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]:

frommpl_toolkitsimportmplot3d

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]:

%matplotlibinlineimportnumpyasnpimportmatplotlib.pyplotasplt

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 linezline = np.linspace(0, 15, 1000) xline = np.sin(zline) yline = np.cos(zline) ax.plot3D(xline, yline, zline, 'gray')# Data for three-dimensional scattered pointszdata = 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 Plots, `mplot3d`

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]:

deff(x, y):returnnp.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');