This work studies the feasibility of a constrained Delaunay triangulation of a set of points on the plane including directionality pointed by the ellipses associated to the points. Generalizations of the Voronoi diagram close to the object of study are presened, the weighted Voronoi diagrams, and the resulting Delaunay triangulations are shown. The height diagram is also described and the properties of the Voronoi diagram and the Delaunay graph with elliptical distances are studied. Finally, several futur work lines are proposed to develop an algorithm which obtains a generalized Delaunay triangulation with the desired features.