A method of displaying graphic image surface information data of an object lying within a three-dimensional space on a two-dimensional display screen when seen from a predetermined observing point is disclosed. A patch of the surface of an object is separated into plural triangular units, and image information data (luminance, visible-nonvisible, and distance) are all represented at the three apexes of each triangular unit area which includes a number of display pixels. The positional data at the three apexes are transformed from three- to two-dimensional space. The other image information data are calculated in accordance with interpolation calculation. Prior to the interpolation calculation a display area is determined and a triangular area including pixels to be processed is determined to reduce the processing time. This process is repeated for the entire surface to be displayed.

A method is provided for combining a first physical object and a second physical object. A first locating point is defined on a first physical object, and a first location of the first locating point is determined by taking at least two measurements with respect to a Cartesian coordinate system. Similarly, a second locating point is defined on a second physical object. After combining the first physical object with the second physical object, a second location of the second locating point is determined by taking at least two measurements. The Cartesian measurement data is transformed into vector data before mean values, including directional mean values, are generated by performing statistical analysis in a Polar coordinate system. The first location can then be analyzed with respect to the second location using these mean values. This method can be applied to numerous applications, including the assembly of two manufactured automotive parts, exact color match of paint, or assessing the fit between an implant abutment and the prosthesis framework.

A system for establishing data defining a path for machining tool such as a three-axes milling machine tool. The machining tool path is established within a three-dimensional rectangular coordinate system which corresponds to a machine coordinate system for numerical control. The tool path is established along a first coordinate axis. The tool path is shifted to an adjacent path along the first coordinate axis in a second axis direction. The shifting pitch of the path corresponds to the interval of said path along the first the coordinate axis. The tool is shifted in third axis direction during travel along the path defined in the first and second axis direction.

A free curved surface generating system and method in which a plurality of cross sectional curves representing cross sectional shapes in an x-y coordinate system are generated, the plurality of cross sectional curves are arranged at desired positions in the x-y-z coordinate system, respectively, and thereafter a curved surface is formed between mutually adjacent cross sectional curves through an interpolation to generate the free curved surface are disclosed. In the free curved surface generating system and method, when the parallel translations and rotations are carried out for the generated cross sectional curves in the x-y-z coordinate system, the parallel translations and rotations are stored for each cross sectional curve into a memory and each cross sectional curve is parallel translated and rotated on the basis of data on the parallel translations and rotations for the corresponding cross sectional curve stored in the memory when the cross sectional curves are moved again into the x-y-z coordinate system.