convex set

Illustration of a convex set shaped like a deformed circle. The line segment joining points x and y lies completely within the set, illustrated in green. Since this is true for any potential locations of two points within the set, the set is convex. Illustration of a non-convex set. The line segment joining points x and y partially extends outside of the set, illustrated in red, and the intersection of the set with the line occurs in two places, illustrated in black.

In geometry, a set of points is convex if it contains every line segment between two points in the set. For example, a solid cube is a convex set, but anything that is hollow or has an indent, such as a crescent shape, is not convex.