3D Parametric Shell Surface using Python

 

import numpy as np

import matplotlib.pyplot as plt

a = 1

b = 0.2

u = np.linspace(0, 2 * np.pi, 100)

v = np.linspace(0, 4 * np.pi, 100)

u, v = np.meshgrid(u, v)

X = a * (1 - v / (2 * np.pi)) * np.cos(v) * np.cos(u)

Y = a * (1 - v / (2 * np.pi)) * np.cos(v) * np.sin(u)

Z = a * (1 - v / (2 * np.pi)) * np.sin(v) + b * u

fig = plt.figure(figsize=(6, 6))

ax = fig.add_subplot(111, projection='3d')

ax.plot_surface(X, Y, Z, cmap='magma', edgecolor='k', alpha=0.9)

ax.set_title("3D Parametric Shell Surface")

ax.set_xlabel("X axis")

ax.set_ylabel("Y axis")

ax.set_zlabel("Z axis")

ax.set_box_aspect([1, 1, 1])

plt.tight_layout()

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Import Libraries

import numpy as np

import matplotlib.pyplot as plt

numpy: Used for numerical computations and creating arrays.

 matplotlib.pyplot: Used for plotting 2D and 3D visualizations.

 2. Define Constants for Shape Control

a = 1

b = 0.2

a: Controls the overall scale of the shell surface.

 b: Adds a vertical twist/extension as the surface rotates.

 3. Create Parameter Grids (u and v)

u = np.linspace(0, 2 * np.pi, 100)

v = np.linspace(0, 4 * np.pi, 100)

u, v = np.meshgrid(u, v)

u: Angle around the circular cross-section (like the shell's rim).

 v: Controls the spiral motion (shell’s growth).

 np.meshgrid: Creates a grid for evaluating parametric equations over 2D domains.

 4. Define Parametric Equations

X = a * (1 - v / (2 * np.pi)) * np.cos(v) * np.cos(u)

Y = a * (1 - v / (2 * np.pi)) * np.cos(v) * np.sin(u)

Z = a * (1 - v / (2 * np.pi)) * np.sin(v) + b * u

These equations generate a spiraling and shrinking shell surface:

 X and Y: Determine the radial coordinates; they shrink over v.

 Z: Adds a vertical twist via b * u, and height via sin(v).

 The structure gets smaller as v increases, mimicking how a shell tightens inward.

 5. Set Up 3D Plotting

fig = plt.figure(figsize=(10, 8))

ax = fig.add_subplot(111, projection='3d')

Initializes a 3D plot.

 figsize=(10, 8): Sets the size of the figure.

 6. Plot the Shell Surface

ax.plot_surface(X, Y, Z, cmap='magma', edgecolor='k', alpha=0.9)

plot_surface: Draws the parametric surface in 3D.

 cmap='magma': Uses a vibrant color map.

 edgecolor='k': Adds black edges for clarity.

 alpha=0.9: Slight transparency for smoother visuals.

  7. Customize Plot Appearance

ax.set_title("3D Parametric Shell Surface")

ax.set_xlabel("X axis")

ax.set_ylabel("Y axis")

ax.set_zlabel("Z axis")

ax.set_box_aspect([1, 1, 1])

Adds axis labels and title.

 8. Display the Plot

plt.tight_layout()

plt.show()

tight_layout(): Avoids label overlaps.

 show(): Renders the 3D plot.