Presumptions

We presuppose two-dimensional Euclid's space and Cartesian rectangular system of co-ordinates. Than we have chosen the following constraints:

• bounding boxes are rectangles parallel to co-ordinate axes
• a hierarchy is represented by a general tree (not restricted to binary)
• bounding-boxes can overlap themselves
• a number of tested objects is much bigger than a number of bounding boxes
• the distribution of probability for location of tested object is constant in the whole space, it means that it has no relation to the distribution of bounding boxes

Time complexity should be better than O(n), it means better than processing bounding-boxes one by one.

There are several methods how can be this problem solved, we have chosen only one for this text, which is based on inserting bounding-boxes into the tree one by one.

It is necessary to point out, that building a tree takes a lots of time. For overall efficiency is advantageous to traverse the tree many times.