{"ID":2857307,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.08973","arxiv_id":"2510.08973","title":"A geometrical approach to solve the proximity of a point to an axisymmetric quadric in space","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2510.08973","url_pdf":"https://arxiv.org/pdf/2510.08973v1","authors":"[\"Bibekananda Patra\",\"Aditya Mahesh Kolte\",\"Sandipan Bandyopadhyay\"]","published":"2025-10-10T03:28:39Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[]","has_code":false}