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Subdividing a concave polygon

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Make sure the winding of your polygin is counter-clockwise, and the winding of all of its holes are clockwise. Then trapezoidalize the polygon and its holes. Then connect the support vertices of the trapezoids which have interior cusps. This converts the polygon and its holes into a set of monotone polygons. Each monotone polygon has two chains, a left one, and a right one. Traverse down both chains simultaneously, and at each vertex of each chain, connect across to the opposite chain to the highest vertex, thus removing that vertex from the chain and the created triangle!

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