我有一个极坐标 (r,theta) 网格（这意味着每个单元都是一个环形部分），其中包含一些物理量（例如温度）的值，我想重新网格（或重新投影，或重新采样）这些值到笛卡尔网格上。是否有任何 Python 包可以做到这一点？
我对将单元格中心的坐标从极坐标转换为笛卡尔坐标不感兴趣 - 这很容易。相反，我正在寻找一个可以真正正确地重新网格化数据的包。
感谢您的任何建议！
【问题讨论】：
感谢您的回答 - 经过更多思考后，我想出了以下代码：
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as mpl
from scipy.interpolate import interp1d
from scipy.ndimage import map_coordinates
def polar2cartesian(r, t, grid, x, y, order=3):
X, Y = np.meshgrid(x, y)
new_r = np.sqrt(X*X+Y*Y)
new_t = np.arctan2(X, Y)
ir = interp1d(r, np.arange(len(r)), bounds_error=False)
it = interp1d(t, np.arange(len(t)))
new_ir = ir(new_r.ravel())
new_it = it(new_t.ravel())
new_ir[new_r.ravel() > r.max()] = len(r)-1
new_ir[new_r.ravel() < r.min()] = 0
return map_coordinates(grid, np.array([new_ir, new_it]),
order=order).reshape(new_r.shape)
# Define original polar grid
nr = 10
nt = 10
r = np.linspace(1, 100, nr)
t = np.linspace(0., np.pi, nt)
z = np.random.random((nr, nt))
# Define new cartesian grid
nx = 100
ny = 200
x = np.linspace(0., 100., nx)
y = np.linspace(-100., 100., ny)
# Interpolate polar grid to cartesian grid (nearest neighbor)
fig = mpl.figure()
ax = fig.add_subplot(111)
ax.imshow(polar2cartesian(r, t, z, x, y, order=0), interpolation='nearest')
fig.savefig('test1.png')
# Interpolate polar grid to cartesian grid (cubic spline)
fig = mpl.figure()
ax = fig.add_subplot(111)
ax.imshow(polar2cartesian(r, t, z, x, y, order=3), interpolation='nearest')
fig.savefig('test2.png')
这不是严格的重新网格化，但可以满足我的需要。只是发布代码以防它对其他人有用。欢迎提出改进建议！
【讨论】：
您可以使用scipy.ndimage.geometric_transform 更简洁地执行此操作。下面是一些示例代码：
import numpy as N
import scipy as S
import scipy.ndimage
temperature = <whatever>
# This is the data in your polar grid.
# The 0th and 1st axes correspond to r and θ, respectively.
# For the sake of simplicity, θ goes from 0 to 2π,
# and r's units are just its indices.
def polar2cartesian(outcoords, inputshape, origin):
"""Coordinate transform for converting a polar array to Cartesian coordinates.
inputshape is a tuple containing the shape of the polar array. origin is a
tuple containing the x and y indices of where the origin should be in the
output array."""
xindex, yindex = outcoords
x0, y0 = origin
x = xindex - x0
y = yindex - y0
r = N.sqrt(x**2 + y**2)
theta = N.arctan2(y, x)
theta_index = N.round((theta + N.pi) * inputshape[1] / (2 * N.pi))
return (r,theta_index)
temperature_cartesian = S.ndimage.geometric_transform(temperature, polar2cartesian,
order=0,
output_shape = (temperature.shape[0] * 2, temperature.shape[0] * 2),
extra_keywords = {'inputshape':temperature.shape,
'center':(temperature.shape[0], temperature.shape[0])})
您可以根据需要更改order=0 以获得更好的插值。输出数组temperature_cartesian 在这里是 2r x 2r，但你可以指定任何你喜欢的大小和原点。
【讨论】：
前段时间，当我尝试做类似的事情时，我来到这篇文章，即将极地数据重新投影到笛卡尔网格中，反之亦然。这里提出的解决方案效果很好。但是，执行坐标变换需要一些时间。我只是想分享另一种方法，它可以将处理时间减少多达 50 倍或更多。
算法使用scipy.ndimage.interpolation.map_coordinates函数。
让我们看一个小例子：
import numpy as np
# Auxiliary function to map polar data to a cartesian plane
def polar_to_cart(polar_data, theta_step, range_step, x, y, order=3):
from scipy.ndimage.interpolation import map_coordinates as mp
# "x" and "y" are numpy arrays with the desired cartesian coordinates
# we make a meshgrid with them
X, Y = np.meshgrid(x, y)
# Now that we have the X and Y coordinates of each point in the output plane
# we can calculate their corresponding theta and range
Tc = np.degrees(np.arctan2(Y, X)).ravel()
Rc = (np.sqrt(X**2 + Y**2)).ravel()
# Negative angles are corrected
Tc[Tc < 0] = 360 + Tc[Tc < 0]
# Using the known theta and range steps, the coordinates are mapped to
# those of the data grid
Tc = Tc / theta_step
Rc = Rc / range_step
# An array of polar coordinates is created stacking the previous arrays
coords = np.vstack((Ac, Sc))
# To avoid holes in the 360º - 0º boundary, the last column of the data
# copied in the begining
polar_data = np.vstack((polar_data, polar_data[-1,:]))
# The data is mapped to the new coordinates
# Values outside range are substituted with nans
cart_data = mp(polar_data, coords, order=order, mode='constant', cval=np.nan)
# The data is reshaped and returned
return(cart_data.reshape(len(y), len(x)).T)
polar_data = ... # Here a 2D array of data is assumed, with shape thetas x ranges
# We create the x and y axes of the output cartesian data
x = y = np.arange(-100000, 100000, 1000)
# We call the mapping function assuming 1 degree of theta step and 500 meters of
# range step. The default order of 3 is used.
cart_data = polar_to_cart(polar_data, 1, 500, x, y)
我希望这对和我有同样情况的人有所帮助。
【讨论】：
是否有任何 Python 包可以做到这一点？
是的！现在至少有一个 Python 包具有将矩阵从笛卡尔坐标重新映射到极坐标的功能：abel.tools.polar.reproject_image_into_polar()，它是PyAbel package 的一部分。
（Iñigo Hernáez Corres 是正确的，scipy.ndimage.interpolation.map_coordinates 是迄今为止我们发现的从笛卡尔坐标重新投影到极坐标的最快方法。）
可以从PyPi 安装 PyAbel，方法是在命令行输入以下内容：
pip install pyabel
然后，在python中，您可以使用以下代码将图像重新投影到极坐标中：
import abel
abel.tools.polar.reproject_image_into_polar(MyImage)
[根据应用程序，您可能会考虑传递 jacobian=True 参数，该参数会重新缩放矩阵的强度，以考虑在您从笛卡尔坐标转换为极坐标。]
这是一个完整的例子：
import numpy as np
import matplotlib.pyplot as plt
import abel
CartImage = abel.tools.analytical.sample_image(501)[201:-200, 201:-200]
PolarImage, r_grid, theta_grid = abel.tools.polar.reproject_image_into_polar(CartImage)
fig, axs = plt.subplots(1,2, figsize=(7,3.5))
axs[0].imshow(CartImage , aspect='auto', origin='lower')
axs[1].imshow(PolarImage, aspect='auto', origin='lower',
extent=(np.min(theta_grid), np.max(theta_grid), np.min(r_grid), np.max(r_grid)))
axs[0].set_title('Cartesian')
axs[0].set_xlabel('x')
axs[0].set_ylabel('y')
axs[1].set_title('Polar')
axs[1].set_xlabel('Theta')
axs[1].set_ylabel('r')
plt.tight_layout()
plt.show()
注意：SO 上有另一个很好的讨论（关于将彩色图像重新映射到极坐标）：image information along a polar coordinate system
【讨论】：
TypeError: 'numpy.float64' object cannot be interpreted as an integer 。如果你是代码的维护者，你应该检查一下。
abel.tools.analytical.SampleImage(501).image[200:-200, 200:-200]，然后将其插值到 100x100 网格（原为 101x101），然后进行转换。
OpenCV 3.4 现在可以通过 warpPolar() 轻松做到这一点
调用非常简单：
import numpy as np
import cv2
from matplotlib import pyplot as plt
# Read in our image from disk
image = cv2.imread('washington_quarter.png',0)
plt.imshow(image),plt.show()
margin = 0.9 # Cut off the outer 10% of the image
# Do the polar rotation along 1024 angular steps with a radius of 256 pixels.
polar_img = cv2.warpPolar(image, (256, 1024), (image.shape[0]/2,image.shape[1]/2), image.shape[1]*margin*0.5, cv2.WARP_POLAR_LINEAR)
# Rotate it sideways to be more visually pleasing
polar_img = cv2.rotate(polar_img, cv2.ROTATE_90_COUNTERCLOCKWISE)
plt.imshow(polar_img),plt.show()
【讨论】：