Star domain

In geometry, a set

in the Euclidean space

is called a star domain (or star-convex set, star-shaped set[1] or radially convex set) if there exists an

the line segment from

This definition is immediately generalizable to any real, or complex, vector space.

Intuitively, if one thinks of

as a region surrounded by a wall,

is a star domain if one can find a vantage point

from which any point

A similar, but distinct, concept is that of a radial set.

Given two points

in a vector space

(such as Euclidean space

), the convex hull of

is called the closed interval with endpoints

of a vector space

is said to be star-shaped at

the closed interval

A set

is star shaped and is called a star domain if there exists some point

is star-shaped at

A set that is star-shaped at the origin is sometimes called a star set.

[2] Such sets are closely related to Minkowski functionals.