We look into the problem of mesh generation with guaranteed quality.
In an earlier work we used weighted Delaunay triangulations to
eliminate slivers. This is well known as sliver exudations.
S. W. Cheng, T. K. Dey, H. Edelsbrunner, M. A. Facello and S.-H. Teng. Sliver exudation Proc. Journal of ACM, Vol.47, (2000), 883--904.
In a later work we extended the sliver exudations to bounded domains by combining Delaunay refinements with the sliver exudation method. We call this Weighted Delaunay Refinements.
S. W. Cheng, T. K. Dey. Quality meshing with weighted Delaunay refinement. Proc. 13th ACM-SIAM Sympos.Discrete Algorithms (SODA2002), (2002), 137--146. Extended version.