A polygon-dissection structure is disclosed incorporated in a system for processing geometric data, e.g. data representing three-dimensional polygons, as by subdividing such polygons to accomplish sorting of the data. The system operates to divide a working volume, e.g. a perspective pyramid, into successively-smaller subvolumes. The separating planes are placed at arbitrary angles to coincide with the edges and surfaces of polygons that define objects to be represented. Polygons which straddle separating planes are dissected into two parts which are thereafter treated separately. Dissection by the system results in simplification in accounting for the polygons in relation to specific subvolumes. The system can be applied to the detection of those polygons which hide others thereby enabling a solution to the hidden-surface problem. Additionally, the system affords a simple mechanism for resolving shadowed portions of polygons as well as portions of polygons obstructed by semi-transparent surfaces and for explicitly computing and displaying implied lines of intersections existing between two inter-penetrating polygons. Alternatively, the system provides an efficient way of detecting if any or a multiplicity of polyhedra solids inter-penetrate.