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.

本文在研究其在平面上的投影（所谓的“割曲线”）的基础上，介绍几种有效且易于使用的工具来分析两个二次曲面之间的相交曲线，以正确执行相应的提升。该方法基于一种有效的方法，该方法通过仅求解一个八阶（最多）单变量方程和几个二次单变量方程，与两对圆锥形相交以及当闭合曲线的参数化无法进行封闭时确定切割曲线的拓扑的有效方法为基础确定后，计算事先知道（实根数）个数的四次单变量无平方多项式的实根。