Abstract: A three-dimensional space may be rendered in a computer graphics system by representing the three-dimensional space as a plurality of convex polyhedra and representing the containment relationships among the plurality of convex polyhedra. Connection relationships among the convex polyhedra, including the location of holes in the connected surfaces, are also preferably represented. Containment and connection relationships are preferably represented using a containment logical tree and a connection logical graph. Three-dimensional graphics representations can thereby be rendered in a real time using a low cost, graphics processor. Efficient movement through three-dimensional space along all six degrees of freedom is also provided by using a two-dimensional pointing device, preferably a mouse, in combination with a function selector, preferably a pair of keys on the mouse.