极坐标下fill_between绘图畸变及变宽螺旋异常点的排查与解决

Hey there! Let's tackle those weird artifacts in your spiral plot and solve the polar coordinate fill_between distortion together.

1. The Random "Spots" on Your Spiral Edges #

What's Causing Them #

The odd points you're seeing (marked by red arrows) come from how you're generating your r_bot and r_top values:

• You're using np.random.uniform(0.1, 0.5, len(r)) to create independent random offsets for every single angle t. This means adjacent points can have huge jumps in radius (e.g., one point has a +0.5 offset, the next has +0.1).
• When fill_between connects these disjointed radius points in polar coordinates, the sudden jumps create sharp, unnatural kinks or "spots" in the otherwise smooth spiral edges.

How to Fix It #

Instead of independent random values, generate smoothly varying random offsets so the radius changes gradually between adjacent angles. Here are two easy ways:

Option 1: Random Walk (Smooth Random Fluctuations)

Create offsets that build on the previous value to avoid sudden jumps:

# Generate small random steps, then accumulate them for smooth variation
step_size = 0.05
offset_top = np.cumsum(np.random.uniform(-step_size, step_size, len(r)))
# Normalize to keep offsets within your original 0.1-0.5 range
offset_top = 0.1 + (0.4 * (offset_top - offset_top.min()) / (offset_top.max() - offset_top.min()))
offset_bot = np.cumsum(np.random.uniform(-step_size, step_size, len(r)))
offset_bot = 0.1 + (0.4 * (offset_bot - offset_bot.min()) / (offset_bot.max() - offset_bot.min()))

r_bot = r - offset_bot
r_top = r + offset_top

Option 2: Gaussian Smoothing

Take your original random offsets and apply a Gaussian filter to smooth out sharp jumps:

from scipy.ndimage import gaussian_filter

# Generate original random offsets
raw_offset_top = np.random.uniform(0.1, 0.5, len(r))
# Smooth with a Gaussian kernel (adjust sigma for more/less smoothness)
offset_top = gaussian_filter(raw_offset_top, sigma=5)
raw_offset_bot = np.random.uniform(0.1, 0.5, len(r))
offset_bot = gaussian_filter(raw_offset_bot, sigma=5)

r_bot = r - offset_bot
r_top = r + offset_top

2. Distortion in Polar Coordinate fill_between #

What's Causing It #

The distortion happens because of how Matplotlib handles fill_between in polar coordinates:

• Matplotlib converts polar coordinates (t, r) to Cartesian (x, y) under the hood before drawing the filled area.
• If your angle step (0.1 in your code) is too large, or if radius changes are abrupt, the converted Cartesian points can form self-intersecting polygons or misaligned edges. This leads to weird "folded" or distorted regions in the filled spiral.

How to Fix It #

You can address this with two key adjustments:

1. Reduce the angle step size: A smaller step (e.g., 0.01 instead of 0.1) gives more dense sampling, making the Cartesian conversion smoother and avoiding misaligned edges.
2. Use smooth radius offsets: As we fixed in the first issue, smooth radius changes prevent sudden jumps that cause distortion.

Full Modified Code #

Here's the complete code that fixes both issues:

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from scipy.ndimage import gaussian_filter

mpl.use('Agg')
plt.ioff()
MY_DPI = 300
BKGD_COLOUR = 'w'
FILL_COLOUR= 'k'
a = 0
b = 0.5
maxRadius = 100
maxTheta = (maxRadius - a) / b

# Smaller step size for smoother sampling
t = np.arange(0, maxTheta, 0.01)
r = a + b * t

fig = plt.figure(figsize=(10,10), dpi=MY_DPI)
ax = fig.add_axes([0,0,1,1], polar=True)
ax.set_rlim(0, maxRadius)
ax.axis('off')

# Generate smooth random offsets using Gaussian filtering
raw_offset_top = np.random.uniform(0.1, 0.5, len(r))
offset_top = gaussian_filter(raw_offset_top, sigma=5)
raw_offset_bot = np.random.uniform(0.1, 0.5, len(r))
offset_bot = gaussian_filter(raw_offset_bot, sigma=5)

r_bot = r - offset_bot
r_top = r + offset_top

# Fill between with smooth edges
ax.fill_between(t, r_bot, r_top, color=FILL_COLOUR, lw=0)

plt.savefig('spiraliser.jpg', facecolor=BKGD_COLOUR, bbox_inches='tight', dpi=MY_DPI)
plt.close()

Quick Notes #

• Adjust the sigma value in gaussian_filter to control how smooth your spiral edges are (higher = smoother, lower = more variation but still no sharp jumps).
• If you don't want to use scipy, the random walk method works great without extra dependencies.

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