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.