What is the monotonicity of a polygon and why is it necessary to check the monotonicity?
2026-03-28 04:34:51.1774672491
What is the monotonicity of a polygon?
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A monotone polygon is such that it is crossed at most two times by lines perpendicular to a given direction.
That means that the polygon can be split in two chains of vertices that are sorted in that direction. Sorted order is beneficial as it can often reduce the complexity of computations.
For instance, the convex hull of a monotone polygon can be computed in time proportional to the number of vertices, O(N).
https://en.wikipedia.org/wiki/Monotone_polygon