在工作中要将激光雷达的3D点云进行球面投影得到2D图像，这就要将笛卡尔空间坐标系中的点 P c = ( x , y , z ) P_c=(x, y, z) Pc​=(x,y,z)表示成球体坐标系中的形式 P s = ( θ , ϕ , r ) P_s=(\theta, \phi, r) Ps​=(θ,ϕ,r)，

其中： θ = a r c t a n ( y x ) ϕ = a r c s i n ( z r ) r = x 2 + y 2 + z 2 \theta=arctan(\frac{y}{x}) \\ \phi=arcsin(\frac{z}{r}) \\ r=\sqrt{x^2+y^2+z^2} θ=arctan(xy​)ϕ=arcsin(rz​)r=x2+y2+z2 ​ 这就要用到相关函数来求 θ \theta θ， ϕ \phi ϕ, r r r的值。根据球坐标的定义，要求 θ ∈ [ − π , π ] \theta\in[-\pi, \pi] θ∈[−π,π]， ϕ ∈ [ − π 2 , π 2 ] \phi\in[-\frac{\pi}{2},\frac{\pi}{2} ] ϕ∈[−2π​,2π​]， r ∈ [ 0 , + ∞ ) r\in[0, +\infty) r∈[0,+∞)。其中 ϕ \phi ϕ由反正弦函数 y = a r c s i n ( x ) y=arcsin(x) y=arcsin(x)得到，它的定义域是 [ − 1 , 1 ] [-1,1] [−1,1],值域是 [ − π 2 , π 2 ] [-\frac{\pi}{2}, \frac{\pi}{2}] [−2π​,2π​]，符合要求， r r r是一个二范数，一定大于等于 0 0 0，满足球坐标定义的要求。但是对于 θ \theta θ就有些麻烦了，我们知道正切函数的周期是 π \pi π，因此反正切函数一般也只取一个周期， y = a r c t a n ( x ) y=arctan(x) y=arctan(x)的定义域是 R \mathbb{R} R，值域是 ( − π 2 , π 2 ) (-\frac{\pi}{2}, \frac{\pi}{2}) (−2π​,2π​)，但是我们的要求是 θ ∈ [ − π , π ] \theta\in[-\pi, \pi] θ∈[−π,π]呀！ 别担心，Numpy早就贴心的准备好解决办法了，它不仅有np.arctan()函数，还准备了np.arctan2()函数，能够满足我们的需求。下面就来看看这两个函数有什么区别。

查看说明文档

Call signature: np.arctan(*args, **kwargs) Type: ufunc String form: File: ~/anaconda3/envs/torch/lib/python3.7/site-packages/numpy/init.py Docstring: arctan(x, /, out=None, *, where=True, casting=‘same_kind’, order=‘K’, dtype=None, subok=True[, signature, extobj]) Trigonometric inverse tangent, element-wise. The inverse of tan, so that if y = tan(x) then x = arctan(y). …(中间其他内容按下不表,有兴趣的同学可自行查看说明文档,只看out部分) out : ndarray or scalar Out has the same shape as x. Its real part is in [-pi/2, pi/2] (arctan(+/-inf) returns +/-pi/2). This is a scalar if x is a scalar.

总结:

查看说明文档

Call signature: np.arctan2(*args, **kwargs) Type: ufunc String form: File: ~/anaconda3/envs/torch/lib/python3.7/site-packages/numpy/init.py Docstring: arctan2(x1, x2, /, out=None, *, where=True, casting=‘same_kind’, order=‘K’, dtype=None, subok=True[, signature, extobj]) Element-wise arc tangent of x1/x2 choosing the quadrant correctly. The quadrant (i.e., branch) is chosen so that arctan2(x1, x2) is the signed angle in radians between the ray ending at the origin and passing through the point (1,0), and the ray ending at the origin and passing through the point (x2, x1). (Note the role reversal: the “y-coordinate” is the first function parameter, the “x-coordinate” is the second.) By IEEE convention, this function is defined for x2 = +/-0 and for either or both of x1 and x2 = +/-inf (see Notes for specific values). This function is not defined for complex-valued arguments; for the so-called argument of complex values, use angle. Parameters x1 : array_like, real-valued y-coordinates. x2 : array_like, real-valued x-coordinates. If x1.shape != x2.shape, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:ufunc docs . Returns angle : ndarray Array of angles in radians, in the range [-pi, pi]. This is a scalar if both x1 and x2 are scalars.

总结