Determining the Intersection of Parametric Surfaces by Solving Ordinary Differential Equations

A method for finding the intersection of two parametrically defined surfaces is discussed. The intersection is represented by parametrized curves in the parameter spaces of each of the two given surfaces. The curves are found by solving a four dimensional system of differential equations by means of a low order numerical ODE solver. Correction of drift is obtained by a variant of the Newton-Raphson technique developed specifically for this problem.