Method and apparatus for producing a three-dimensional curved surface from two-dimensional section curves

A method of creating and machining a curved surface of a three-dimensional curved body, comprising:

• entering, into the apparatus, section data specifying first and second sections of the three-dimensional curved body, section curve data specifying respective first and second section curves of said three-dimensional curved body for said first and second sections, and data specifying a three-dimensional curve which contains points P.sub.1, P.sub.1 ' on the first and second section curves, respectively, and which indicates at least a part of the external shape of the three-dimensional curved body between said two sections, the data specifying said three-dimensional curve being data for specifying a first projection curve and a second projection curve obtained by projecting said three-dimensional curve onto respective ones of two adjacent planes in a rectangular coordinate system,
• generating an intermediate section for each of plural partition points that partition said three-dimensional curve into a multiplicity of line elements, each intermediate section containing the respective partition point, where generating of each said intermediate section including finding a tangent to the three-dimensional curve at the respective partition point, and generating, as the respective intermediate section, a plane containing the partition point and which is perpendicular to said tangent,
• calculating a respective intermediate section curve in each said intermediate section by using the section curve data of said two sections and position information indicative of the respective partition point on said three dimensional curve,
• creating said three-dimensional curved surface with the plurality of intermediate section curves, and
• machining the workpiece in dependence on the three-dimensional curved surface.