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.

翻译：本文提出将一般二次曲面分类为轴对称二次曲面（AQ），并解决了给定点到AQ的距离问题。该距离问题在$R^3$中被简化为$R^2$中的等价问题，此方法在现有文献中未见报道。基于圆锥曲线的几何特性（如次法距、半长轴长度、离心率、斜率和半径），采用了一种新方法求解$R^2$中的问题。此外，根据点的位置将$R^2$中的问题进一步分类：抛物线分为两种子情形，椭圆/双曲线分为三种子情形，据作者所知这是一种创新性方法。所提方法适用于C等通用编程语言实现，并验证其速度快于Bullet等商业库。