Convex set
In Euclidean space, a region is a convex set if the following is true. For any two points inside the region, a straight line segment can be drawn. If every point on that segment is inside the region, then the region is convex.
The point is that a convex curve forms the boundary of a convex set. So, any shape which is concave, or has a hollow, cannot be a convex set.
Convex Set Media
Blaschke-Santaló (r, D, R) diagram for planar convex bodies. \mathbb{L} denotes the line segment, \mathbb{I}_{\frac{\pi}{3}} the equilateral triangle, \mathbb{RT} the Reuleaux triangle and \mathbb{B}_2 the unit circle.
Minkowski addition of sets. The sum of the squares Q1=[0,1]2 and Q2=[1,2]2 is the square Q1+Q2=[1,3]2.
