Abstract: A method and apparatus is presented in which a physical object is formed on the basis of data that represents a free-form surface. A free-form surface is formed by entering into a designing device a series of input points. A free-form surface forming unit of the designing device then generates geometric data that represents an object to be formed. The free-form surface forming unit uses this geometric data to control a milling machine, which sculpts an object in accordance with the geometric data.

Abstract: A three-dimensional physical quantity calculating system calculates the physical quantities of the whole cubic body composed of a plurality of elementary cubic bodies. The system includes a table calculating section for calculating the physical quantities of the whole cubic body on the basis of physical parameters inputted through an input section. The physical quantities of the respective elementary cubic bodies are calculated by an elementary cubic body physical quantity calculating section in accordance with predetermined calculation formula.

Abstract: A method and an apparatus for generating sculptured surfaces which enables a sculptured surface of a specified radius to be generated easily between two free curves. A plurality of base points are set on a first free curve, and a plurality of planes are generated at each of the base points using, as the normal, a tangent of the first free line, the planes including that base point. A plurality of intersections of the second free curve and the plurality of planes are determined. A plurality of circular arcs of a specified radius are generated on each of the plurality of planes using the base point and the intersection as endpoints. A sculptured surface is then generated based on the first free curve, the second free curve, and the plurality of circular arcs.

Abstract: The present invention relates to a free-from surface creation method and apparatus thereof which can automatically determine such internal control points that allow a plurality of patches to form a smooth surface. Based on the four normal lines (N.sub.00, N.sub.01, N.sub.10, N.sub.11) to a quadrilateral patch A at its corners and on its four edges (E.sub.1, E.sub.2, E.sub.3, E.sub.4), reference normal lines at a plurality of points defined on each edge (E.sub.1, E.sub.2, E.sub.3, E.sub.4) are determined, and each reference normal line determined on the respective plurality of points are approximated to the normal line corresponding to the plurality of points which are defined on the edges of which are shared with the quadrilateral patch A and the adjacent patch. Therefore, the internal control points of the quadrilateral patch A are determined.

Abstract: In a method for forming free-form curves and free-form surfaces, the nodal points of the object to be projected and a series of points set on the object to be projected are projected onto a patch. Free-form curves are generated on the patch on the basis of the result of projection. Thereby, free-form curves of the geometry projecting free-form curves may be generated readily and with high accuracy on the patch and, further, the free-form curves may be used to generate a framing space, or a free-form surface.

Abstract: A free-form surface data generating method for creating a free-form surface by forming trilateral patches expressed by predetermined vector functions over frame spaces. When specifying a transformation of a common boundary, the common boundary is arbitrarily transformed and, simultaneously, the first and second trilateral patches are connected while keeping a relation in surface geometry. When specifying non-transformation of the common boundary, a curvilinear configuration of the common boundary is maintained, and the first and second patches are connected by arbitrarily transforming the surface geometries of the first and second trilateral patches so that the surface geometries of the first and second trilateral patches are selectable by specifying whether the common boundary is transformed or not.

Abstract: Methods for generating free curves and sculptured surfaces illustratively for use with a computer aided design/computer aided manufacturing (CAD/CAM) apparatus whereby Bezier curves and surfaces are readily generated with reference to point sequences, point groups and surfaces. In operation, a starting point and an end point for a sequence of points are set as nodes, and a free curve is temporarily established thereby. Then control points are repeatedly established to minimize the shortest distances between the points in the sequence and the free curve. By use of the coordinates of a plurality of points, the shortest distance is found between each of these points and a reference patch. The internal control points are set so as to minimize the total sum of these shortest distances.

Abstract: A method for displaying an image of an object surface on a screen in which a non-linear transformation is applied to the luminance value at points on the surface of the object in accordance with an illumination model, accounting for only ambient light and diffusedly reflected light. Lighter and darker portions of the surface are emphasized to express glossiness of the surface in a simulated manner. Color of the image can be designated by selecting a point in a chart having a fixed value of lightness of a color cube, the color cube having coordinate axes representing hue, lightness, and saturation of color.

Abstract: Disclosed is a shape data processing method illustratively for use with a CAD,CAM (computed aided design/ computer aided manufacturing) system. The method involves measuring the volume of a target product based on the shape data of that product. In operation, a virtual projection surface is established for the target object to be measured. The surface of the object is divided into small regions. A column portion is formed as an extension from each small region to the projection surface. The volume of the column portion is measured for each small region. The measured volumes are accumulated in accordance with the orientation of the normal vector to each small region. This method allows the volume of the target object to be measured easily and with precision even if the shape thereof is complex.

Abstract: In a method for generating data defining the machining depth along a tool path, grid points are generated according to split points indicating a form of a model, and rough machining data for contour milling is generated according to the grid points, so that rough machining data which presents overcutting can be prepared. Contour points are generated and drilling points are set according to a comparison with cut planes so that the drilling points can be set easily and automatically. The contour points are retrieved successively so as to easily generate a tool path for contour milling.

Abstract: A method for generating data defining a tool path for a numerically controlled machine is designed for generating machining tool path data without establishing offset plane data so that the machining tool path depth data can be established for discontinuous, surfaced, offset planes which might otherwise cause interference in the tool path. The method includes the steps of forming a plurality of patches defining a three-dimensional plane to be machined, subdividing each patch into a predetermined number of segments as divided by a plurality of dividing points, with the number of segments being variable depending upon the distance between adjacent dividing points so that the distance is maintained to be smaller than the machining area of a machine tool. The machining depth at each dividing point within the tool path is derived with respect to the maximum height position at which the machining tool comes into contact with the dividing point.

Abstract: 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.

Abstract: A method for generating offset surface data representing a tool path of a tool traversing patches which are mutually adjoining at boundary lines where there is no continuity of the osculating planes. The offset surface data is interpolated for the parts of the surface at which the offset surface data become mutually discontinuous at the boundary lines or for a patch having a sharp corner. The present invention is applicable to a NC (Numerical Control) machining center which can control a machine tool so as to prevent excessive milling by the tool at the discontinuous parts of the offset surface.

Abstract: A method and system for effecting a transformation of video image on a video screen applicable to a system for producing a special visual effect on, e.g., a television screen, in which a two-dimensional address plane is defined within a memory area, input video image is stored within the memory area, a cylinder shaped virtual image is placed on the address plane, a part of the address plane is wound on the cylinder shaped image, and when the cylinder shaped image is displaced along a predetermined direction on the address plane with a radius of a circle in vertical section thereof being varied with time, the address plane can be viewed as if it were turned over. If the input address data within the memory area is read out on the basis of output address data indicating the above-described displacement of the address plane, the output video image on the video screen can be viewed therethrough as if the video image were being turned over.

Abstract: 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.

Abstract: 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.