Example: Subdividing Surfaces with Equal Area

Hi All,

I've taken the method from an old definition by Jacek Jaskolski in 2009 (original found here) that subdivides surfaces into subdivisions of equal area (as opposed to a proportional UV subdivision) and rewritten for the current version of GH. I've added a few of what I hope are improvements:

Instead of evaluating area, instead surfaces are meshed and then mesh area is calculated, as it seems this is far lighter computationally with a very slightly larger margin of error.
Definition now works with both single and multiple surfaces simultaneously and provides U and V subdivision for both.
Some helpful statistics that show how close to "true" equal-area the subdivisions are. Nothing is perfect, but the comparison to a standard proportional subdivision should show the difference.

Let me know if there are any questions. There are some... interesting data structure workarounds that work but I'm not 100% happy with - if anyone has any improvements that simplify the operations, please do share!

Cheers,

Dan

Attachments:

SrfDiv_EquiArea_3.gh, 40 KB
srfdiv_def.png, 2.9 MB

Replies to This Discussion

Permalink Reply by Mohamed Naeim on January 9, 2017 at 8:44am

like this?

Attachments:

similar areas.gh, 6 KB

Permalink Reply by Dan Cascaval on January 9, 2017 at 11:43am

No, not exactly - the idea would be to take one (or more!) pre-exisiting surfaces and be able to subdivide with a controllable grid, but still have the areas of each UV cell be as close to equivalent as possible. This is quite simple on a rectangle, but a little more complex as you begin to introduce distortion into the shape. The definition as I have it solves this by calculating and varying the UV proportion of each subdivision as it is more or less warped to achieve an equivalent cartesian area, like so: