Conics, Their Pencils and Intersections in Geometric Algebra

被引：0

作者：

Chomicki, Clement ^{[1
]}

Breuils, Stephane ^{[2
]}

Biri, Venceslas ^{[1
]}

Nozick, Vincent ^{[1
]}

机构：

[1] Univ Gustave Eiffel, LIGM, CNRS, Paris, France

[2] Univ Savoie Mont Blanc, LAMA, CNRS, Le Bourget Du Lac, France

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2025年 / 35卷 / 01期

关键词：

Conics; Geometric algebra; Projective geometry; Clifford algebra; Quadric conformal geometric algebra (QCGA); Geometric algebra for conics (GAC); Pencil;

D O I：

10.1007/s00006-024-01356-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：29

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