A recursive sweep-plane algorithm,determining all cells of a finite division of Rd

“Sweep-plane” algorithms seem to become more and more important for the solution of certain geometrical problems. We present an algorithm of this kind that enumerates the cells of all dimensions into whichR ^d is partitioned by a finite set of hyperplanesF _i ⁰ . A plane sweeping through space (remaining parallel to itself) finds new cells each time it includes an intersection of someF _i ⁰ (normally a point). An analysis of the intersection-properties allows the construction of an algorithm recursive with respect to the dimension of space. Full generality has been one of our main objectives.