Latin square and intersection of surface

摘要

A technique is developed here to estimate an unknown curve joining two points in a three dimensional Euclidean space. A special application presented here is a computer procedure to determine the intersection of two arbitrary given smooth surfaces. The method used is to assume that y is a function of x and the set (x,y(x)) lies on the projection of the intersection of two surfaces. The function y is determined by least square curve fitting on a Latin square of experimental values. The procedure is written in APL (A Programming Language). A set of preliminary results is presented. The results indicate that this is a successful procedure for some simple surfaces, including some conic surfaces.