Iso Surface marching Cube using Python

 

import numpy as np

import matplotlib.pyplot as plt

from skimage import measure

n = 64

x, y, z = np.ogrid[-1:1:n*1j, -1:1:n*1j, -1:1:n*1j]

sphere = x**2 + y**2 + z**2

verts, faces, normals, values = measure.marching_cubes(sphere, level=0.5)

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

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

mesh = ax.plot_trisurf(

    verts[:, 0], verts[:, 1], faces, verts[:, 2],

    cmap='Spectral', lw=1, alpha=0.9

)

ax.set_title('Iso-Surface Plot (Marching Cubes)')

ax.set_xlabel('X axis')

ax.set_ylabel('Y axis')

ax.set_zlabel('Z axis')

plt.tight_layout()

plt.show()

#source code --> clcoding.com 

Code Explanation:

Libraries Imported

import numpy as np

import matplotlib.pyplot as plt

from skimage import measure

numpy → for numerical calculations and creating 3D grid.

 matplotlib.pyplot → for 3D plotting.

 measure from scikit-image → contains marching_cubes for surface extraction.

Step 1: Create a Scalar Field (3D Grid of Values)

n = 64

x, y, z = np.ogrid[-1:1:n*1j, -1:1:n*1j, -1:1:n*1j]

sphere = x**2 + y**2 + z**2

np.ogrid creates 3D grid coordinates with n = 64 steps in each dimension.

 sphere = x² + y² + z² defines a scalar field that increases with distance from the center.

This effectively creates a spherical shape within the volume.

 Step 2: Extract Iso-Surface Using Marching Cubes

verts, faces, normals, values = measure.marching_cubes(sphere, level=0.5)

marching_cubes() extracts the surface where the scalar field equals 0.5.

 Returns:

 verts: the coordinates of the vertices that form the mesh.

 faces: the triangles that connect those vertices.

 normals: surface normals for shading (not used here).

 values: scalar field values at the vertices (not used here).

 Step 3: Plot the Mesh in 3D

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

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

Sets up a 3D plot figure and axis.

 mesh = ax.plot_trisurf(

    verts[:, 0], verts[:, 1], faces, verts[:, 2],

    cmap='Spectral', lw=1, alpha=0.9

)

plot_trisurf() creates a triangular surface from the mesh.

 verts[:, 0], verts[:, 1], verts[:, 2] → the x, y, z coordinates of the vertices.

 faces → triangle indices.

 cmap='Spectral' → colorful colormap.

 alpha=0.9 → almost opaque surface.

 Step 4: Labeling and Display

 ax.set_title('Iso-Surface Plot (Marching Cubes)')

ax.set_xlabel('X axis')

ax.set_ylabel('Y axis')

ax.set_zlabel('Z axis')

plt.tight_layout()

plt.show()

Adds axis labels and a title.

 plt.tight_layout() adjusts padding.

 plt.show() renders the final 3D plot.