如何用Matplotlib在等高线图（热力图）上绘制指定半径的圆形

Got it, let's tackle this visualization problem step by step. You want to turn your ultrasonic sensor's radius measurements into a heatmap where regions matching those radii are brighter, right? This will make it super easy to spot all possible object positions in the sensor's field of view.

Here's a complete, customizable solution using Matplotlib and Numpy:

import numpy as np
import matplotlib.pyplot as plt

# Replace this with your actual measured radii array
measured_radii = [0, 3.4, 5.1, 7.2, 9.0]

# 1. Create a coordinate grid covering the sensor's full field of view
max_radius = max(measured_radii) + 1  # Add a small buffer to avoid cutting off outer circles
x = np.linspace(-max_radius, max_radius, 500)  # 500 points for smooth resolution
y = np.linspace(-max_radius, max_radius, 500)
X, Y = np.meshgrid(x, y)

# 2. Calculate distance from the sensor (origin) for every grid point
distance_from_sensor = np.sqrt(X**2 + Y**2)

# 3. Build the intensity heatmap
intensity = np.zeros_like(distance_from_sensor)
sigma = 0.1  # Controls ring sharpness: smaller = sharper, larger = softer (adjust for your sensor's precision)

for radius in measured_radii:
    # Use a Gaussian kernel to create a bright, smooth ring around each measured radius
    intensity += np.exp(-((distance_from_sensor - radius)**2) / (2 * sigma**2))

# 4. Plot the heatmap
plt.figure(figsize=(8, 8))
heatmap = plt.imshow(
    intensity,
    extent=[-max_radius, max_radius, -max_radius, max_radius],
    cmap='viridis',  # Swap with 'plasma'/'inferno' for different color schemes
    origin='lower'
)
plt.colorbar(heatmap, label='Detection Intensity')

# 5. Overlay dashed circles for each measured radius
for radius in measured_radii:
    circle = plt.Circle((0, 0), radius, color='white', linestyle='--', linewidth=1.5, fill=False)
    plt.gca().add_artist(circle)
    # Optional: Add text labels for each radius
    plt.text(radius, 0, f'r={radius}', color='white', fontsize=10, ha='left', va='center')

# 6. Polish the plot
plt.xlabel('X Position (match your radius units: cm/m/etc.)')
plt.ylabel('Y Position (match your radius units: cm/m/etc.)')
plt.title('Ultrasonic Sensor Object Positions Heatmap')
plt.axis('equal')  # Critical to keep circles round (not elliptical)
plt.show()

Key Details & Customization Tips: #

• Grid Resolution: The 500 in linspace controls how smooth your heatmap is. Higher numbers = smoother, but slower to render.
• Sigma Adjustment: If your sensor has noisy measurements, increase sigma (e.g., to 0.2 or 0.3) to widen the bright rings. For precise readings, keep it small.
• Colormaps: Swap viridis with other Matplotlib colormaps like plasma, inferno, or magma to match your preference.
• Duplicate Radii: If you have repeated radius values, the intensity will stack automatically—making those regions even brighter, which is great for highlighting frequent detections.
• Units: Don't forget to update the axis labels to match your radius units (centimeters, meters, etc.).

内容的提问来源于stack exchange，提问作者Martin1