Plot Matplotlib 3D plot_surface with contour plot projection

To create a 3D surface plot with contour projections in Matplotlib, we combine plot_surface() for the main surface and contourf() for projecting contours onto the coordinate planes.

Understanding the Components

A surface plot with contour projections consists of:

• A 3D surface using plot_surface()

• Contour projections on the XY, XZ, and YZ planes using contourf()

• The zdir parameter controls which plane the contour is projected onto

Basic Example

Here's how to create a surface plot with contour projections ?

import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# Set figure size
plt.rcParams["figure.figsize"] = [10, 8]
plt.rcParams["figure.autolayout"] = True

# Create data points
x = np.arange(-5, 5, 0.1)
y = np.arange(-5, 5, 0.1)
X, Y = np.meshgrid(x, y)
Z = X * np.exp(-X**2 - Y**2)

# Create 3D plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# Create surface plot
surf = ax.plot_surface(X, Y, Z, rstride=8, cstride=8, alpha=0.8, cmap="viridis")

# Add contour projections
ax.contourf(X, Y, Z, zdir='z', offset=np.min(Z), cmap="plasma", alpha=0.6)
ax.contourf(X, Y, Z, zdir='x', offset=-5, cmap="coolwarm", alpha=0.6)
ax.contourf(X, Y, Z, zdir='y', offset=5, cmap="spring", alpha=0.6)

# Set labels
ax.set_xlabel('X axis')
ax.set_ylabel('Y axis')
ax.set_zlabel('Z axis')
ax.set_title('3D Surface with Contour Projections')

plt.show()

Understanding the Parameters

Advanced Example with Customization

Create a more complex surface with better styling ?

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# Create data
x = np.linspace(-3, 3, 50)
y = np.linspace(-3, 3, 50)
X, Y = np.meshgrid(x, y)
Z = np.sin(np.sqrt(X**2 + Y**2))

# Create figure and axis
fig = plt.figure(figsize=(12, 8))
ax = fig.add_subplot(111, projection='3d')

# Main surface plot
surface = ax.plot_surface(X, Y, Z, 
                         rstride=2, cstride=2,
                         alpha=0.7, 
                         cmap='jet',
                         linewidth=0,
                         antialiased=True)

# Contour projections
contour_z = ax.contourf(X, Y, Z, zdir='z', offset=-1.2, 
                       cmap='Reds', alpha=0.5, levels=10)
contour_x = ax.contourf(X, Y, Z, zdir='x', offset=-3, 
                       cmap='Blues', alpha=0.5, levels=10)
contour_y = ax.contourf(X, Y, Z, zdir='y', offset=3, 
                       cmap='Greens', alpha=0.5, levels=10)

# Customize the plot
ax.set_xlim(-3, 3)
ax.set_ylim(-3, 3)
ax.set_zlim(-1.2, 1.2)

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('Sine Wave Surface with Contour Projections')

# Add colorbar
plt.colorbar(surface, ax=ax, shrink=0.5)

plt.show()

Key Points

• Use meshgrid() to create coordinate arrays for 3D plotting

• The offset parameter positions the contour projection

• Different colormaps help distinguish between projections

• Alpha transparency prevents projections from hiding the main surface

• Use rstride and cstride to control surface resolution

Conclusion

Combining plot_surface() with contourf() projections creates informative 3D visualizations. Use different colormaps and transparency to clearly distinguish between the surface and its projections on coordinate planes.