Developed by CongLin Lu at Brown University.

This Java applet shows the Delaunay Triangulation of the input points. You can insert new points by clicking in the orange area. If you want to remove a point, you can do it by shift-clicking on that point. Furthermore, you can move a point by dragging the mouse.
Click to add point; SHIFT-click to delete point; Drag to move point.
The Convex Hull and the Voronoi Diagram, which is the dual graph of the Delaunay Triangulation, are also shown in this demo. They are updated everytime you add, delete or move a point. The Delaunay Triangulation is blue, the Voronoi Diagram is magenta, and the Convex Hull is dark green.

The algorithm used here is an incremental method, as described in the paper by L. Cuibas & J. Stolfi: Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagram. Basically, when a new point is added, the algorithm first determines in which triangle this point lies, then connects this point to the three nodes of that triagle. If any of these new edges violates the Delaunay Triagulation property, then appropriate changes are made until the Triangulation is got. The Voronoi Diagram is obtained by finding  the dual graph of Delaunay Triangulation.