Convex polygon

A polygon whose interior contains every line segment joining two of its points. Equivalently, every interior angle is less than 180 degrees.

Polygon: A closed plane figure formed from a finite sequence of straight line segments joined end to end. A convex polygon is a polygon satisfying an additional condition on its interior.
Cross product: A vector operation in three dimensions whose result is perpendicular to both input vectors. In the plane, signed cross products reveal whether consecutive turns keep one orientation.
Computational geometry: The study of algorithms for geometric problems involving points, lines, and other spatial objects. Convex polygons are basic objects in geometric algorithms and spatial data structures.
Concave polygon: A simple polygon with at least one interior angle greater than 180 degrees. A concave polygon fails the segment condition that defines convexity.
Convex set: A set in a real vector space that contains every line segment joining any two of its points. The polygon’s defining property is convexity applied to its interior.
Half-plane: One of the two regions into which a line divides a plane, together with the dividing line or excluding it. Each side of a convex polygon bounds a half-plane containing the whole polygon.
Point location: The problem of determining which region of a geometric subdivision contains a given point. Convexity enables efficient tests for whether a point lies inside a polygon.
Star polygon: A polygonal figure whose edges or extensions form a star-like pattern, often with self-intersections. Its crossing structure differs from the ordinary convex polygon boundary.
Interior angle: An angle formed inside a polygon by two consecutive sides. Every interior angle of a convex polygon is less than 180 degrees.
Supporting line: A line that touches a convex set while leaving the entire set in one of its closed half-planes. Every side line of a convex polygon supports the polygon.

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