Intersection of Parametric Surfaces and a Plane

An algorithm is presented for approximating all the intersection curves between a plane and an arbitrary parametric surface patch. This is accomplished by a two-stage recursive procedure that simultaneously generates approximations to the curve(s) in 3-D space and the associated pre-image curve(s) in 2-D parameter space. The algorithm provides an accurate mathematical representation based on a tolerance that can be defined by the particular application.