HELP! PLANARIZE ISSUE

Replies to This Discussion

Permalink Reply by Andrew Heumann on January 1, 2012 at 9:46pm

Aren't you trying to do something impossible? Hexagons tile in a plane - you can't cover a non-planar shape with nothing but regular hexagons...

Permalink Reply by Manuel on January 2, 2012 at 6:58am

try only planarize polygon on exploded vertices...

Permalink Reply by Daniel Piker on January 2, 2012 at 7:31am

If you think about trying to tile a cylinder with planar hexagons, I believe the only possible solution is for some of the edges of each hexagon to become collinear (so they actually become rectangles) like so  :

It is possible in this way for the edge lengths of the hexagons to be regular, but not the angles.

It looks from your images like your surface is close to developable so you'd expect a solution something along these lines.

For the optimization to find its way to a solution like this I think you'd need to give it a slightly closer starting configuration.

Also - if there is any negative Gaussian curvature then the hexagons will need to become concave.

You may find you need to include some sort of smoothing or angular forces to stop it completely crumpling.

(as a side note - I can think of one more shape other than the plane that can be covered by regular hexagons : http://www.uwgb.edu/dutchs/Graphics-Other/POLYHEDR/HYPERBOL/SKEW4X6...

but I think that's all)

Permalink Reply by Davide on January 2, 2012 at 10:24am

Thanks everybody.

Daniel, now I got it!!

Obviouvsly I have some gap in "architectural geometry";) Can you link some resource I could refer to??

Permalink Reply by Davide on January 2, 2012 at 11:18am

Daniel,

does Kangaroo allows me to planarize by hexagons a sphere in order to obtain a "soccer ball"?
I know that a closed surface like a sphere needs hexagons + pentagons to be planarized.

thanks