My major research activities in Computational Geometry involved Voronoi Diagrams and various types of triangulations. These include study of the 2-point site Voronoi diagram, work on minimum triangulations, and recent work on minimum-bend path computations. I have been reading papers in the area of surface reconstruction algorithms, but have not made contributions in this area.
The 2-point site Voronoi diagram is a generalization of the standard Voronoi diagram where the distance measures the ``distance'' from a point to a pair of sites. Some examples are the sum of the distances and the product of the distances from the given point to the pair of sites. G. Barequet, M. Dickerson, and I found algorithms and time and space bounds for a number of these distance functions.
I also studied an algorithm for computing the minimum weight triangulation (MWT) of a set of points invented by Dickerson. The algorithm works surprisingly well in practice, although nobody really understands why. I invented a method for speeding up the algorithm by eliminating possible edges quickly by using an exclusion region around the edge. The edge cannot be in the MWT the two halves of the exclusion region both contain a point from the set. McElfresh, Snoeyink, and I found a larger exclusion region than the ones previously known. We also showed that a related low-weight triangulation has no such exclusion region.
Cliff Stein and I have been supervising David Wagner as a graduate student. Part of his thesis is an algorithm that finds the minimum-bend rectilinear path between a pair of points in the presence of rectilinear obstacles in time. This improves on an algorithm that appeared in a robotics paper.