好像是用了什么神奇的公式：$\frac{2}{\rho}=\frac{1}{\rho_x}+\frac{1}{\rho_y}$.
这个公式是说，空间中一点的曲率，是这一点在过其的两个正交平面内曲率的平均。就是分别在xz平面、yz平面里看，曲率半径分别是$\rho_x$,$\rho_y$，那么xyz空间中的曲率半径$\rho$可用上述公式计算。
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第一种思路，如果你学过隐函数求导那那个直接暴力求导即可，如果是没学过隐函数求导的话你可以试试用运动学方法求解曲率半径，构造一个天体椭圆轨道，算出那点的向心加速度和速度，用向心加速度公式算曲率半径
- Radius of curvature in the x-direction:
$R_x = \frac{a^2}{\sqrt{a^2\sin^2\phi + b^2\cos^2\phi}^3}$
where $a$ is the semi-major axis, $b$ is the semi-minor axis, and $\phi$ is the angle between the x-axis and the plane normal to the surface at the point of interest.
- Radius of curvature in the y-direction:
$R_y = \frac{ab^2}{\sqrt{a^2\cos^2\phi + b^2\sin^2\phi}^3}$
where $a$ is the semi-major axis, $b$ is the semi-minor axis, and $\phi$ is the angle between the y-axis and the plane normal to the surface at the point of interest.
- Radius of curvature in the z-direction:
$R_z = \frac{b^2}{\sqrt{a^2\cos^2\phi + b^2\sin^2\phi}^3}$
where $a$ is the semi-major axis, $b$ is the semi-minor axis, and $\phi$ is the angle between the z-axis and the plane normal to the surface at the point of interest.