In this paper, we pr es ent s ome pr act i cal r es ul t s concer ni ng t he i mpl e - ment at i on of t he al gor i t hmdes cr i bed i n [DMT] whi ch comput es dynamicallytheDel aunay tr i angul at i on of a set of s i tes i n the pl ane i n l ogar i thmic expected update ti me. More preci sel y,we s howt hat t he hypot hes es of non degener at e pos i t i ons can be dropped and the probl emof preci si on can be treated correctl y. R'esum'e Cet ar t i c l e pr 'esent e que l ques r 'e s ul t at s pr at i ques concer nant l 'i mpl antationpratique de l'algorithme[DMT] qui cal cul e dynami quement l a tri - angul at i on de De l aunay d' un ens embledepointsduplanentemps moyen de mise`a jour l ogar i thmi que . Pl us pr'eci s'ement , nous montrons que l es hypoth`es es de non d'eg'en'erescence peuventet r e s uppr i m'ees et l es probl `emes de pr 'eci si on num'er i ques r'esol us correctement. 1