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Breaking a polygon into monotone polygons. A simple polygon may be easily cut into monotone polygons in O(n log n) time. However, since a triangle is a monotone polygon, polygon triangulation is in fact cutting a polygon into monotone ones, and it may be performed for simple polygons in O(n) time with a complex algorithm. [6]
A simple polygon is monotone with respect to a line L, if any line orthogonal to L intersects the polygon at most twice. A monotone polygon can be split into two monotone chains. A polygon that is monotone with respect to the y-axis is called y-monotone. A monotone polygon with n vertices can be triangulated in O(n) time. Assuming a given ...
And Delaunay triangulation is clearly applicable and relevant to polygon triangulation. Please don't remove that note. 95.25.208.67 18:54, 19 February 2012 (UTC) Delaunay triangulation is a completely different problem from polygon triangulation; it is a form of point set triangulation.
A monotone planar subdivision with some monotone chains highlighted. A (vertical) monotone chain is a path such that the y-coordinate never increases along the path. A simple polygon is (vertical) monotone if it is formed by two monotone chains, with the first and last vertices in common. It is possible to add some edges to a planar subdivision ...
A polygonal chain is called monotone if there is a straight line L such that every line perpendicular to L intersects the chain at most once. Every nontrivial monotone polygonal chain is open. In comparison, a monotone polygon is a polygon (a closed chain) that can be partitioned into exactly two monotone chains. [2]
Special cases of PSLGs are triangulations (polygon triangulation, point-set triangulation). Point-set triangulations are maximal PSLGs in the sense that it is impossible to add straight edges to them while keeping the graph planar. Triangulations have numerous applications in various areas. PSLGs may be seen as a special kind of Euclidean ...
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However since a triangle is a monotone polygon, polygon triangulation is in fact cutting a polygon into monotone ones, and it may be performed in O(n) time." seems to indicate that polygon triangulation can be performed in O(n) time, where I think it is supposed to be saying that polygon triangulation of a simple polygon can be done in O(n ...