sharing!
Oct 5, 2012
Dedackelzucht
Yeah! Awesome! Thanks for sharing!
Oct 5, 2012
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.
Oct 5, 2012
Roig
awesome¡¡ thanks4sharing
Oct 5, 2012
Behnood Eghbali
thx for sharing! very helpful!
Oct 5, 2012
first1
HI, Daniel, I can't open the quasiisothermic. gh file, why? my version is rhino5 ,gh 0.9.0006
Oct 6, 2012
PEPE ALGECIRAS
Hi, Daniel, I'm unable to open it too, although my version is gh 0.9.0006 but in Rhino 4
Nov 15, 2012
GuangYang
thank you very much!!!!
Apr 1, 2014
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.
May 23, 2017
Abderrahman Taha
Very nice work! Thanks for sharing
Nov 4, 2017
Angel Antequera
the files are no longer available, can somebody send me the files please...
thanks in advance.
Jan 27, 2018
jasonroc
the link of the gh&3dm file was lost~ could plz attach them again? thank you very much
Dec 24, 2018