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 apparatus comprises at least two spaced parallel discs having a relatively small thickness and mounted on one rotary shaft, and an intermediate disc having a relatively large thickness and mounted on the other shaft between the discs of small thickness. The two shafts are spaced from each other and the discs having small and large thicknesses have diameters such that the peripheral portions of the discs overlap one upon the other to form intersections therebetween on the rear and front sides. The yarn to be twisted is threaded through an intersection on the rear side, about the periphery of the intermediate disc and then through an intersection on the front side.