In this work we present a tool based on the new concept of local dual contributions for directly representing the topology and the approximated geometry of the dual of a block mesh. This tool allows us to obtain a valid block decomposition of a given geometry without a previous discretization of its boundary. Specifically, our tool is composed of a hierarchical scheme and a set of matching rules that explicitly insert descriptions of dual surfaces and handle their intersections. That is, the proposed tool generates a dual of the block mesh with intersections of the proper multiplicity without gaps and which respects the boundary features of the domain. Finally, we present several examples that illustrate the applicability of the tool. Copyright © 2010 John Wiley & Sons, Ltd.