starconvex

Starconvex is a term used in mathematics, particularly in the field of convex geometry, to describe a set that is star-shaped with respect to a single point. A set is star-shaped with respect to a point if, for every point within the set, the line segment connecting that point to the reference point lies entirely within the set. In other words, a starconvex set is one where you can "see" the entire set from a single point without any obstruction.

The concept of starconvexity is closely related to that of convexity. A convex set is starconvex with respect to any of its points, but not all starconvex sets are convex. For example, a star-shaped polygon is starconvex with respect to its center, but it is not necessarily convex.

Starconvex sets are often used in various mathematical and computational applications, such as in the study of visibility problems, motion planning, and computational geometry. The study of starconvex sets provides insights into the structure and properties of more general shapes and spaces.