Python / SciPy：将DataFrame从极性网格转换为笛卡尔网格的问题

Question

I have measurements (PPI arc scans) taken with a doppler wind lidar. The data is stored in a pandas dataframe where rows represent azimuth angle and columns represent radial distance (input shape = 30x197). Link to example scan, (csv) . I want to transform this to a cartesian coordinate system, and output a 2d array which is re-gridded into x,y coordinates instead of polar with the values stored in the appropriate grid cell. Interpolation (nearest neighbor) is ok and so is zero or NaN padding of areas where no data exists.

Ideally the X and Y grid should correspond to the actual distances between points, but right now I'm just trying to get this working. This shouldn't be terribly difficult, but I'm having trouble obtaining the result I want. So far, I have working code which plots on a polar axis beautifully (example image) but this won't work for the next steps of my analysis.

I have tried many different approaches with scipy.interpolate.griddata , scipy.ndimage.geometric_transform , and scipy.ndimage.map_coordinates but haven't gotten the correct output. Here is an example of my recent attempt (df_polar is the csv file linked):

# Generate polar and cartesian meshgrids
r = df_polar.columns
theta = df_polar.index
theta = np.deg2rad(theta)

# Polar meshgrid
rad_c, theta_c = np.meshgrid(r,theta)

# Cartesian meshgrid
X = rad_c * np.cos(theta_c)
Y = rad_c * np.sin(theta_c)
x,y = np.meshgrid(X,Y)

# Interpolate from polar to cartesian grid
new_grid = scipy.interpolate.griddata(
    (rad_c.flatten(), theta_c.flatten()), 
    np.array(df_polar).flatten(), (x,y), method='nearest')

The result is not correct at all, and from reading the documentation and examples I don't understand why. I would greatly appreciate any tips on where I have gone wrong. Thanks a lot!!

Answer 1

I think you might be feeding griddata the wrong points. It wants cartesian points and if you want the values interpolated over a regular x/y grid you need to create one and provide that too.

Try this and let me know if it produces the expected result. It's hard for me to tell if this is what it should produce:

from scipy.interpolate import griddata
import pandas as pd
import numpy as np

df_polar = pd.read_csv('onescan.txt', index_col=0)

# Generate polar and cartesian meshgrids
r = pd.to_numeric(df_polar.columns)
theta = np.deg2rad(df_polar.index)

# Polar meshgrid
rad_c, theta_c = np.meshgrid(r, theta)

# Cartesian equivalents of polar co-ordinates
X = rad_c*np.cos(theta_c)
Y = rad_c*np.sin(theta_c)

# Cartesian (x/y) meshgrid
grid_spacing = 100.0   # You can change this
nx = (X.max() - X.min())/grid_spacing
ny = (Y.max() - Y.min())/grid_spacing
x = np.arange(X.min(), X.max() + grid_spacing, grid_spacing)
y = np.arange(Y.min(), Y.max() + grid_spacing, grid_spacing)
grid_x, grid_y = np.meshgrid(x, y)

# Interpolate from polar to cartesian grid
new_grid = griddata(
    (X.flatten(), Y.flatten()),
    df_polar.values.flatten(),
    (grid_x, grid_y),
    method='nearest'
)

The resulting values look something like this (with grid_spacing = 10 and flipping x and y):

import matplotlib.pyplot as plt
plt.imshow(new_grid.T, cmap='hot')

Clearly interpolate "nearest" needs taming...