Created with Cinderella

The above polygon was triangulated with Polygon Triangulation Monotone Partition Algorithm. The polygon was sweeped horizontally according to the y-axis in order to form the resulting trapezoidalization. A diagonal was drawn between the two interior cusps that were found (purple line) in order to divide the polygon into two sub-monotone polygons. Those two polygons were then respectively triangulated in linear time. Diagonals formed from two vertices on separate chains were drawn by green lines. Diagonals formed from the edges of a previous convex angle were drawn in blue.