Interveinal region. The region between veins. Much better than Remigium.
I refactored so that the logic for generating cross veins in each interveinal region (ahh, that sounds better, doesn’t it?) is handled by a separate class. Now I have two classes: VeinRenderer and InterveinalRegionRenderer. With that it was very easy to expand the logic for cross-veins to more than one interveinal region.
Check it out.
Yes, those Voronoi shapes are still kinda nasty but at least now the code that generates them is encapsulated so improving it won’t require as much mental gymnastics.
I wondered briefly whether a mechanism exists in natural wing venation to prevent cross-veins for adjacent regions from starting at the same point. Referring back to the image of the grasshopper wing, though, it doesn’t seem to be the case. There are plenty of instances of cross-veins starting in the same place.
It’ll be up to me to reject results that don’t look nice. Like, look at that second image above.
There is a series of cross-veins that form a nearly straight line spanning five—well, four-and-a-half—interveinal regions. Unacceptable.
But more importantly right now, I want to deal with the very uneven distribution of inhibitory centers with Lloyd’s algorithm.
Oh, and I should also address an error that’s occurring when I try to randomize the parameters. I think it’s complaining about calculating an intersection with an invalid polygon.
File "/home/nmclaren/Code/InsectWings/interveinal_region_renderer.py", line 65, in _get_voronoi_polygons
return intersection(normalize(voronoi_polygons(inhibitory_centers, extend_to=extent)).geoms, extent)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/nmclaren/Code/InsectWings/venv/lib/python3.12/site-packages/shapely/decorators.py", line 77, in wrapped
return func(*args, **kwargs)
^^^^^^^^^^^^^^^^^^^^^
File "/home/nmclaren/Code/InsectWings/venv/lib/python3.12/site-packages/shapely/set_operations.py", line 131, in intersection
return lib.intersection(a, b, **kwargs)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
shapely.errors.GEOSException: TopologyException: side location conflict at -92.641145940852468 680.89274971239547. This can occur if the input geometry is invalid.
Relaxation Using Lloyd’s Algorithm #
Sweeet.
Shapely sure made it easy to implement Lloyd’s algorithm. And it’s looking pretty sweet.
I’m particularly happy with how most of the wings ended up with a ladder-like arrangement of cross-veins with the rungs evenly-spaced. The other exciting feature is how the inhibitory centers begin to alternate to take up more space as the interveinal region gets wider.