This work presents two generalizations of the algorithm for obtaining a constrained Delaunay triangulation of a general planar graph presented in [Vig97] and [Vig95]. 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 presented.