This work follows the general framework of polymer injection moulding simulation whose objectives are the mastering of the injection moulding process. The models of numerical simulation make it possible to predict the propagation of the molten polymer during the filling phase from the positioning of one point of injection or more. The objective of this paper is to propose a particular way to optimize the geometry of mold cavity in accordance with physical laws. A direct correlation is pointed out between geometric parameters issued from skeleton transformation and Hausdorff's distance and results provided by implementation of a classical model based on the Hele-Shaw equations which are currently used in the main computer codes of polymer injection.