Whether via a GIS or a programming language, I am trying to split a polygon into different polygon parts based on the weight of the raster.

To make it more clear, suppose I have four points within a polygon (see picture) and there are different raster values on the polygon. What I wish to do is split the polygon into four (not necessarily equal) polygons respective to the points, but the size of the split polygons to be based on the raster values.

Attached is an example of the split polygon into four different polygons depending on the raster values (yellow is a low value and red is a high value)

I'm certain there is a better way to explain this - apologies if it isn't so clear. Is there some kind of methodology or a paper that does this? Thanks in advance.

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