3D Checkboard Surface Pattern using python

 

import numpy as np

import matplotlib.pyplot as plt

x = np.linspace(-5, 5, 100)

y = np.linspace(-5, 5, 100)

x, y = np.meshgrid(x, y)

z = np.sin(x) * np.cos(y)  

checkerboard = ((np.floor(x) + np.floor(y)) % 2) == 0

colors = np.zeros(x.shape + (3,))

colors[checkerboard] = [1, 1, 1] 

colors[~checkerboard] = [0, 0, 0]  

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

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

ax.plot_surface(x, y, z, facecolors=colors, rstride=1, cstride=1)

ax.set_title("3D Checkerboard Surface", fontsize=14)

ax.set_box_aspect([1, 1, 0.5])  

ax.axis('off')  

plt.tight_layout()

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Import Libraries

import numpy as np

import matplotlib.pyplot as plt

numpy (as np): Used for creating grids and performing numerical calculations (like sin, cos, floor, etc.).

matplotlib.pyplot (as plt): Used for plotting graphs and rendering the 3D surface.

 

2. Create Grid Coordinates (x, y)

x = np.linspace(-5, 5, 100)

y = np.linspace(-5, 5, 100)

x, y = np.meshgrid(x, y)

np.linspace(-5, 5, 100): Generates 100 evenly spaced values from -5 to 5 for both x and y.

np.meshgrid(x, y): Creates 2D grids from the 1D x and y arrays — necessary for plotting surfaces.

 

3. Define Surface Height (z values)

z = np.sin(x) * np.cos(y)

This creates a wavy surface using a trigonometric function.

Each (x, y) point gets a z value, forming a 3D landscape.

 

4. Generate Checkerboard Pattern

checkerboard = ((np.floor(x) + np.floor(y)) % 2) == 0

np.floor(x): Takes the floor (integer part) of each x and y coordinate.

Adds the floored x + y, and checks if the sum is even (i.e., divisible by 2).

If so → True (white square), else → False (black square).

This results in a checkerboard-like boolean mask.

 

5. Assign Colors to Checkerboard

colors = np.zeros(x.shape + (3,))

colors[checkerboard] = [1, 1, 1]

colors[~checkerboard] = [0, 0, 0]

colors = np.zeros(x.shape + (3,)): Initializes an array for RGB colors (shape: rows × cols × 3).

For True cells in checkerboard, assign white [1, 1, 1].

For False cells, assign black [0, 0, 0].

 

6. Set Up 3D Plot

fig = plt.figure(figsize=(8, 6))

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

Creates a figure and a 3D subplot using projection='3d'.

 

7. Plot the Checkerboard Surface

ax.plot_surface(x, y, z, facecolors=colors, rstride=1, cstride=1)

Plots the 3D surface using x, y, z data.

facecolors=colors: Applies the checkerboard color pattern.

rstride and cstride: Row/column steps for rendering — set to 1 for full resolution.

 

8. Customize the View

ax.set_title("3D Checkerboard Surface", fontsize=14)

ax.set_box_aspect([1, 1, 0.5])

ax.axis('off')

set_title(): Sets the plot title.

set_box_aspect(): Controls aspect ratio: x:y:z = 1:1:0.5 (compressed z).

axis('off'): Hides axis ticks and labels for a clean look.

 

9. Render the Plot

plt.tight_layout()

plt.show()

tight_layout(): Adjusts spacing to prevent overlap.

show(): Renders the 3D checkerboard surface.