Abstract: In the conventional CAD or CAM system, when a shape must be defined, it should use mathematical models which are formed by B-Reps or CSG method. B-Reps method is more complicated than CSG in data structure and in processing. This invention attempts to utilize merits of the CSG method, express component elements of a three-dimensional solid model in a hierarchical structure so that an element of a a higher order can relocate another element of a lower order on its coordinate system, and an interactive operation can be employed in defining. This method allows an operator to ascertain the progress of the works with his/her own eyes to greatly simplify the works of shape defining of solid models.

Abstract: The issue of tool path generation has so far been approached from points of automatic programming system on typified by APT. In the automatic programming system, however, patterns of workpieces should be recognized by operators, and if the workpieces are of complicated shapes, it should require much skill and time. Studies have been conducted in recent years to generate tool paths by building up in advance solid models in a computer, and modifying the models for a particular problem everytime it needs to be solved. According to this invention method, a required shape and an environmental model including a workpiece are modeled in three-dimensions by using CSG models, and are offset in a normal direction of the surface in correspondence to the tool radius to convert the tool into a line tool so that the problem is replaced with a graphic problem viewed from the tool axis direction.