Stellar Spectrum Mesh Grid Pattern using Python

 

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

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

z = np.linspace(-2, 2, 100)

theta, z = np.meshgrid(theta, z)

r = z**2 + 1

x = r * np.sin(theta)

y = r * np.cos(theta)

fig = plt.figure(figsize=(12, 8))

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

colors = np.sin(z) * np.cos(theta)

surf = ax.plot_surface(x,y,z,facecolors=plt.cm.viridis((colors - colors.min()) /

(colors.max() - colors.min())), rstride=1, cstride=1, antialiased=True)

ax.set_xlabel('X Axis')

ax.set_ylabel('Y Axis')

ax.set_zlabel('Z Axis')

ax.set_title('Stellar Spectrum Mesh: 3D Waveform using Matplotlib')

plt.colorbar(surf, shrink=0.5, aspect=5)

plt.show()

#source code --> clcoding.com

Code Explanation:

1. Importing Libraries

import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

numpy (np): Used for numerical operations, creating arrays, and mathematical functions.

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

 mpl_toolkits.mplot3d: Provides tools for 3D plotting using Matplotlib.

 Axes3D: Enables 3D plotting capabilities.

 

2. Create Data for the Mesh Grid

a) Generate Angles (Theta) and Z Values

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

z = np.linspace(-2, 2, 100)

np.linspace(start, stop, num):

 Generates 100 evenly spaced values.

 theta ranges from 0 to 2π, representing a full circular rotation in radians.

 z ranges from -2 to 2, representing the vertical axis.

 

b) Create a Mesh Grid

theta, z = np.meshgrid(theta, z)

np.meshgrid():

 Creates a 2D grid of coordinates from theta and z.

 Every combination of theta and z is represented in a matrix form.

 Used for surface plotting.

 

3. Calculate Radius and Coordinates

a) Calculate Radius (r)

r = z**2 + 1

r=z 2+1

 The radius expands as z moves away from zero.

This results in a wavy, expanding, circular mesh.

 

b) Compute X and Y Coordinates

x = r * np.sin(theta)

y = r * np.cos(theta)

X and Y Coordinates:

x = r × sin(θ) and y = r × cos(θ) are parametric equations for a circular shape.

The radius r scales the size of the circle, and theta controls the angular position.

The expanding radius forms a spiral effect.

 

4. Plot the 3D Surface

a) Initialize the Figure and Axis

fig = plt.figure(figsize=(12, 8))

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

fig = plt.figure(figsize=(12, 8)):

Creates a figure of size 12x8 inches.

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

Creates a 3D axis using projection='3d'.

111 indicates 1 row, 1 column, and first subplot.

 

5. Apply Colors Using a Spectrum

a)Generate Color Values

colors = np.sin(z) * np.cos(theta)

This applies a color effect using a mathematical combination of sine and cosine.

 np.sin(z) creates a wave pattern along the Z-axis.

 np.cos(theta) creates variations based on angular position.

 Multiplying them results in a dynamic, swirling color effect.

 b) Plot the Surface with Colors

surf = ax.plot_surface(

    x, y, z,

    facecolors=plt.cm.viridis((colors - colors.min()) / (colors.max() - colors.min())),

    rstride=1,

    cstride=1,

    antialiased=True

)

ax.plot_surface():

 Plots a 3D surface using the computed X, Y, and Z coordinates.

 facecolors applies a gradient from the Viridis colormap (plt.cm.viridis).

 This ensures color values are scaled between 0 and 1.

 rstride=1 and cstride=1 determine the resolution of the mesh by setting row and column strides.

 antialiased=True smoothens the surface edges.

 

6. Customize the Plot

a) Add Axis Labels and Title

ax.set_xlabel('X Axis')

ax.set_ylabel('Y Axis')

ax.set_zlabel('Z Axis')

ax.set_title('Stellar Spectrum Mesh: 3D Waveform using Matplotlib')

Labels the axes for clarity.

 The title provides a meaningful description of the plot.

 b) Add a Colorbar

plt.colorbar(surf, shrink=0.5, aspect=5)

plt.colorbar():

 Adds a colorbar to represent the color mapping on the surface.

 shrink=0.5: Adjusts the colorbar size to 50% of its original size.

 aspect=5: Adjusts the aspect ratio of the colorbar for better readability.

 

7. Display the Plot

plt.show()

This function renders and displays the plot.