What is the difference between a convex and a non-convex polygon?

An area of a plane is called convex when every segment of a line, which has its ends within the area, has all its points within the area.

• For instance, the following polygon is convex since the segment of a line [A,B] also contains all the points of the segment “within” the area, no matter where we move it and only if the points A and B remain “within” the polygon.

• In this second example the following polygon is not convex because the segment of a line [C,D] has points that are “out” in spite of having its ends “within” the polygon.

Another way to verify if the polygon is convex or concave (non-convex) is to analyse the amplitude of the internal angles of the polygon. If all the angles are inferior to 180º, it is convex. On the contrary, if at least one angle is superior to 180º, the polygon is concave.

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