Determining intersection curves between surfaces of two solids

Abstract

Intersection curves between two parametric surfaces are numerically computed using continuation methods. A starting point to initiate the algorithm is determined using the Moore-Penrose pseudo-inverse. Singularities along the curve are detected using a row-rank deficiency of the Jacobian. At singular points where two or more curves intersect, bifurcation points are calculated. To numerically compute a multiple of curves at a bifurcation point, a 2nd-order expansion method is used to render the equation into a quadratic form, such that the tangents are computed. The solution is then switched to a bifurcation branch. The method is demonstrated for two intersecting surfaces having two intersecting curves. The method is also validated for special cases through a number of examples. Copyright © 1996 Elsevier Science Ltd.