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.

Practice

1. What does a 3D surface plot in matplotlib primarily show?

easy

A. The relationship between two input variables and one output variable as a curved surface

B. A simple 2D line graph of data points

C. Only the distribution of a single variable

D. A bar chart comparing categories

Solution

1. Step 1: Understand the purpose of 3D surface plots

   3D surface plots visualize how two inputs relate to an output by showing a curved surface in three dimensions.

2. Step 2: Compare with other plot types

   Unlike 2D line graphs or bar charts, 3D surface plots show a continuous surface representing output values over a grid of inputs.

3. Final Answer:

   The relationship between two input variables and one output variable as a curved surface -> Option A

4. Quick Check:

   3D surface plot = curved surface of inputs and output [OK]

Hint: 3D surface plots show two inputs and one output as a surface [OK]

Common Mistakes:

• Confusing 3D surface plots with 2D line plots
• Thinking it shows only one variable distribution
• Mixing up bar charts with surface plots

2. Which of the following is the correct way to import the 3D plotting toolkit in matplotlib?

easy

A. import matplotlib.pyplot as plt3d

B. from matplotlib import surface3d

C. from mpl_toolkits.mplot3d import Axes3D

D. import mpl3d as m3d

Solution

1. Step 1: Recall the standard import for 3D plotting

   Matplotlib uses mpl_toolkits.mplot3d to enable 3D plotting, and the correct import is from mpl_toolkits.mplot3d import Axes3D.

2. Step 2: Check other options for correctness

   Options A, C, and D are not valid matplotlib import statements for 3D plotting.

3. Final Answer:

   from mpl_toolkits.mplot3d import Axes3D -> Option C

4. Quick Check:

   3D import = mpl_toolkits.mplot3d Axes3D [OK]

Hint: Use mpl_toolkits.mplot3d import Axes3D for 3D plots [OK]

Common Mistakes:

• Trying to import non-existent modules
• Using wrong aliases like plt3d
• Assuming 3D is included by default in pyplot

3. What will the following code output?

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

x = np.linspace(-5, 5, 10)
y = np.linspace(-5, 5, 10)
X, Y = np.meshgrid(x, y)
Z = X**2 + Y**2

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

medium

A. A 3D surface plot showing a bowl-shaped paraboloid

B. A flat 2D plot with points scattered

C. A syntax error due to missing import

D. A 3D scatter plot of random points

Solution

1. Step 1: Analyze the function Z = X^2 + Y^2

   This function creates a paraboloid shape, which looks like a bowl opening upwards.

2. Step 2: Understand the plot_surface call

   plot_surface plots the Z values over the grid defined by X and Y, producing a smooth 3D surface.

3. Final Answer:

   A 3D surface plot showing a bowl-shaped paraboloid -> Option A

4. Quick Check:

   plot_surface with X^2+Y^2 = bowl shape [OK]

Hint: Z = X² + Y² forms a bowl shape in 3D surface plots [OK]

Common Mistakes:

• Confusing surface plot with scatter plot
• Expecting 2D plot instead of 3D
• Missing meshgrid usage for X, Y

4. Identify the error in this code snippet for creating a 3D surface plot:

import numpy as np
import matplotlib.pyplot as plt

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))

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

medium

A. Z calculation is incorrect

B. Missing projection='3d' in add_subplot

C. meshgrid is not needed for surface plots

D. plt.show() is missing

Solution

1. Step 1: Check subplot creation for 3D plotting

   To plot 3D surfaces, the subplot must have projection='3d'. The code misses this, so ax is 2D.

2. Step 2: Verify other parts

   Z calculation and meshgrid usage are correct. plt.show() is present.

3. Final Answer:

   Missing projection='3d' in add_subplot -> Option B

4. Quick Check:

   3D plot needs projection='3d' [OK]

Hint: Always add projection='3d' for 3D subplots [OK]

Common Mistakes:

• Forgetting projection='3d' in add_subplot
• Misusing meshgrid or Z calculation
• Omitting plt.show()

5. You want to visualize the function Z = sin(X) * cos(Y) over the range -π to π for both X and Y with a smooth surface and a color map that highlights height differences. Which of the following code snippets correctly achieves this?

hard

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

x = np.linspace(-np.pi, np.pi, 100)
y = np.linspace(-np.pi, np.pi, 100)
X, Y = np.meshgrid(x, y)
Z = np.sin(X) * np.cos(Y)

fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot_surface(X, Y, Z, cmap='coolwarm')
plt.show()

B. import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-np.pi, np.pi, 100)
y = np.linspace(-np.pi, np.pi, 100)
X, Y = np.meshgrid(x, y)
Z = np.sin(X) * np.cos(Y)

plt.plot_surface(X, Y, Z, cmap='plasma')
plt.show()

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

x = np.linspace(-np.pi, np.pi, 50)
y = np.linspace(-np.pi, np.pi, 50)
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)
plt.show()

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

x = np.linspace(-np.pi, np.pi, 100)
y = np.linspace(-np.pi, np.pi, 100)
X, Y = np.meshgrid(x, y)
Z = np.sin(X) * np.cos(Y)

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

Solution

1. Step 1: Check function and range correctness

   The correct code uses Z = np.sin(X) * np.cos(Y) over -np.pi to np.pi with 100 points for smoothness.

2. Step 2: Verify 3D plotting and color map usage

   The correct code uses projection='3d', plot_surface with cmap='viridis', and adds a colorbar to highlight height differences.

3. Step 3: Identify errors in other options

   import numpy as np import matplotlib.pyplot as plt x = np.linspace(-np.pi, np.pi, 100) y = np.linspace(-np.pi, np.pi, 100) X, Y = np.meshgrid(x, y) Z = np.sin(X) * np.cos(Y) plt.plot_surface(X, Y, Z, cmap='plasma') plt.show() misses 3D axis creation; import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D x = np.linspace(-np.pi, np.pi, 50) y = np.linspace(-np.pi, np.pi, 50) 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) plt.show() uses wrong function Z and fewer points; import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D x = np.linspace(-np.pi, np.pi, 100) y = np.linspace(-np.pi, np.pi, 100) X, Y = np.meshgrid(x, y) Z = np.sin(X) * np.cos(Y) fig = plt.figure() ax = fig.add_subplot(111) ax.plot_surface(X, Y, Z, cmap='coolwarm') plt.show() misses projection='3d' in subplot.

4. Final Answer:

   The code with projection='3d', cmap='viridis', colorbar, correct Z, and 100 points -> Option D

5. Quick Check:

   projection='3d' + cmap='viridis' + colorbar + Z=sin(X)*cos(Y) + 100 pts [OK]

Hint: Use projection='3d', meshgrid, and cmap for smooth colored surfaces [OK]

Common Mistakes:

• Forgetting projection='3d' in subplot
• Using wrong function for Z
• Not adding color map or colorbar
• Calling plot_surface without axis object