The first step of trapezoidalization can be visualized as seen here. A horizontal line has been drawn through every vertex of the polygon. In a program implementing trapezoidalization, the polygon edges crossed by a horizontal line "moving" from vertex to vertex would be stored in a data structure.
Here the horizontal lines have been clipped to only those portions dividing the interior of the polygon. This is the actual trapezoidalization; notice that the polygon is now divided into trapezoids, each with one upper and one lower supporting vertex. The red lines are those indicating interior cusps (i.e., the supporting vertex s in the middle of the line.)
Here diagonals (in black) have been drawn connecting all interior cusp vertices to the supporting vertex on the opposite edge of the trapezoid. These black diagonals serve to divide the polygon into monotone pieces (indicated here by alternating bakcground colors.)
Created with Cinderella
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