Parametric interpolation of three-dimensional surfaces

摘要

A method is described for defining complex two- and three-dimensional objects with a minimal amount of data. The method employs a "preprocessor" which receives the coordinate values of an ordered set of points on the object and calculates one or more state vectors which concisely define the object. Two numerical control systems are described in which these state vectors are applied to a "mapping" interpolator that controls the servomechanisms of a machine tool. The mapping interpolator controls machine tool motion to generate a three-dimensional surface which not only passes through each of the data points used to describe the object, but which also assumes a smooth shape of minimum strain energy.