3D surface plots in Matplotlib - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of a simple 3D surface plot code

What will be the shape of the Z array used in this 3D surface plot code?

Matplotlib

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

x = np.linspace(-5, 5, 50)
y = np.linspace(-5, 5, 50)
X, Y = np.meshgrid(x, y)
Z = np.sin(np.sqrt(X**2 + Y**2))

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z)
plt.show()

A (50, 50)

B (50,)

C (100, 100)

D (25, 25)

💡 Hint

Remember how meshgrid works with two 1D arrays of length 50.

The meshgrid creates two 2D arrays X and Y of shape (50, 50). The function applied element-wise produces Z of the same shape.

❓ data_output

intermediate

Number of faces in a 3D surface plot

Given the following code, how many quadrilateral faces will the 3D surface plot have?

Matplotlib

import numpy as np
x = np.linspace(0, 1, 20)
y = np.linspace(0, 1, 30)
X, Y = np.meshgrid(x, y)
Z = X * Y

A 552

B 551

C 570

D 550

💡 Hint

Number of faces = (rows - 1) * (columns - 1)

X and Y have shape (30, 20). Number of faces = (30-1)*(20-1) = 29*19 = 551.

❓ visualization

advanced

Effect of stride parameters on 3D surface plot

Which option shows the correct effect of setting rstride=5 and cstride=5 in ax.plot_surface(X, Y, Z, rstride=5, cstride=5)?

Matplotlib

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

x = np.linspace(-3, 3, 60)
y = np.linspace(-3, 3, 60)
X, Y = np.meshgrid(x, y)
Z = np.exp(-0.1*(X**2 + Y**2))

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, rstride=5, cstride=5)
plt.show()

A The surface mesh is colored randomly due to stride parameters.

B The surface mesh is finer with more grid lines, showing a smooth appearance.

C The surface mesh is invisible because stride values are too large.

D The surface mesh is coarser with fewer grid lines, showing a blocky appearance.

💡 Hint

Stride controls the step size for sampling the grid points.

Higher stride values skip points, resulting in fewer grid lines and a blockier mesh.

🔧 Debug

advanced

Identify the error in 3D surface plot code

What error will this code raise when executed?

Matplotlib

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

x = np.linspace(-2, 2, 40)
y = np.linspace(-2, 2, 40)
X, Y = np.meshgrid(x, y)
Z = np.sin(X) + np.cos(Y)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, cmap='nonexistent_cmap')
plt.show()

A ValueError: 'nonexistent_cmap' is not a valid colormap name

B TypeError: plot_surface() got an unexpected keyword argument 'cmap'

C AttributeError: 'Axes3D' object has no attribute 'plot_surface'

D No error, plot displays normally

💡 Hint

Check if the colormap name is valid in matplotlib.

Using an invalid colormap name causes a ValueError when plot_surface tries to apply it.

🚀 Application

expert

Interpreting 3D surface plot data output

Given the code below, what is the maximum Z value computed?

Matplotlib

import numpy as np
x = np.linspace(-1, 1, 100)
y = np.linspace(-1, 1, 100)
X, Y = np.meshgrid(x, y)
Z = np.exp(-(X**2 + Y**2)) * np.cos(5 * (X**2 + Y**2))

A 1.0

B 0.0

C Approximately 0.98

D -1.0

💡 Hint

Consider the function behavior at the origin (0,0).

At (0,0), Z = exp(0)*cos(0) = 1*1 = 1, but due to discretization and floating point, max is slightly less than 1.