The simulation of point defect production in crystal lattices by irradiation presents many difficult problems in computational geometry. Shapes such as lobes, ‘starbursts', and chains are common at many scales of measure. With the exception of molecular dynamics methods, simulation techniques use simple, distance based models to detect the interaction of these complex objects. A constructive procedure based on recursive space partitioning and a data structure called ak-dBSP tree has been developed and applied to simulating the spontaneous recombination of unstable Frenkel pairs. Frenkel pair distributions were obtained for BCC iron from displacement cascades simulated using the binary collision approximation. Approximately 57% of the Frenkel pairs generated by these displacement cascades were found to be unstable.