Difference between revisions of "PM Quadtree"
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== PM1 Quadtree == | == PM1 Quadtree == | ||
| − | [[Image: | + | [[Image:Pm1_example3.png|PM1 Quadtree example]] |
A PM1 Quadtree follows the following rules: | A PM1 Quadtree follows the following rules: | ||
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== PM2 Quadtree == | == 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. | ||
| − | |||
| − | |||
== PM3 Quadtree == | == PM3 Quadtree == | ||
| − | [[Image: | + | [[Image:Pm3_example3.png|PM3 Quadtree example]] |
A PM3 Quadtree follows the following rules: | A PM3 Quadtree follows the following rules: | ||
Latest revision as of 14:36, 3 October 2014
A PM (Polygonal Map) Quadtree describes a collection of quadtrees that can store points and edges. A q-edge refers to a subset of an edge formed by the partitions of the PM Quadtree.
PM1 Quadtree[edit]
A PM1 Quadtree follows the following rules:
- 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 no vertices, then it can contain, at most, one q-edge.
- Each region's quadtree leaf node is maximal.
PM2 Quadtree[edit]
A PM2 Quadtree follows the following rules:
- 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 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.
PM3 Quadtree[edit]
A PM3 Quadtree follows the following rules:
- At most, one vertex can lie in a region represented by a quadtree leaf node.
- Each region's quadtree leaf node is maximal.
Applications[edit]
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.
