Bowyer–Watson algorithm

In computational geometry, the Bowyer–Watson algorithm is a method for computing the Delaunay triangulation of a finite set of points in any number of dimensions. The algorithm can be used to obtain a Voronoi diagram of the points, which is the dual graph of the Delaunay triangulation.

The Bowyer-Watson algorithm is incremental: it works by adding points one at a time to a valid Delaunay triangulation of a subset of the desired points. After every insertion, any triangles whose circumcircles contain the new point are marked as invalid. Next the invalid triangles are deleted, leaving a convex polygon hole which is then re-triangulated using the new point.

The algorithm is sometimes known just as the Bowyer Algorithm or the Watson Algorithm. Adrian Bowyer and David Watson devised it independently of each other at the same time, and each published a paper on it in the same issue of The Computer Journal (see below).

See also

• Fortune's algorithm
• Delaunay triangulation
• Computational geometry

References

• Adrian Bowyer (1981). Computing Dirichlet tessellations, The Computer Journal, 24(2):162–166. doi:10.1093/comjnl/24.2.162.
• David F. Watson (1981). Computing the n-dimensional tessellation with application to Voronoi polytopes, The Computer Journal, 24(2):167–172. doi:10.1093/comjnl/24.2.167.
• Henrik Zimmer, Voronoi and Delaunay Techniques, lecture notes, Computer Sciences VIII, RWTH Aachen, 30 July 2005.