This notebook contains an excerpt from the Python Programming and Numerical Methods - A Guide for Engineers and Scientists, the content is also available at Berkeley Python Numerical Methods.
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< 12.1 2D Plotting | Contents | 12.3 Working with Maps >
In order to plot 3D figures use matplotlib, we need to import the mplot3d toolkit, which adds the simple 3D plotting capabilities to matplotlib.
import numpy as npfrom mpl_toolkits import mplot3dimport matplotlib.pyplot as pltplt.style.use('seaborn-poster')
Once we imported the mplot3d toolkit, we could create 3D axes and add data to the axes. Let’s first create a 3D axes.
fig = plt.figure(figsize = (10,10))ax = plt.axes(projection='3d')plt.show()
The ax = plt.axes(projection=’3d’) created a 3D axes object, and to add data to it, we could use plot3D function. And we could change the title, set the x,y,z labels for the plot as well.
TRY IT! Consider the parameterized data set t is a vector from 0 to \(10\pi\) with a step \(\pi/50\), x = sin(t), and y = cos(t). Make a three-dimensional plot of the (x,y,t) data set using plot3. Turn the grid on, make the axis equal, and put axis labels and a title. Let’s also activate the interactive plot using %matplotlib notebook, so that you can move and rotate the figure as well.
%matplotlib notebook
fig = plt.figure(figsize = (8,8))ax = plt.axes(projection='3d')ax.grid()t = np.arange(0, 10*np.pi, np.pi/50)x = np.sin(t)y = np.cos(t)ax.plot3D(x, y, t)ax.set_title('3D Parametric Plot')# Set axes labelax.set_xlabel('x', labelpad=20)ax.set_ylabel('y', labelpad=20)ax.set_zlabel('t', labelpad=20)plt.show()
"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info[2] var cell = fig.cell_info[0];};mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable() $(fig.parent_element).html('
'); fig.close_ws(fig, msg);}mpl.figure.prototype.close_ws = function(fig, msg){ fig.send_message('closing', msg); // fig.ws.close()}mpl.figure.prototype.push_to_output = function(remove_interactive) { // Turn the data on the canvas into data in the output cell. var width = this.canvas.width/mpl.ratio var dataURL = this.canvas.toDataURL(); this.cell_info[1]['text/html'] = '';}mpl.figure.prototype.updated_canvas_event = function() { // Tell IPython that the notebook contents must change. IPython.notebook.set_dirty(true); this.send_message("ack", {}); var fig = this; // Wait a second, then push the new image to the DOM so // that it is saved nicely (might be nice to debounce this). setTimeout(function () { fig.push_to_output() }, 1000);}mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element = $('
') nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind][0]; var tooltip = mpl.toolbar_items[toolbar_ind][1]; var image = mpl.toolbar_items[toolbar_ind][2]; var method_name = mpl.toolbar_items[toolbar_ind][3]; if (!name) { continue; }; var button = $(''); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); nav_element.append(button); } // Add the status bar. var status_bar = $(''); nav_element.append(status_bar); this.message = status_bar[0]; // Add the close button to the window. var buttongrp = $('
'); var button = $(''); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar')); titlebar.prepend(buttongrp);}mpl.figure.prototype._root_extra_style = function(el){ var fig = this el.on("remove", function(){fig.close_ws(fig, {}); });}mpl.figure.prototype._canvas_extra_style = function(el){ // this is important to make the div 'focusable el.attr('tabindex', 0) // reach out to IPython and tell the keyboard manager to turn it's self // off when our div gets focus // location in version 3 if (IPython.notebook.keyboard_manager) { IPython.notebook.keyboard_manager.register_events(el); } else { // location in version 2 IPython.keyboard_manager.register_events(el); }}mpl.figure.prototype._key_event_extra = function(event, name) { var manager = IPython.notebook.keyboard_manager; if (!manager) manager = IPython.keyboard_manager; // Check for shift+enter if (event.shiftKey && event.which == 13) { this.canvas_div.blur(); event.shiftKey = false; // Send a "J" for go to next cell event.which = 74; event.keyCode = 74; manager.command_mode(); manager.handle_keydown(event); }}mpl.figure.prototype.handle_save = function(fig, msg) { fig.ondownload(fig, null);}mpl.find_output_cell = function(html_output) { // Return the cell and output element which can be found *uniquely* in the notebook. // Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook" // IPython event is triggered only after the cells have been serialised, which for // our purposes (turning an active figure into a static one), is too late. var cells = IPython.notebook.get_cells(); var ncells = cells.length; for (var i=0; i
Try to rotate the above figure, and get a 3D view of the plot. You may notice that we also set the labelpad=20 to the 3-axis labels, which will make the label not overlap with the tick texts.
We could also plot 3D scatter plot using scatter function.
TRY IT! Make a 3D scatter plot with randomly generate 50 data points for x, y, and z. Set the point color as red, and size of the point as 50.
# We can turn off the interactive plot using %matplotlib inline%matplotlib inline
x = np.random.random(50)y = np.random.random(50)z = np.random.random(50)fig = plt.figure(figsize = (10,10))ax = plt.axes(projection='3d')ax.grid()ax.scatter(x, y, z, c = 'r', s = 50)ax.set_title('3D Scatter Plot')# Set axes labelax.set_xlabel('x', labelpad=20)ax.set_ylabel('y', labelpad=20)ax.set_zlabel('z', labelpad=20)plt.show()
Many times we would like a surface plot rather than a line plot when plotting in three dimensions. In three-dimensional surface plotting, we wish to make a graph of some relationship f (x, y). In surface plotting all (x,y) pairs must be given. This is not straightforward to do using vectors. Therefore, in surface plotting, the first data structure you must create is called a mesh. Given lists/arrays of x and y values, a mesh is a listing of all the possible combinations of x and y. In Python, the mesh is given as two arrays X and Y where X (i,j) and Y (i,j) define possible (x,y) pairs. A third array, Z, can then be created such that Z (i,j) = f (X (i,j), Y (i,j)). A mesh can be created using the np.meshgrid function in Python. The meshgrid function has the inputs x and y are lists containing the independent data set. The output variables X and Y are as described earlier.
TRY IT! Create a mesh for x = [1, 2, 3, 4] and y = [3, 4, 5] using the meshgrid function.
x = [1, 2, 3, 4]y = [3, 4, 5]X, Y = np.meshgrid(x, y)print(X)
[[1 2 3 4] [1 2 3 4] [1 2 3 4]]
print(Y)
[[3 3 3 3] [4 4 4 4] [5 5 5 5]]
We could plot 3D surfaces in Python too, the function to plot the 3D surfaces is plot_surface(X,Y,Z), where X and Y are the output arrays from meshgrid, and \(Z = f (X,Y)\) or \(Z (i,j) = f (X (i,j),Y (i,j))\). The most common surface plotting functions are surf and contour.
TRY IT! Make a plot of the surface \(f(x,y) = sin(x)\cdot cos(y) for -5\le x\le5, -5\le y\le5\) using the plot_surface function. Take care to use a sufficiently fine discretization in x and y to make the plot look smooth.
fig = plt.figure(figsize = (12,10))ax = plt.axes(projection='3d')x = np.arange(-5, 5.1, 0.2)y = np.arange(-5, 5.1, 0.2)X, Y = np.meshgrid(x, y)Z = np.sin(X)*np.cos(Y)surf = ax.plot_surface(X, Y, Z, cmap = plt.cm.cividis)# Set axes labelax.set_xlabel('x', labelpad=20)ax.set_ylabel('y', labelpad=20)ax.set_zlabel('z', labelpad=20)fig.colorbar(surf, shrink=0.5, aspect=8)plt.show()
You will notice that the surface plot shows different colors for different elevations, yellow for higher and blue for lower, since we used the colormap plt.cm.cividis in the surface plot. You can change to different color schemes for the surface plot. These are left as exercises. We also plotted a colorbar to show the corresponding colors to different values.
We could have subplots of different 3D plots as well. We could use the add_subplot function from the figure object we created to generate the subplots for 3D cases.
‘TRY IT! Make a 1 by 2 subplot to plot the above X, Y, Z data in wireframe plot and surface plot.
fig = plt.figure(figsize=(12,6))ax = fig.add_subplot(1, 2, 1, projection='3d')ax.plot_wireframe(X,Y,Z)ax.set_title('Wireframe plot')ax = fig.add_subplot(1, 2, 2, projection='3d')ax.plot_surface(X,Y,Z)ax.set_title('Surface plot')plt.tight_layout()plt.show()
There are many more functions related to plotting in Python and this is in no way an exhaustive list. However, it should be enough to get you started so that you can find the plotting functions in Python that suit you best and provide you with enough background to learn how to use them when you encounter them. You can find more examples of different type 3D plots on the mplot3d tutorial website.
< 12.1 2D Plotting | Contents | 12.3 Working with Maps >
