In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersects every line into a single line segment (possibly empty).For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The notion of a convex set can be generalized as described below.