In the pure sense, the question is largely unrelated to boost-interprocess.
You want to know allocation patterns (not just net allocation volume, but also the effective "pool" use due to fragmentation.
What you could do is statistics on allocator use (good question: is there some kind of statistics-gathering allocator adaptor?) and work it out.
Of course you'll be in approximation territory, but given enough simulation runs you should have usable information.
As a last resort the source/developers of Boost Geometry would be the people to ask.
Other angles
With regards to Boost Interprocess, we don't know what you're using. I will assume managed_mapped_file
/managed_heap_memory
/managed_external_buffer
. Note that when using these with the default memory allocation strategy (rbtree_best_fit) there can be considerable fragmentation or just allocation overhead (for node-based containers, which likely includes rtree).
Relevant example:

This immediately gives you some ideas to use:
shm.get_free_memory()
to get a raw number for space remaining in the segment
- using a memory profiler (like Valgrind Massif) when using the rtree outside of a managed memory segment
Out Of The Box:
Lastly, don't forget that it can be very cheap to allocate a sparse file, even of say 10 GiB, and just allocate into that using a shared memory manager: only the pages actually in use will be committed to disk, so the actual disk usage will closely match the actual required size.
Sparse files are magic.