A Linear Least Squares Method for Describing and Comparing Gently Curved Three-Dimensional Surfaces

Abstract

A simple method is developed for fully describing gently curved surfaces with the aid of a computer, using a finite number of point measurements as input data. By means of this method, cut sections through a surface in various directions may be computed and graphically displayed. Similar surfaces, corresponding to a workpiece and its desired shape, may then be compared along a cut section on a command from an operator, resulting in the visual display of the section curves. This technique should prove useful in iterative forming of shallow panels (e.g., aircraft wing sections) and other applications involving gently curved surfaces.