object MonotoneChainIndexer

MonotoneChains are a way of partitioning the segments of an edge to allow for fast searching of intersections. Specifically, a sequence of contiguous line segments is a monotone chain iff all the vectors defined by the oriented segments lies in the same quadrant.

Monotone Chains have the following useful properties:

  • the segments within a monotone chain will never intersect each other
  • the envelope of any contiguous subset of the segments in a monotone chain is simply the envelope of the endpoints of the subset.

Property 1 means that there is no need to test pairs of segments from within the same monotone chain for intersection. Property 2 allows binary search to be used to find the intersection points of two monotone chains. For many types of real-world data, these properties eliminate a large number of segment comparisons, producing substantial speed gains.

Note that due to the efficient intersection test, there is no need to limit the size of chains to obtain fast performance.

Version

1.7

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