Convex

From DmWiki

A convex solid object is one that is curved outward, like a circle - it contains no dents or indentations. One easy way to define a convex object is: standing on the inside of its surface, you can see any other point on that surface with a direct line of sight. More precisely, a solid object is called convex if all line segments connecting two points on its surface lie entirely within the object. If there exists a line segment connecting two points on the surface that falls partly outside the object, it is not convex, and is called concave. The definition can be applied to define convex polygons and 2D shapes, as well as convex polyhedra (3D shapes).

Below are some examples of various shapes. The top row are all convex; the bottom row are all concave.

One important property of triangles is that they are always convex. It is impossible to make a non-convex triangle (though it is possible to make a degenerate one).

For a given set of points, the smallest convex shape enclosing all the points is called the convex hull of that set of points. The convex hull can be used to make a concave shape convex, by "filling in" the dents that prevent it from being convex.