In this work, we propose to define a new space that will be called locally Cartesian space (Saidou’Spaces). It is a space defined by a new topology whose fundamental system of neighborhood are compact cartesian subsets, theses subsets were already defined during our previous work, “Geometrical introduction to Cartesian geometry in complex shapes see . It will have the same properties of a Banach space. Then, we will give the steps of a cartesianization method of complex shapes or region in this space. The objective sought by this technique is to find a cartesian form (denoted Car(A)), that approximates any form A, see Figure1 below. It should be noted that cartesianization will be a generalization of the polygonization whish remains the object of research for several researchers in the spaces R2 Ref   .