Convex Hull and Delaunay Triangulation

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send