3D surface plots in Matplotlib - Mini Project: Build & Apply

3D Surface Plots with Matplotlib

📖 Scenario: You are a data scientist exploring how to visualize three-dimensional data. Imagine you want to show how temperature changes over a flat area depending on two directions: east-west and north-south.

🎯 Goal: You will create a 3D surface plot using matplotlib to visualize a mathematical function that depends on two variables. This will help you understand how to make and display 3D surface plots.

📋 What You'll Learn

Create two 1D arrays for the X and Y coordinates using numpy.linspace.

Create a 2D grid of X and Y values using numpy.meshgrid.

Calculate Z values using a mathematical function of X and Y.

Use matplotlib to create a 3D surface plot.

Display the plot with labels for axes.

💡 Why This Matters

🌍 Real World

3D surface plots help scientists and engineers visualize how a value changes over two directions, like temperature over a landscape or pressure over a wing surface.

💼 Career

Data scientists and analysts use 3D plots to explore complex data and communicate insights clearly to teams and stakeholders.

1

Create X and Y coordinate arrays

Create two variables called x and y using numpy.linspace. Set x to 50 points from -5 to 5, and y to 50 points from -5 to 5.

Matplotlib

import numpy as np
# Create x and y arrays with 50 points from -5 to 5
# Your code here

Hint

Use np.linspace(start, stop, num_points) to create evenly spaced points.

2

Create 2D grid from X and Y

Use numpy.meshgrid with x and y to create two 2D arrays called X and Y.

Matplotlib

import numpy as np

x = np.linspace(-5, 5, 50)
y = np.linspace(-5, 5, 50)
# Create 2D grid arrays X and Y from x and y
# Your code here

Hint

Use X, Y = np.meshgrid(x, y) to create grid arrays.

3

Calculate Z values using a function

Create a variable called Z that calculates np.sin(np.sqrt(X**2 + Y**2)).

Matplotlib

import numpy as np

x = np.linspace(-5, 5, 50)
y = np.linspace(-5, 5, 50)

X, Y = np.meshgrid(x, y)
# Calculate Z as sin of the square root of X squared plus Y squared
# Your code here

Hint

Use np.sin and np.sqrt to calculate Z.

4

Create and display the 3D surface plot

Import matplotlib.pyplot as plt and Axes3D from mpl_toolkits.mplot3d. Create a figure and 3D axes. Use ax.plot_surface(X, Y, Z, cmap='viridis') to plot the surface. Label the X, Y, and Z axes as 'X axis', 'Y axis', and 'Z axis'. Finally, use plt.show() to display the plot.

Matplotlib

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

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))

# Create figure and 3D axes
# Plot surface with cmap='viridis'
# Label axes
# Show plot
# Your code here

Hint

Use fig = plt.figure() and ax = fig.add_subplot(111, projection='3d') to create 3D axes.

Use ax.plot_surface to draw the surface.

Label axes with ax.set_xlabel, ax.set_ylabel, and ax.set_zlabel.

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