GEOMPACK is a suite of Fortran 77 codes by Barry Joe of the University of Alberta, for 2- and 3-dimensional triangulation and convex decomposition problems. In particular, it does both Delaunay triangulation and convex decompositions of polygonal and polyhedral regions, as well as arbitrary dimensional Delaunay triangulations. These codes are well respected, and worth checking out. They can be obtained from ftp://ftp.cs.ualberta.ca/pub/geompack.
Papers describing the algorithms used for each program are available at the ftp site.
The GEOMPACK software package is copyrighted and made available here for noncommercial use only. If you want to include any GEOMPACK routines in a commercial software product, please contact Barry Joe about obtaining a license.