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This is a drawing of a spiral polygon with the start of trapezoidalization process. You can see the horizontal sweeping lines at each vertex.
This is the next, more clearer picture where only the horizontal lines that create the trapezoids are shown. They have been clipped to look cleaner.
This next one shows the diagonals drawn according to the algorithm, so that the whole polygon can be partitioned into monotone polygons.
This one shows the final product of the whole process where you can see each monotone polygon colored differently
Created with Cinderella