In this work, two generalizations of the algorithm for obtaining a constrained Delaunay triangulation of a general planar graph set forth in [7] and [8] are presented. While the first generalization works with elliptical distances, the second one can deal with a set of deforming ellipses associated to each point of the plane. The pseudo-code of the procedures involved in the algorithms is included, the suitability of the algorithms is analyzed, and several examples are given.