Changes

# If a quadtree leaf node's region contains no vertices, then it can contain, at most, one q-edge.

# If a quadtree leaf node's region contains no vertices, then it can contain, at most, one q-edge.

# Each region's quadtree leaf node is maximal.

# Each region's quadtree leaf node is maximal.

== PM2 Quadtree ==

== PM2 Quadtree ==

# If a quadtree leaf node's region contains no vertices, then it can contain only q-edges that meet at a common vertex exterior to the region.

# If a quadtree leaf node's region contains no vertices, then it can contain only q-edges that meet at a common vertex exterior to the region.

# Each region's quadtree leaf node is maximal.

# Each region's quadtree leaf node is maximal.

== PM3 Quadtree ==

== PM3 Quadtree ==

# At most, one vertex can lie in a region represented by a quadtree leaf node.

# At most, one vertex can lie in a region represented by a quadtree leaf node.

# Each region's quadtree leaf node is maximal.

# Each region's quadtree leaf node is maximal.

== Applications ==

== Applications ==

PM Quadtrees are useful in determining the region in which a point lies, the determination of the boundaries of all regions lying within a given distance of a point, and overlaying two maps.

PM Quadtrees are useful in determining the region in which a point lies, the determination of the boundaries of all regions lying within a given distance of a point, and overlaying two maps.