Python conversion between coordinates
Solution 1:
Using numpy, you can define the following:
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)
Solution 2:
The existing answers can be simplified:
from numpy import exp, abs, angle
def polar2z(r,theta):
return r * exp( 1j * theta )
def z2polar(z):
return ( abs(z), angle(z) )
Or even:
polar2z = lambda r,θ: r * exp( 1j * θ )
z2polar = lambda z: ( abs(z), angle(z) )
Note these also work on arrays!
rS, thetaS = z2polar( [z1,z2,z3] )
zS = polar2z( rS, thetaS )
Solution 3:
You can use the cmath module.
If the number is converted to a complex format, then it becomes easier to just call the polar method on the number.
import cmath
input_num = complex(1, 2) # stored as 1+2j
r, phi = cmath.polar(input_num)
Solution 4:
If you can't find it in numpy or scipy, here are a couple of quick functions and a point class:
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)