几何代数中的圆锥曲线、其铅笔和交点

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-11-05 DOI:10.1007/s00006-024-01356-5

Clément Chomicki, Stéphane Breuils, Venceslas Biri, Vincent Nozick

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引用次数: 0

摘要

本文提出了一种利用铅笔概念从圆锥交点提取点的方法。该方法基于 QC2GA--QCGA（Quadric Conformal Geometric Algebra，四元共形几何代数）的二维版本--经证明等同于 GAC（Geometric Algebra for Conics，圆锥几何代数）。基于圆锥曲线铅笔和点空间元素，提出了对 QC2GA 及其对象的新解释，从而能够创建、约束和利用圆锥曲线铅笔。还将介绍计算圆锥的判别式和中心点的几何代数方法，从而提出从圆锥交点对象中提取点的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Conics, Their Pencils and Intersections in Geometric Algebra

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Conics, Their Pencils and Intersections in Geometric Algebra

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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.