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Convex Hull and Delaunay Triangulation

For three or more points, you can see the convex hull (blue), the Delaunay triangulation (red), or the Voronoi diagram (green).

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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 Pj. In the graph theory sense, the Voronoi diagram is the dual graph of the Delaunay triangulation.
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