Convex Hull and Delaunay Triangulation
![](/img/demonstrations-branding.png)
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
For three or more points, you can see the convex hull (blue), the Delaunay triangulation (red), or the Voronoi diagram (green).
Contributed by: Marko Petkovic (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The convex hull of a given set is the smallest convex set that contains
. If
is finite, that is, if
, where the
are points, then the convex hull is always a polygon whose vertices are a subset of
.
The Delaunay triangulation of a given set of points is a triangulation of the convex hull of
such that no point of
is inside the circumcircle of any triangle of
.
The Voronoi diagram of the set of points is the plane partition containing the regions
of points whose distance from
is no greater than the distance from any other point
. In the graph theory sense, the Voronoi diagram is the dual graph of the Delaunay triangulation.
Permanent Citation