Abstract: A pattern processing method is provided which performs the following steps with regard to a region in an n-dimensional space: providing a procedure (relative expression procedure) for generating relative positional data of any desired point in the n-dimensional space with respect to the region by the use of a series of data determining the region (the relative positional data including data indicating whether the point is inside or outside the region, the distance from the point to the boundary of the region, etc.

Abstract: A three-dimensional shape as a synthesis of three-dimensional geometry entities is controlled and displayed. The geometry entities are controlled in accordance with information defining the geometry entities, and layout information arranged in a three-dimensional space. An interface between graphic display apparatus using this graphic display method and an application system is practiced in that the transfer of the information on the geometry entities is carried out. The three-dimensional shape is divided into its geometry entities, and the display of an object having a three-dimensional shape is done as a synthesis of the geometry entities, the transfer of shape data being done separately for each geometry entity.

Abstract: A three-dimensional shape of an object is recognized by developing enveloping surfaces of the object by a cone-silhouetting method, wherein the object is picked up by a binocular three-dimensional vision method by making use of geometrical restraint conditions derived by the cone-silhouetting method. The binocular parallax is increased to thereby ensure the recognition of the three-dimensional shape with improved accuracy. Local concave portions which can not be recognized by the cone-silhouetting method by itself are recognized with higher accuracy.

Abstract: A graphic display processing system is disclosed, in which a two-dimensional pattern or an image of a three-dimensional pattern can be displayed on the display screen of a display device, and moreover it can be rapidly judged whether or not each graphic data on a display list formed in a graphic data buffer corresponds to a pattern in a pattern pick region (namely, pick aperture) set on the display screen. In more detail, display color data in the pick aperture is first read out of a frame memory for storing image data. In a case where an image of a three-dimensional pattern is displayed, depth values in the pick aperture are read out of a Z-buffer for storing depth values with respect to a displayed pattern.