Laguerre (or weighted Voronoi) diagrams are used as geometric idealization of 2-d polycrytals. The approximation is satisfactory. These cell structures are entirely defined by a set of weighted sites, and their motion (including the induced topological transformations) is transferred to that of the sites. Grain growth is modelled by solving a specific motion equation derived from v=MP. First simulation results are satisfactory. The approach is 3-D generalizable.