Higher Order Delaunay Triangulations

triangulations that is an extension of the Delaunay triangulation.
Instead of requiring that for each triangle the circle through
its vertices contains no points of P inside, we require that at
most k points are inside the circle. Since there are many different
higher order Delaunay triangulations for a point set, other useful
criteria for triangulations can be incorporated without sacrificing
the well-shapedness too much. Applications include realistic terrain
modeling, and mesh generation.