Can an unsorted binary tree be balanced using a distance-function?

Question

I´ve got the following theoretical problem:
I have an amount n of cuboids in 3-dimensional space. They are aligned to the coordinate-system, so that one cuboid can be described via a point (x,y,z) and dimensions (dimX,dimY,dimZ). I want to organize these cuboids in a way that I´m able to check if a newly inserted cuboid intersecs with one of the existing (collision detection). To do this I decided to use hierarchical bounding-boxes. So in sum I have a binary-tree-structure of bounding volumes. Insertion is then done by determining recursively the distance to both children (=the distance between the two centers of two cuboids) and inserting in the path with the smallest distance. Collision detection works similar, but we take all bounding volumes in a sub-path which are intersecting a given cuboid.
The tricky part is, how to balance this tree to get better performance if some cuboids are very close to each other and others are far away. So far, I´ve found no way to use e.g. an AVL-tree because then I´d have to be able to compare two cuboids in some way that does not break the conditions on which collision detection depends.
P.S.: I know there are libraries to do this, but I want to understand the principles of collision detection e.g. in games in detail and therefore want to implement this by myself.

Answer 1

I´ve now tried it with space-partitioning instead of object-partitioning. That´s not exactly what I wanted to do but I found much more helpful information about it, e.g.: https://en.wikipedia.org/wiki/Kd-tree
With this information it should be possible to implement it.