如何在Matplotlib中计算极坐标图密度并实现按密度着色散点图？

Hey there! Let's break down what's going wrong with your polar scatter plot and how to fix it to get that crisp, density-colored visualization you're aiming for.

Why sorting leads to unexpected results (Figure 2) #

The core issue in your code is a mismatch between the coordinates you're plotting and the density values you're using for coloring. Let's walk through your code step-by-step:

1. You calculate the density values z correctly using gaussian_kde.
2. You sort the indices by density and create sorted versions of your x (saccade_orientation_PP), y (saccade_amplitude_PP), and z values.
3. But then you plot the original unsorted coordinates, paired with the sorted z values!

This means each original point is getting assigned a density value that belongs to a completely different point, leading to the scrambled, incorrect look in Figure 2. The sorting step itself is a good idea (we want densest points plotted last so they're on top), but you just didn't use the sorted coordinates in your scatter plot.

Fixed code for the desired density-colored plot #

Here's the corrected version of your code, with the key fix highlighted:

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import gaussian_kde

# Calculate the point density: Saccade Orientation is an angle, Amplitude is the radial value
xy = np.vstack([saccade_orientation_PP, saccade_amplitude_PP])
z = gaussian_kde(xy)(xy)

# Sort the points by density, so that the densest points are plotted last
idx = z.argsort()
x_sorted, y_sorted, z_sorted = np.array(saccade_orientation_PP)[idx], np.array(saccade_amplitude_PP)[idx], z[idx]

ax1 = plt.subplot(121, polar=True)
# Use the SORTED coordinates and matching sorted density values here
ax1.scatter(x_sorted, y_sorted, c=z_sorted, edgecolor='', alpha=0.75)

# Optional: Add a colorbar to show density scale
plt.colorbar(label='Point Density')
plt.show()

What this fixes: #

• Now each point's color corresponds to its own calculated density value, eliminating mismatches.
• By plotting the least dense points first and densest points last, dense clusters will be visible on top of sparser points, making your Figure 1-style data much clearer.

Extra tips for better polar density visualization #

• Use a perceptually uniform colormap like cmap='viridis' (add it to the scatter call) to make density differences easier to interpret.
• Adjust the alpha value if you have a lot of points: lower values (like 0.5) let overlapping points blend naturally while still showing density.
• If your angle data wraps around (0 to 2π), ensure gaussian_kde accounts for circularity if needed—though for most visualization cases, the standard implementation works well.

内容的提问来源于stack exchange，提问作者bigPoppa350