A method for rendering a three dimensional scene on a displaying screen comprises: generating for a tile of a current scene a hierarchical z-buffer which comprises a plurality of levels organized according to depth values; calculating a minimum depth value d of a submitted primitive; calculating an intersection area associated with said primitive with respect to said tile; providing a multiplicity of aligned regions each associated with a level of the hierarchical z-buffer so that the exact area calculated is suitable to be covered, at least entirely, by the union of such aligned regions; comparing the minimum depth value d of the submitted primitive with corresponding maximum depth values v1, v2, . . . , vN each read from the levels of the hierarchical z-buffer; discarding said primitive whether the minimum depth value d is bigger than all maximum depth values v1, v2, . . . , vN.