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# Three-Dimensional Plotting in Matplotlib

##### Jake VanderPlas december 10, 2019
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Matplotlib was initially designed with only two-dimensional plotting in mind. Around the time of the 1.0 release, some three-dimensional plotting utilities were built on top of Matplotlib’s two-dimensional display, and the result is a convenient (if somewhat limited) set of tools for three-dimensional data visualization. three-dimensional plots are enabled by importing the mplot3d toolkit, included with the main Matplotlib installation:In [1]:

from mpl_toolkits import mplot3d


Once this submodule is imported, a three-dimensional axes can be created by passing the keyword projection='3d' to any of the normal axes creation routines:In [2]:

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt


In [3]:

fig = plt.figure()
ax = plt.axes(projection='3d')


With this three-dimensional axes enabled, we can now plot a variety of three-dimensional plot types. Three-dimensional plotting is one of the functionalities that benefits immensely from viewing figures interactively rather than statically in the notebook; recall that to use interactive figures, you can use %matplotlib notebook rather than %matplotlib inline when running this code.

## Three-dimensional Points and Lines

The most basic three-dimensional plot is a line or collection of scatter plot created from sets of (x, y, z) triples. In analogy with the more common two-dimensional plots discussed earlier, these can be created using the ax.plot3D and ax.scatter3D functions. The call signature for these is nearly identical to that of their two-dimensional counterparts, so you can refer to Simple Line Plots and Simple Scatter Plots for more information on controlling the output. Here we’ll plot a trigonometric spiral, along with some points drawn randomly near the line:In [4]:

ax = plt.axes(projection='3d')

# Data for a three-dimensional line
zline = np.linspace(0, 15, 1000)
xline = np.sin(zline)
yline = np.cos(zline)
ax.plot3D(xline, yline, zline, 'gray')

# Data for three-dimensional scattered points
zdata = 15 * np.random.random(100)
xdata = np.sin(zdata) + 0.1 * np.random.randn(100)
ydata = np.cos(zdata) + 0.1 * np.random.randn(100)
ax.scatter3D(xdata, ydata, zdata, c=zdata, cmap='Greens');


Notice that by default, the scatter points have their transparency adjusted to give a sense of depth on the page. While the three-dimensional effect is sometimes difficult to see within a static image, an interactive view can lead to some nice intuition about the layout of the points.

## Three-dimensional Contour Plots

Analogous to the contour plots we explored in Density and Contour Plotsmplot3d contains tools to create three-dimensional relief plots using the same inputs. Like two-dimensional ax.contour plots, ax.contour3D requires all the input data to be in the form of two-dimensional regular grids, with the Z data evaluated at each point. Here we’ll show a three-dimensional contour diagram of a three-dimensional sinusoidal function:In [5]:

def f(x, y):
return np.sin(np.sqrt(x ** 2 + y ** 2))

x = np.linspace(-6, 6, 30)
y = np.linspace(-6, 6, 30)

X, Y = np.meshgrid(x, y)
Z = f(X, Y)


In [6]:

fig = plt.figure()
ax = plt.axes(projection='3d')
ax.contour3D(X, Y, Z, 50, cmap='binary')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z');


Sometimes the default viewing angle is not optimal, in which case we can use the view_init method to set the elevation and azimuthal angles. In the following example, we’ll use an elevation of 60 degrees (that is, 60 degrees above the x-y plane) and an azimuth of 35 degrees (that is, rotated 35 degrees counter-clockwise about the z-axis):In [7]:

ax.view_init(60, 35)
fig


Out[7]:

Again, note that this type of rotation can be accomplished interactively by clicking and dragging when using one of Matplotlib’s interactive backends.

## Wireframes and Surface Plots

Two other types of three-dimensional plots that work on gridded data are wireframes and surface plots. These take a grid of values and project it onto the specified three-dimensional surface, and can make the resulting three-dimensional forms quite easy to visualize. Here’s an example of using a wireframe:In [8]:

fig = plt.figure()
ax = plt.axes(projection='3d')
ax.plot_wireframe(X, Y, Z, color='black')
ax.set_title('wireframe');


A surface plot is like a wireframe plot, but each face of the wireframe is a filled polygon. Adding a colormap to the filled polygons can aid perception of the topology of the surface being visualized:In [9]:

ax = plt.axes(projection='3d')
ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
cmap='viridis', edgecolor='none')
ax.set_title('surface');


Note that though the grid of values for a surface plot needs to be two-dimensional, it need not be rectilinear. Here is an example of creating a partial polar grid, which when used with the surface3D plot can give us a slice into the function we’re visualizing:In [10]:

r = np.linspace(0, 6, 20)
theta = np.linspace(-0.9 * np.pi, 0.8 * np.pi, 40)
r, theta = np.meshgrid(r, theta)

X = r * np.sin(theta)
Y = r * np.cos(theta)
Z = f(X, Y)

ax = plt.axes(projection='3d')
ax.plot_surface(X, Y, Z, rstride=1, cstride=1,
cmap='viridis', edgecolor='none');