classification of convex and concave polygon with example

A convex polygon is a simple polygon whose interior is a convex set. The following properties of a simple polygon are all equivalent to convexity:

• Every internal angle is less than or equal to 180 degrees.
• Every line segment between two vertices remains inside or on the boundary of the polygon.

A simple polygon is strictly convex if every internal angle is strictly less than 180 degrees. Equivalently, a polygon is strictly convex if every line segment between two nonadjacent vertices of the polygon is strictly interior to the polygon except at its endpoints.

Every nondegenerate triangle is strictly convex.

A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have an interior angle with a measure that is greater than 180 degrees.

It is always possible to partition a concave polygon into a set of convex polygons. A polynomial-time algorithm for finding a decomposition into as few convex polygons as possible is described by Chazelle & Dobkin (1985).

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