# How to Create 3D Contour Plots with Matplotlib in Python

Rate this post

π‘ Problem Formulation: Visualizing complex data can be challenging, especially when dealing with three-dimensional space. In this article, we solve the problem of representing three-dimensional surfaces by creating 3D contour plots using Python’s Matplotlib library. The input will be a set of data points in 3D, and the desired output is a visual representation that captures the contours of the surface formed by these points.

## Method 1: Using the `contourf()` and `scatter()` Functions

This method involves plotting filled contours with the `contourf()` function and then using the `scatter()` function to overlay data points. The `contourf()` function creates a contour plot with filled areas between the lines, making surfaces distinguishable, while the `scatter()` function helps in marking the individual data points for reference.

Here’s an example:

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

X = np.linspace(-5, 5, 100)
Y = np.linspace(-5, 5, 100)
X, Y = np.meshgrid(X, Y)
Z = np.sin(np.sqrt(X**2 + Y**2))

fig = plt.figure()
ax.contourf(X, Y, Z, 50)
ax.scatter(X, Y, Z, color='k')
plt.show()```

The output of this code is a 3D contour plot with dark spots representing the data points.

This code snippet begins by generating a mesh grid of `X` and `Y` values, calculates `Z` as a function of `X` and `Y`, and then creates a 3D plot. The `contourf()` call adds filled contours to the plot while `scatter()` overlays the data points.

## Method 2: Utilizing the `plot_surface()` Function with Contours

Here, the `plot_surface()` function is used in conjunction with contour plots to visualize the surface and its contours in two separate views. The `plot_surface()` function renders a 3D surface mesh, and by adding contours on the bottom plane, the relation between the two visualizations is clarified.

Here’s an example:

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

x = np.linspace(-5, 5, 100)
y = np.linspace(-5, 5, 100)
x, y = np.meshgrid(x, y)
z = np.sin(np.sqrt(x**2 + y**2))

fig = plt.figure()
ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap='viridis', edgecolor='none')
ax.contourf(x, y, z, zdir='z', offset=-2, cmap='viridis')

plt.show()```

The output is a 3-dimensional surface plot with an additional contour plot displayed on the xy-plane.

The code snippet above first defines the grid and function values for `z`. Then, it creates a 3D plot where `plot_surface()` is used to draw the surface and `contourf()` is used to add the contours to the xy-plane, giving a different view of the surface.

## Method 3: Generating Contour Lines with `contour()`

In this method, `contour()` is used instead of `contourf()` to generate contour lines rather than filled contours. This can give a clearer view of the precise values of the contours. The `contour()` function is straightforward and allows for an easier interpretation of the data’s structure.

Here’s an example:

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

x = np.linspace(-5, 5, 100)
y = np.linspace(-5, 5, 100)
x, y = np.meshgrid(x, y)
z = np.sin(np.sqrt(x**2 + y**2))

fig = plt.figure()
ax.contour(x, y, z, 50, cmap='winter')
plt.show()```

The output is a 3D plot featuring the contour lines of the function’s surface.

This concise snippet creates a mesh grid and calculates the function `z`. The `contour()` call then adds the contour lines to the 3D plot. By specifying the number of levels, the granularity of contour lines can be adjusted.

## Method 4: Combining Surface and Contour Plots

This method combines the visual details of the surface plot with the contour plot by using `plot_surface()` and `contour()` together. The technique allows for a comprehensive view that includes both the smoothness of the surface and the precision of contour lines.

Here’s an example:

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

x = np.linspace(-5, 5, 100)
y = np.linspace(-5, 5, 100)
x, y = np.meshgrid(x, y)
z = np.sin(np.sqrt(x**2 + y**2))

fig = plt.figure()
ax.plot_surface(x, y, z, cmap='coolwarm', alpha=0.5)
ax.contour(x, y, z, zdir='z', offset=np.min(z), cmap='coolwarm')
plt.show()```

The output combines a translucent 3D surface plot with the contour lines on the bottom plane.

This technique initializes a 3D plot and employs both `plot_surface()` and `contour()`. The alpha parameter in `plot_surface()` makes the surface plot semi-transparent, which allows the contour lines beneath to be visible, offering a dual representation of the data.

## Bonus One-Liner Method 5: Creating Inline 3D Contour Plot

This quick and compact method creates a 3D contour plot using a one-liner code with the combination of PyPlot’s features. Ideal for quick and simple visualizations without customization.

Here’s an example:

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

fig = plt.figure()
ax.contour3D(*np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100)), np.sin(np.sqrt(X**2 + Y**2)), 50)
plt.show()```

The output is a 3-dimensional plot showing the contours of the surface in question.

This one-liner is an effective method when speed and brevity are desired. It leverages Python’s unpacking with `*` to pass the meshgrid directly into the `contour3D()` function. This can be used to quickly draft a visualization when working with familiar datasets.

## Summary/Discussion

• Method 1: Using `contourf()` and `scatter()`. Strength: Provides filled contours with clear data point markers. Weakness: May not clearly represent precise contour levels.
• Method 2: Utilizing `plot_surface()` with Contours. Strength: Offers a detailed 3D view of the surface with informative contours. Weakness: Can be computationally intensive for large datasets.
• Method 3: Generating Contour Lines with `contour()`. Strength: Offers precise contour lines for clearer data structure. Weakness: Lacks the visual appeal of filled contours.
• Method 4: Combining Surface and Contour Plots. Strength: Provides a comprehensive visualization combining both surface and contours. Weakness: Contour details may be obscured by the surface plot.
• Bonus Method 5: Creating Inline 3D Contour Plot. Strength: Quick visualization for straightforward data. Weakness: Lacks flexibility for more complex or specific customization.