3D surface plots in Matplotlib - Step-by-Step Execution

Concept Flow - 3D surface plots

Import matplotlib and numpy

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Create grid data (X, Y)

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Calculate Z values from X, Y

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Create 3D plot figure

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Plot surface with X, Y, Z

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Show plot on screen

The flow starts by preparing data grids, computing Z values, then plotting the 3D surface and displaying it.

Execution Sample

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))

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

This code creates a 3D surface plot of a sine wave based on distance from origin.

Execution Table

Step	Action	Variables Created/Updated	Result/Output
1	Import numpy and matplotlib	numpy, matplotlib modules loaded	Modules ready for use
2	Create 1D arrays X and Y with 50 points from -5 to 5	X, Y arrays	Arrays with 50 values each
3	Create 2D meshgrid from X and Y	X, Y meshgrid arrays	2D grids for X and Y coordinates
4	Calculate Z = sin(sqrt(X^2 + Y^2))	Z array	Z values computed for each (X,Y) point
5	Create figure and 3D axes	fig, ax	Empty 3D plot ready
6	Plot surface with X, Y, Z and colormap 'viridis'	ax.plot_surface	3D surface plotted
7	Show plot window	plt.show()	Plot window displayed
8	End of script	-	Execution complete

💡 All steps executed; plot displayed and script ends

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
X	undefined	1D array (50 values)	2D meshgrid array (50x50)	2D meshgrid array (50x50)	2D meshgrid array (50x50)	2D meshgrid array (50x50)	2D meshgrid array (50x50)
Y	undefined	1D array (50 values)	2D meshgrid array (50x50)	2D meshgrid array (50x50)	2D meshgrid array (50x50)	2D meshgrid array (50x50)	2D meshgrid array (50x50)
Z	undefined	undefined	undefined	2D array (50x50) with sin values	2D array (50x50)	2D array (50x50)	2D array (50x50)
fig	undefined	undefined	undefined	undefined	Figure object created	Figure object created	Figure object created
ax	undefined	undefined	undefined	undefined	3D axes object created	3D axes with surface plotted	3D axes with surface plotted

Key Moments - 3 Insights

Why do we use meshgrid for X and Y instead of just 1D arrays?

Meshgrid creates 2D coordinate grids needed to calculate Z values for every (X, Y) pair, as shown in execution_table step 3 and variable_tracker where X and Y become 2D arrays.

What does the Z array represent in the plot?

Z holds the height values for each (X, Y) point on the surface, calculated in step 4. This defines the shape of the 3D surface.

Why do we need to specify 'projection="3d"' when adding subplot?

This tells matplotlib to create a 3D plot area, enabling 3D plotting functions like plot_surface, as seen in step 5.

Visual Quiz - 3 Questions

Look at the execution_table at step 4. What is the shape of the Z variable?

A 1D array with 50 values

B 2D array with 50x50 values

C Scalar value

D 3D array

💡 Hint

Refer to execution_table step 4 and variable_tracker for Z after step 4

At which step is the 3D axes object created?

A Step 5

B Step 4

C Step 3

D Step 6

💡 Hint

Check execution_table step 5 and variable_tracker for ax variable

If we skip meshgrid and use 1D arrays X and Y directly in plot_surface, what will happen?

A Plot will be 2D instead of 3D

B Plot will show correctly

C Error or incorrect plot because X, Y must be 2D grids

D Plot will be empty

💡 Hint

Recall key_moments about meshgrid necessity and execution_table step 3

Concept Snapshot

3D Surface Plots with matplotlib:
- Use numpy.meshgrid to create 2D grids for X and Y
- Compute Z values for each (X, Y) pair
- Create 3D axes with fig.add_subplot(projection='3d')
- Plot surface using ax.plot_surface(X, Y, Z, cmap='color_map')
- Show plot with plt.show()

Full Transcript

This visual execution traces how to create a 3D surface plot using matplotlib in Python. First, numpy and matplotlib modules are imported. Then, 1D arrays X and Y are created with 50 points each from -5 to 5. These arrays are converted into 2D meshgrid arrays to represent coordinate grids. Next, Z values are calculated as the sine of the distance from the origin for each (X, Y) point. A figure and 3D axes are created, and the surface is plotted with a color map. Finally, the plot window is displayed. Variables X, Y, and Z change from undefined to 1D arrays, then 2D grids, and finally Z holds the height values. Key moments include understanding why meshgrid is needed, what Z represents, and why 3D projection is required. The quizzes test understanding of array shapes, step order, and meshgrid importance. The snapshot summarizes the key steps to create 3D surface plots.