Python conversion between coordinates

问题

Are there functions for conversion between different coordinate systems?

For example, Matlab has [rho,phi] = cart2pol(x,y) for conversion from cartesian to polar coordinates. Seems like it should be in numpy or scipy.

回答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)

回答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 )

回答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)

回答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)

回答5:

There is a better way to write polar(), here it is:

def polar(x,y):
  `returns r, theta(degrees)`
  return math.hypot(x,y),math.degrees(math.atan2(y,x))

回答6:

If your coordinates are stored as complex numbers you can use cmath

回答7:

Thinking about it in general, I would strongly consider hiding coordinate system behind well-designed abstraction. Quoting Uncle Bob and his book:

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)

With interface like that any user of Point class may choose convenient representation, no explicit conversions will be performed. All this ugly sines, cosines etc. will be hidden in one place. Point class. Only place where you should care which representation is used in computer memory.

来源：https://stackoverflow.com/questions/20924085/python-conversion-between-coordinates