What is being monotone for a polygon?

A simple polygon is called monotone with respect to a line l if for any line l' perpendicular to l the intersection of the polygon with l' is connected. In other words, the intersection should be a line segment, a point, or empty. A polygon that is monotone with respect to the y-axis is called y-monotone. The following property is characteristic for y-monotone polygons: if we walk from a topmost to a bottommost vertex along the left (or the right) boundary chain, then we always move downwards or horizontally, never upwards.

This application shows available line orientation which makes a polygon monoton. Left you can modify position of the polygon points. Points which make polygon concave will appear as colored, others are black.

You will immediately see resulting line orientation at the right pane. At the right pane, above figure shows inner angle of concave points and below is their intersection.

For more information you can refer to: /wiki/Monotone_polygon