Algorithms for Conic Fitting Through Given Proper and Improper Waypoints in Geometric Algebra for Conics

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2024-01-09 DOI:10.1007/s00006-023-01308-5

Pavel Loučka, Petr Vašík

引用次数: 0

Abstract

As an addition to proper points of the real plane, we introduce a representation of improper points, i.e. points at infinity, in terms of Geometric Algebra for Conics (GAC) and offer possible use of both types of points. More precisely, we present two algorithms fitting a conic to a dataset with a certain number of points lying on the conic precisely, referred to as the waypoints. Furthermore, we consider inclusion of one or two improper waypoints, which leads to the asymptotic directions of the fitted conic. The number of used waypoints may be up to four and we classify all the cases.

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圆锥曲线几何代数中通过给定适当和不适当航点进行圆锥拟合的算法

作为实平面适当点的补充，我们用圆锥几何代数（GAC）引入了不适当点（即无穷远处的点）的表示方法，并提供了这两类点的可能用途。更确切地说，我们提出了两种将圆锥拟合到数据集的算法，其中有一定数量的点精确地位于圆锥上，这些点被称为航点。此外，我们还考虑加入一个或两个不恰当的航点，从而得出拟合圆锥的渐近方向。使用的航点数量最多为四个，我们将所有情况进行分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.