The tree is constructed by inserting the points of the plan into the tree starting from the root and recursively adding the two points in depth if the quadrant is already occupied.

The example below shows an animation of the insertion of the plan points in the order D, C, F, B, A, E, G. Obviously the insertion order has no influence on the shape of the final quaternary tree, but modifies the states of the intermediate tree. However, it is possible to understand the insertion algorithm by observing the animation below.