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 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: 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: 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.