A ray tracing method for construction an image of a notional scene from data concerning a plurality of objects in the scene and the illumination of the scene, involves allocating surfaces of objects in the scene into a plurality of subsets, projecting from a notional viewing position a plurality of straight line paths and storing data for all said paths, determining which, if any, of those straight line paths intersect any surface in a selected subset or a zone of illumination, and repeating that step for all the other subsets until all the paths have been tested for intersections against all surfaces in the scene. The method also determines, for each path, which intersection is nearest the viewing position and stores data on the co-ordinates for that intersection and on the surface of the object or zone of illumination at that intersection. The intensity in colour of light which will pass along the path through the notional viewing position from that intersection is then calculated and stored, and the stored intensity and/or colour is then used to produce a picture signal for a visual display. A plurality of paths are tested for intersections against a given subset of surfaces before the paths are considered in relation to other subsets, thereby reducing the number of times the subsets have to be called up from the database. The method can be conducted on apparatus which uses parallel ray processors.