1. A method of creating and machining a curved surface of a three-dimensional curved body on a workpiece using a curve generating apparatus, 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, 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, calculating a respective intermediate section curve in each said intermediate section by using partitioning ratios of the section curve data of said two sections and position information indicative of the respective partition point of 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.