A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex, while an indented pentagon is not. A planar polygon that is not convex is said to be a concave polygon. Let a simple polygon have n vertices x_i for i = 1, 2, ..., n, and define the edge vectors as v_i = x_(i + 1) - x_i, where x_(n + 1) is understood to be equivalent to x_1. Then the polygon is convex iff all turns from one edge vector to the next have the same sense.
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