Why would someone select "quad" trees in particular, instead of binary splitting at each level (in alternating dimensions; something like a K-D tree)? I.e., what are the tradeoffs? The article briefly mentions K-D trees at the very end, but doesn't elaborate on differences:

> The quadtree is the two-dimensional case of a broader family of space-partitioning data structures. Octrees extend the same idea to three dimensions (splitting cubes into eight children), KD-trees use alternating axis-aligned splits (splitting along x, then y, then x again), and R-trees group nearby objects into bounding rectangles. Each variant makes different tradeoffs between construction time, query speed, and update cost.

Finally, I'll add: the presentation is very high quality and served as a great introduction of the concept.