We demonstrate that a resolution-r PR quadtree containing n points has
, in the worst case, at most 8n(r - [log4(n/2)]) + 8n/3 - 1/3 nodes. T
his captures the fact that as n tends towards 4r, the number of nodes
in a PR quadtree quickly approaches O(n). This is a more precise estim
ation of the worst case space requirement of a PR quadtree then has be
en attempted before.