A Fast and Robust Algorithm for Planar Intersection of Two Cones

Abstract

Abstract In general, two quadric surfaces intersect in a space quartic curve. However, the intersection curve frequently degenerates to a collection of planar curves. These degenerate cases are often required by design. For example, to blend two cones with a Dupin cyclide or a quadric surface, the cones must have planar intersection. Moreover, degeneracies normally introduce problems into the general intersection algorithms and are difficult to implement in a reliable way. In this paper, we shall present a fast and robust algorithm to detect and compute the planar intersection curves, as well as a technique to find the types of the curves without actually computing them.