A geometrical approach to solve the proximity of a point to an axisymmetric quadric in space
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917001667018752 |
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| author | Patra, Bibekananda Kolte, Aditya Mahesh Bandyopadhyay, Sandipan |
| author_facet | Patra, Bibekananda Kolte, Aditya Mahesh Bandyopadhyay, Sandipan |
| contents | This paper presents the classification of a general quadric into an axisymmetric quadric (AQ) and the solution to the problem of the proximity of a given point to an AQ. The problem of proximity in $R^3$ is reduced to the same in $R^2$, which is not found in the literature. A new method to solve the problem in $R^2$ is used based on the geometrical properties of the conics, such as sub-normal, length of the semi-major axis, eccentricity, slope and radius. Furthermore, the problem in $R^2$ is categorised into two and three more sub-cases for parabola and ellipse/hyperbola, respectively, depending on the location of the point, which is a novel approach as per the authors' knowledge. The proposed method is suitable for implementation in a common programming language, such as C and proved to be faster than a commercial library, namely, Bullet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A geometrical approach to solve the proximity of a point to an axisymmetric quadric in space Patra, Bibekananda Kolte, Aditya Mahesh Bandyopadhyay, Sandipan Robotics This paper presents the classification of a general quadric into an axisymmetric quadric (AQ) and the solution to the problem of the proximity of a given point to an AQ. The problem of proximity in $R^3$ is reduced to the same in $R^2$, which is not found in the literature. A new method to solve the problem in $R^2$ is used based on the geometrical properties of the conics, such as sub-normal, length of the semi-major axis, eccentricity, slope and radius. Furthermore, the problem in $R^2$ is categorised into two and three more sub-cases for parabola and ellipse/hyperbola, respectively, depending on the location of the point, which is a novel approach as per the authors' knowledge. The proposed method is suitable for implementation in a common programming language, such as C and proved to be faster than a commercial library, namely, Bullet. |
| title | A geometrical approach to solve the proximity of a point to an axisymmetric quadric in space |
| topic | Robotics |
| url | https://arxiv.org/abs/2510.08973 |