Compact circle packing with a set radii range on a trimmed 3D surface

Grasshopper
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1

Has anyone been able to solve this yet?

Hi Everyone!! Thank you so much for taking the time to help me out- here’s the problem I’m facing:

We are trying to pack circles of a given radius [say, a diameter of 8", 10", 14", 22", and 27"] on a hemisphere with archways cut out as shown below. Mathematically I think it may only be possible to do a range of diameters from 8"-27". Please share any information you think may help!
image

The circles should be compact and tangent to the edges of the provided surface.

We have tried several attempts documented in the files linked below. These attempts have covered kangaroo gravity, re-meshing by color, bouncy solvers, and so on. I am not sure of the best way to move forward as each method comes close but does not solve the problem. Perhaps a scripting component could help pack the circles so they fulfill the requirements.

Included is a rhino file with more information and several grasshopper files with varied attempts. Here are the files that illustrate the problem and constraints:
circlepack_attempts_1_10_2024.zip (3.3 MB)

Here are some relevant threads that have informed some of my past attempts:
compact circle packing on a complex surface
circle packing with fixed radius and fixed number of circles for each radius
circle packing on a half-sphere with a hole
about circle packing

2

Ideally, the radii would be a set of ranges to allow flexibility to achieve a compact packing. This is our target range set for circle diameter with bonus points if we can somewhat control the proportion each range is represented:

8% (+/- 3%) of circles will be 8.75"-9" (volleyball),
16% (+/- 3%) of circles will be 8.75"-9.5" (soccerballs),
17% (+/- 3%) of circles will be 9.25" -10.25" (basketballs)
12% (+/- 3%) of circles will be 12.25"-13.25" (marble, kickballs)
7% (+/- 3%) of circles will be 13.25"-14.25" (beachballs)
7% (+/- 3%) of circles will be 15.25"-16.25" (kickballs)
15% (+/- 3%) of circles will be 16.25 to 18.25" (exercise balls)
7% (+/- 3%) of circles will be 17.75"-20.25" (exercise balls)
6% (+/- 3%) of circles will be 20.25"-22.25" (exercise balls)
5% (+/- 3%) of circles will be 22.25"-24.25" (beachballs)

The +/- 3% is intended to help solve for a compact circle packing and can be flexed if necessary!