3D Rose Surface Plot using Python

 

import numpy as np

import matplotlib.pyplot as plt

k=8

theta=np.linspace(0,2*np.pi,300)

phi=np.linspace(0,np.pi,300)

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

r = np.sin(k * theta) * np.sin(phi)

x = r * np.sin(phi) * np.cos(theta)

y = r * np.sin(phi) * np.sin(theta)

z = r * np.cos(phi)

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

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

surf=ax.plot_surface(x,y,z,cmap='inferno',edgecolor='none')

ax.set_title('3D Rose Surface Plot')

ax.axis('off')

plt.show()

#source code --> clcoding.com 

Code Explanation:

1. Import Libraries

import numpy as np

import matplotlib.pyplot as plt

numpy: For numerical calculations and creating coordinate grids.

 matplotlib.pyplot: For plotting the 3D surface.

 2. Set the Parameter

k = 5  # Number of petals (can be any float or integer)

The variable k controls the number of "petals" in the rose pattern.

 A higher or fractional k gives more complex shapes.

 3. Create Meshgrid for Angles

theta = np.linspace(0, 2 * np.pi, 300)  # Azimuthal angle

phi = np.linspace(0, np.pi, 300)        # Polar angle

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

theta: Goes from 0 to

2π, wrapping around the z-axis (like longitude).

phi: Goes from 0 to

π, spanning from top to bottom of the sphere (like latitude).

np.meshgrid creates a grid of angle values used for surface plotting.

 4. Define the Rose Function

r = np.sin(k * theta) * np.sin(phi)

This defines the radius r at each angle based on the polar rose formula:

 r(θ,ϕ)=sin(kθ)⋅sin(ϕ)

sin(kθ) makes the petal pattern.

 sin(φ) ensures the pattern wraps over the sphere rather than staying flat.

 5. Convert to 3D Cartesian Coordinates

 x = r * np.sin(phi) * np.cos(theta)

y = r * np.sin(phi) * np.sin(theta)

z = r * np.cos(phi)

This converts spherical coordinates

(r,θ,ϕ) to Cartesian coordinates (x,y,z):

 x=r⋅sin(ϕ)⋅cos(θ)

y=r⋅sin(ϕ)⋅sin(θ)

z=r⋅cos(ϕ)

 This gives a 3D shape based on the rose function wrapped over a sphere.

 6. Plot the Surface

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

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

surf = ax.plot_surface(x, y, z, cmap='inferno', edgecolor='none')

Creates a 3D plot (projection='3d').

 plot_surface() draws the rose surface using x, y, z.

 cmap='inferno' adds color based on height/intensity.

 edgecolor='none' smooths the surface by hiding grid lines.

 7. Final Touches

ax.set_title(f"3D Rose Surface Plot (k = {k})")

ax.axis('off')

plt.show()

Adds a title showing the value of k.

 Turns off axis for a clean visual.