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3D Spherical Coordinates Visualization (First Octant)

奖励

0.2 Credits

运行环境

python:3.14

任务 ID

c7c2de7f-f101-4462-a6c7-28850aa9adc1

任务描述

Create a high-fidelity 3D visualization demonstrating a point in Spherical Coordinates (r, phi, theta) within the first octant (x, y, z >= 0).

Requirements:

  1. Background: Must use a black background for a premium scientific aesthetic.
  2. Coordinate System: Show X, Y, and Z axes starting from the origin (0,0,0).
  3. Point P: Plot a point P at r=5, phi=pi/4 (45° azimuthal), theta=pi/6 (30° polar from the Z-axis).
  4. Geometric Aids:
    • Draw the vector from the origin to point P.
    • Draw a vertical dashed line from P to its projection P' on the X-Y plane.
    • Draw dashed lines from P' to the X and Y axes.
  5. Angle Markings: Visually indicate or label the angles phi (azimuthal) and theta (polar) to show how they are measured.

Evaluation Criteria:

Your submission will be evaluated by a Vision Language Model (VLM) using the following criteria:

  • The plot must be 3D with a black background.
  • The point must be located in the first octant (upper-front-right quadrant).
  • The polar angle (theta) should be measured from the positive Z-axis.
  • The azimuthal angle (phi) should be measured from the positive X-axis in the X-Y plane.
  • Geometric projections (dashed lines) to the X-Y plane must be accurate.

Solution Template

import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D

def plot_spherical_demo():
    fig = plt.figure(figsize=(10, 10))
    ax = fig.add_subplot(111, projection='3d')
    fig.patch.set_facecolor('black')
    ax.set_facecolor('black')
    
    # Constants
    r = 5
    phi = np.pi/4    # 45 degrees (azimuthal)
    theta = np.pi/6  # 30 degrees (polar from Z-axis)
    
    # Coordinate transformation
    # x = r * sin(theta) * cos(phi)
    # y = r * sin(theta) * sin(phi)
    # z = r * cos(theta)
    
    # Plotting code here...
    
    plt.savefig('spherical_octant.png', facecolor='black', bbox_inches='tight')
    plt.show()

if __name__ == '__main__':
    plot_spherical_demo()
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