
Hi,
Thanks for the kind remarks. =)
3D Delaunay is something I have yet to do any serious research into, although the interest is there; it's still an active field of academic research and there's not as much info on it as for 2D Delaunay.
Not too much code to do the triangulator itself, maybe 1000 lines total. Mathwise, about all you need is some knowledge of graph theory and geometry to understand the basic principles.
The incremental method I used is basically the one proposed by Guibas and Stolfi in their 1985 paper called something like "Primitives for the manipulation of Voronoi diagrams" (don't have it under my nose). The next thing I would try to implement out of that paper would be the divideandconquer algorithm which is provably the best performancewise (not necessarily the easiest to implement).
What's it used for? Well, it has applications in FEM (Finite EleMent) related research where scientists need to do some kind of a simulation on a building or structure and they need to turn the structure into a mesh using the best possible triangulation; also, AI pathfinding as mentioned above, computer graphics (also, the geometric dual of a Delaunay Triangulation is a Voronoi Diagram  which are widely used in CG). A concrete example of its use in CG is for generating triangles for 3D Text by simply extruding the outline and using the tris generated during the triangulation as end caps for the extruded character. Similarly, arbitrarily complex end caps for other types of extrusion objects can be generated. I'm sure one can think of other uses besides these...
Jason
