This paper presents an approach for extracting points from conic intersections by using the concept of pencils. This method is based on QC2GA—the two-dimensional version of QCGA (Quadric Conformal Geometric Algebra)—that is demonstrated to be equivalent to GAC (Geometric Algebra for Conics). A new interpretation of QC2GA and its objects based on pencils of conics and point space elements is presented, enabling the creation, constraining, and exploitation of pencils of conics. A Geometric Algebra method for computing the discriminants and center point of a conic will also be presented, enabling the proposition of an algorithm for extracting points from a conic intersection object.

本文提出了一种使用铅笔概念从圆锥交点中提取点的方法。该方法基于 QC2GA（QCGA（二次共形几何代数）的二维版本），被证明等同于 GAC（圆锥几何代数）。提出了基于圆锥铅笔和点空间元素的 QC2GA 及其对象的新解释，从而能够创建、约束和利用圆锥铅笔。还将介绍一种用于计算圆锥的判别式和中心点的几何代数方法，从而提出一种从圆锥交点对象中提取点的算法。