有不同坐标系之间转换的函数吗？
例如，Matlab 有
[rho,phi] = cart2pol(x,y)使用 numpy，您可以定义以下内容：
import numpy as np
def cart2pol(x, y):
rho = np.sqrt(x**2 + y**2)
phi = np.arctan2(y, x)
return(rho, phi)
def pol2cart(rho, phi):
x = rho * np.cos(phi)
y = rho * np.sin(phi)
return(x, y)
现有答案可以简化：
from numpy import exp, abs, angle
def polar2z(r,theta):
return r * exp( 1j * theta )
def z2polar(z):
return ( abs(z), angle(z) )
甚至：
polar2z = lambda r,θ: r * exp( 1j * θ )
z2polar = lambda z: ( abs(z), angle(z) )
注意这些也适用于数组！
rS, thetaS = z2polar( [z1,z2,z3] )
zS = polar2z( rS, thetaS )
您可以使用 cmath 模块。
如果数字转换为复杂格式，那么只需对数字调用极坐标方法就会变得更容易。
import cmath
input_num = complex(1, 2) # stored as 1+2j
r, phi = cmath.polar(input_num)
如果你在 numpy 或 scipy 中找不到它，这里有几个快速函数和一个点类：
import math
def rect(r, theta):
"""theta in degrees
returns tuple; (float, float); (x,y)
"""
x = r * math.cos(math.radians(theta))
y = r * math.sin(math.radians(theta))
return x,y
def polar(x, y):
"""returns r, theta(degrees)
"""
r = (x ** 2 + y ** 2) ** .5
theta = math.degrees(math.atan2(y,x))
return r, theta
class Point(object):
def __init__(self, x=None, y=None, r=None, theta=None):
"""x and y or r and theta(degrees)
"""
if x and y:
self.c_polar(x, y)
elif r and theta:
self.c_rect(r, theta)
else:
raise ValueError('Must specify x and y or r and theta')
def c_polar(self, x, y, f = polar):
self._x = x
self._y = y
self._r, self._theta = f(self._x, self._y)
self._theta_radians = math.radians(self._theta)
def c_rect(self, r, theta, f = rect):
"""theta in degrees
"""
self._r = r
self._theta = theta
self._theta_radians = math.radians(theta)
self._x, self._y = f(self._r, self._theta)
def setx(self, x):
self.c_polar(x, self._y)
def getx(self):
return self._x
x = property(fget = getx, fset = setx)
def sety(self, y):
self.c_polar(self._x, y)
def gety(self):
return self._y
y = property(fget = gety, fset = sety)
def setxy(self, x, y):
self.c_polar(x, y)
def getxy(self):
return self._x, self._y
xy = property(fget = getxy, fset = setxy)
def setr(self, r):
self.c_rect(r, self._theta)
def getr(self):
return self._r
r = property(fget = getr, fset = setr)
def settheta(self, theta):
"""theta in degrees
"""
self.c_rect(self._r, theta)
def gettheta(self):
return self._theta
theta = property(fget = gettheta, fset = settheta)
def set_r_theta(self, r, theta):
"""theta in degrees
"""
self.c_rect(r, theta)
def get_r_theta(self):
return self._r, self._theta
r_theta = property(fget = get_r_theta, fset = set_r_theta)
def __str__(self):
return '({},{})'.format(self._x, self._y)
有更好的办法，写一个从笛卡尔坐标转换为极坐标的方法；这是：
import numpy as np
def polar(x, y) -> tuple:
"""returns rho, theta (degrees)"""
return np.hypot(x, y), np.degrees(np.arctan2(y, x))
如果您的坐标存储为复数，您可以使用 cmath
混合以上所有适合我的答案：
import numpy as np
def pol2cart(r,theta):
'''
Parameters:
- r: float, vector amplitude
- theta: float, vector angle
Returns:
- x: float, x coord. of vector end
- y: float, y coord. of vector end
'''
z = r * np.exp(1j * theta)
x, y = z.real, z.imag
return x, y
def cart2pol(x, y):
'''
Parameters:
- x: float, x coord. of vector end
- y: float, y coord. of vector end
Returns:
- r: float, vector amplitude
- theta: float, vector angle
'''
z = x + y * 1j
r,theta = np.abs(z), np.angle(z)
return r,theta
如果像我一样，您试图控制一个接受基于操纵杆值的速度和航向值的机器人，请使用它（它将弧度转换为度数：
def cart2pol(x, y):
rho = np.sqrt(x**2 + y**2)
phi = np.arctan2(y, x)
return(rho, math.degrees(phi))
如果您有一组
(x,y)(rho, phi)函数返回转换后的坐标数组。
import numpy as np
def combine2Coord(c1, c2):
return np.concatenate((c1.reshape(-1, 1), c2.reshape(-1, 1)), axis=1)
def cart2pol(xyArr):
rho = np.sqrt((xyArr**2).sum(1))
phi = np.arctan2(xyArr[:,1], xyArr[:,0])
return combine2Coord(rho, phi)
def pol2cart(rhoPhiArr):
x = rhoPhiArr[:,0] * np.cos(rhoPhiArr[:,1])
y = rhoPhiArr[:,0] * np.sin(rhoPhiArr[:,1])
return combine2Coord(x, y)
您关心速度吗？使用
cmathnumpypython 2使用
ipythonimport cmath, numpy as np
def polar2z(polar):
rho, phi = polar
return rho * np.exp( 1j * phi )
def z2polar(z):
return ( np.abs(z), np.angle(z) )
def cart2polC(xy):
x, y = xy
return(cmath.polar(complex(x, y))) # rho, phi
def pol2cartC(polar):
rho, phi = polar
z = rho * cmath.exp(1j * phi)
return z.real, z.imag
def cart2polNP(xy):
x, y = xy
rho = np.sqrt(x**2 + y**2)
phi = np.arctan2(y, x)
return(rho, phi)
def pol2cartNP(polar):
rho, phi = polar
x = rho * np.cos(phi)
y = rho * np.sin(phi)
return(x, y)
xy = (100,100)
polar = (100,0)
%timeit cart2polC(xy)
%timeit pol2cartC(polar)
%timeit cart2polNP(xy)
%timeit pol2cartNP(polar)
%timeit z2polar(complex(*xy))
%timeit polar2z(polar)
373 ns ± 4.76 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
337 ns ± 0.976 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
4.3 µs ± 34.2 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
3.41 µs ± 5.78 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
3.4 µs ± 5.4 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
1.39 µs ± 3.86 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
您可以使用 astropy 中的内置函数 spherical_to_cartesian。
这里的文档： https://docs.astropy.org/en/stable/api/astropy.coordinates.spherical_to_cartesian.html
总的来说，我会强烈考虑将坐标系隐藏在精心设计的抽象后面。引用鲍勃叔叔和他的书：
class Point(object)
def setCartesian(self, x, y)
def setPolar(self, rho, theta)
def getX(self)
def getY(self)
def getRho(self)
def setTheta(self)
通过这样的接口，Point 类的任何用户都可以选择方便的表示形式，而不会执行显式转换。所有这些丑陋的正弦、余弦等都将隐藏在一个地方。点类。仅在您应该关心计算机内存中使用哪种表示形式的地方。