Dividing an area (circle but would be better to be general) based on the weighting

I’m trying to divide a surface (and further subdivide) into areas that correspond to the sum of vectors that will pass through certain portions of the surface. For example, if I want to divide up a surface into 3 parts (an input), then if the sum of vectors projected onto a the flat surface is greater in a portion of the surface, I want that portion to have a proportionally greater area when it is divided up into the the three portions and the same would go for the other two portions. The division would be about the centroid of the surface or another defined point. I’m having a lot of trouble figuring this out, but it’s a core part of what I’m building.
The basic idea is to continue subdividing a surface into portions weighted by randomly placed vectors of varying magnitude and location. The initial amount of divided portions is defined as is the subsequent divisions which is based on a different value.
Thanks for the help in advance!

What am I to imagine with regards to these vectors?

A napkin sketch would be nice to have.


I’m loading the red shell below with varying magnitude loads at the green points:

These load points are randomly turned on and off as a gene pool.

The load points are projected on to a flat surface that is divided into a certain number of divisions as mentioned before. Then subdivided again and again a certain number of times.

The resultant of the loads in each subdivision is intersected at planes at different levels to create connection points.

I just want the subdivisions to be more meaningfully created.

I’ll clarify. The vectors (loads) within each subdivision determine the point at which each new subdivision occurs.

The above is a subdivision of three after an initial division of five.

So this primary subdivision into five wedges is due to five points selected (randomly?) from that cloud using a gene pool?

So the five points correspond to the five resultant vectors passing through the surfaces. The five resultant vectors are the resultant vectors of the collection of vector projections contained within each of those five surfaces.

The points on the dome mesh above are assigned to be turned on or off. I am showing all of them on.

Apologies. I’ll try to be more clear. The primary subdivision into the five wedges is just from a point created by a line through a surface. The subsequent divisions are also due to lines going through each of the five wedges. The divisions after this are also due to lines through the surfaces.

I’m still confused. There’s a single line which intersects the surface at a point, and that point is the splitting locus for the first step? I.e. based on that central location, the surface is split into N parts, all of which ought to have the same area?

Yes and Yes. Subsequently, these new split surfaces will now generate one line each that will intersect their surface. These new points will now be the dividing locus to further subdivide each into N parts.
I’m happy to supply any other sketches or answer any more questions. I can even provide my script if need be. I’m new to this world, so to speak, so I’m learning the capabilities.