I have a bounding box of a city containing points. I would like to divide this bounding box into sub boxes according to the importance of the points. For example, regions with more points should correspond to higher number of sub-boxes. Regions with less points should respond to less boxes with larger width.
I understood that a good data structure for that is a quad tree or maybe a KD-Tree. It turns out that most of these libraries just return me the nearest neighbor (This is their main use). I would like to have not the nearest neighbor but the sub box of a point. (lets say leaf id) Is this possible? or event the Quadtree-Data structure the correct to use ? In other words I need the quad tree just to divide the region into sub boxes and not to be used as an index.
The naive solution is to just to divide the bounding box into equal sub boxes.
This is essentially what an R-Tree does. It produces a more or less balanced tree, based on bounding rectangles (boxes), but based on the number of geometric objects that fit inside the box, not on the boxes's area. KD-Trees, on the other hand, recursively divide a space first in the x and then in the y direction, which can make for very efficient searching, but can not be adjusted for areas with a lower or higher density of points. There is a Python implementation of R-Trees here, https://pypi.python.org/pypi/Rtree/. I have never used this (it is built into Postgres/Postgis which I use all the time), but I looks like it could be useful for what you describe.