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== PM1 Quadtree ==
== PM1 Quadtree ==
[[Image:Pm1_example3.png|PM1 Quadtree example]]
A PM1 Quadtree follows the following rules:
A PM1 Quadtree follows the following rules:
# 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.
[http://wam.umd.edu/~bzoller/cmsc420/pm1_example.png Here] is an example.
== PM2 Quadtree ==
[[Image:Pm2_example3.png|PM2 Quadtree example]]
A PM2 Quadtree follows the following rules:
A PM2 Quadtree follows the following rules:
# 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.
# If a quadtree leaf node's region contains a vertex, then it can contain no q-edge that does not include that vertex.
# If a quadtree leaf node's region contains a vertex, then it can contain no q-edge that does not include that vertex.
# 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.
[http://wam.umd.edu/~bzoller/cmsc420/pm2_example.png Here] is an example.
== PM3 Quadtree ==
[[Image:Pm3_example3.png|PM3 Quadtree example]]
A PM3 Quadtree follows the following rules:
A PM3 Quadtree follows the following rules:
# 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.