几何代数中二次曲线的多条件拟合

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-05-13 DOI:10.1007/s00006-023-01277-9

Pavel Loučka, Petr Vašík

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引用次数: 0

摘要

通过在优化问题中加入附加条件，我们介绍了几何代数中圆锥拟合的几种修改。这些额外条件中的每一个都确保了拟合圆锥曲线的额外几何特性，特别是坐标系原点的中心点位置、与坐标轴的轴向对齐，或者最终两者的组合。所有导出的算法都伴随着对底层代数和计算优化问题的讨论。最后，我们给出了在样本数据集上使用的示例，并提供了算法的可能应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

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On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

We introduce several modifications of conic fitting in Geometric algebra for conics by incorporating additional conditions into the optimisation problem. Each of these extra conditions ensure additional geometric properties of a fitted conic, in particular, centre point position at the origin of coordinate system, axial alignment with coordinate axes, or, eventually, combination of both. All derived algorithms are accompanied by a discussion of the underlying algebra and computational optimisation issues. Finally, we present examples of use on a sample dataset and offer possible applications of the algorithms.

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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.