Tools for analyzing the intersection curve between two quadrics through projection and lifting

Abstract

This article introduces several efficient and easy-to-use tools to analyze the intersection curve between two quadrics, on the basis of the study of its projection on a plane (the so-called cutcurve) to perform the corresponding lifting correctly. This approach is based on an efficient way of determining the topology of the cutcurve through only solving one degree eight (at most) univariate equation and several quadratic univariate equations, intersecting two pairs of conics and, when the parameterization of the cutcurve in closed form cannot be determined, computing the real roots of several degree four univariate squarefree polynomials whose number (of real roots) is known in advance.