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Triangul_monotone

# Triangul_monotone - Triangulation of Monotone Polygon...

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Triangulating a monotone polygon, introduction The algorithm to triangulate a monotone polygon depends on its monotonicity. Developed in 1978 by Garey, Johnson, Preparata, and Tarjan, it is described in both Preparata pp. 239-241 (1985) and Laszlo pp. 128-135 (1996). The former uses y -monotone polygons, the latter uses x -monotone. Initialization Sort the N vertices of monotone polygon P in order by decreasing y coordinate. (Here N is the number of vertices of P , not S .) The sort can be done in O ( N ) time, not O ( N log N ), by merging the two monotone chains of P . Let u 1 , u 2 , …, u N be the sorted sequence of vertices, so y ( u 1 ) > y ( u 2 ) > … > y ( u N ). Because of the regularization process and the monotonicity of P , for every u i 1 i < N there exists u j 1 < j N such that edge u i u j is an edge of P . Triangulation of Monotone Polygon

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Description of the processing The algorithm processes one vertex at a time in order of decreasing y coordinate, creating diagonals of polygon P . Each diagonal bounds a triangle, and leaves a polygon with one less side still to be triangulated. Stack The algorithm uses a stack to store vertices that have been visited but not yet connected with a diagonal.
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