Graphing with MATLAB
Plotting basics.

GraphingWithMATLAB

A picture is worth a thousand words, particularly visual representation of data in engineering is very useful. MATLAB has powerful graphics tools and there is a very helpful section devoted to graphics in MATLAB Help: Graphics. Students are encouraged to study that section; what follows is a brief summary of the main plotting features.

Two-Dimensional Plots

The
plot
Statement

Probably the most common method for creating a plot is by issuing plot(x, y) statement where function y is plotted against x.

Type in the following statement at the MATLAB prompt:

x=[-pi:.1:pi]; y=sin(x); plot(x,y);

After we executed the statement above, a plot named Figure1 is generated:

Graph of sin(x)
Plot

Having variables assigned in the Workspace, x and y=sin(x) in our case, we can also select x and y, and right click on the selected variables. This opens a menu from which we choose plot(x,y). See the figure below.

Creating a plot from Workspace.
PlotFromWorkspace

Annotating Plots

Graphs without labels are incomplete and labeling elements such as plot title, labels for x and y axes, and legend should be included. Using up arrow, recall the statement above and add the annotation commands as shown below.

x=[-pi:.1:pi];y=sin(x);plot(x,y);title('Graph of y=sin(x)');xlabel('x');ylabel('sin(x)');grid on

Run the file and compare your result with the first one.

Graph of sin(x) with Labels.
sinxLabels

Type in the following at the MATLAB prompt and learn additional commands to annotate plots:
help gtext
help legend
help zlabel

Superimposed Plots

If you want to merge data from two graphs, rather than create a new graph from scratch, you can superimpose the two using a simple trick:

% This script generates sin(x) and cos(x) plot on the same graph
% initialize variables
x=[-pi:.1:pi];      %create a row vector from -pi to +pi with .1 increments
y0=sin(x);          %calculate sine value for each x
y1=cos(x);          %calculate cosine value for each x
% Plot sin(x) and cos(x) on the same graph
plot(x,y0,x,y1);
title('Graph of sin(x) and cos(x)'); %Title of graph
xlabel('x');                %Label of x axis
ylabel('sin(x), cos(x)');   %Label of y axis
legend('sin(x)','cos(x)');  %Insert legend in the same order as y0 and y1 calculated
grid on                     %Graph grid is turned

Graph of sin(x) and cos(x) in the same plot with labels and legend.
sinxLabelsLegend

Multiple Plots in a Figure

Multiple plots in a single figure can be generated with subplot in the Command Window. However, this time we will use the built-in Plot Tools. Before we initialize that tool set, let us create the necessary variables using the following script:

% This script generates sin(x) and cos(x) variables
clc                 %Clears command window
clear all           %Clears the variable space
close all           %Closes all figures
X1=[-2*pi:.1:2*pi];  %Creates a row vector from -2*pi to 2*pi with .1 increments
Y1=sin(X1);          %Calculates sine value for each x
Y2=cos(X1);          %Calculates cosine value for each x
Y3=Y1+Y2;            %Calculates sin(x)+cos(x)
Y4=Y1-Y2;            %Calculates sin(x)-cos(x)

Note that the above script clears the command window and variable workspace. It also closes any open Figures. After running the script, we will have X1, Y1, Y2, Y3 and Y4 loaded in the workspace. Next, select File > New > Figure, a new Figure window will open. Click "Show Plot Tools and Dock Figure" on the tool bar.

Plot Tools
PlotTools

Under New Subplots > 2D Axes, select four vertical boxes that will create four subplots in one figure. Also notice, the five variables we created earlier are listed under Variables.

Creating four sub plots.
Plot Tools

After the subplots have been created, select the first supblot and click on "Add Data". In the dialog box, set X Data Source to X1 and Y Data Source to Y1. Repeat this step for the remaining subplots paying attention to Y Data Source (Y2, Y3 and Y4 need to be selected in the subsequent steps while X1 is always the X Data Source).

Adding data to axes.
PlotTools

Next, select the first item in "Plot Browser" and activate the "Property Editor". Fill out the fields as shown in the figure below. Repeat this step for all subplots.

Using "Property Editor".
PlotTools

Save the figure as sinxcosx.fig in the current directory.

The four subplots generated with "Plot Tools".
PlotTools

The four subplots in a single figure.
SubPlot

Three-Dimensional Plots

3D plots can be generated from the Command Window as well as by GUI alternatives. This time, we will go back to the Command Window.

The
plot3
Statement

With the X1,Y1,Y2 and Y2 variables still in the workspace, type in plot3(X1,Y1,Y2) at the MATLAB prompt. A figure will be generated, click "Show Plot Tools and Dock Figure".

A raw 3D figure is generated with plot3.
Plot

Use the property editor to make the following changes.

3D Property Editor.
Plot

The final result should look like this:

3D graph of x, sin(x), cos(x)
Plot

Use help or doc commands to learn more about 3D plots, for example, image(x), surf(x) and mesh(x).

Quiver or Velocity Plots

To plot vectors, it is useful to draw arrows so that the direction of the arrow points the direction of the vector and the length of the arrow is vector’s magnitude. However the standard plot function is not suitable for this purpose. Fortunately, MATLAB has quiver function appropriately named to plot arrows. quiver(x,y,u,v) plots vectors as arrows at the coordinates (x,y) with components (u,v). The matrices x, y, u, and v must all be the same size and contain corresponding position and velocity components.

Calculate the magnitude of forces OA, OB and the resultant R of OA and OB shown below. Plot all three forces on x-y Cartesian coordinate system1.

Quiver Plot.
Resultant1

% Preparation
clear   % removes all variables from the current workspace, 
        % releasing them from system memory.
clc     % clears all input and output from the Command Window display, 
        % giving you a "clean screen."
% Input and Computation
OA=[600 320];    % Force 1
magOA=sqrt(sum(OA.^2));
OB=[-200 -480];  % Force 2
magOB=sqrt(sum(OB.^2));
OC=OA+OB;        % The resultant of OA and OB
magOC=sqrt(sum(OC.^2)); % The magnitude of resultant force OC
angleMag=atan(OC(2)/OC(1))*180/pi; % angle of OC in degrees
% Output
disp(' ')                     % Display blank line
str1= ['The magnitude of the resultant force is ', num2str(magOC), ' N.'];
disp(str1); 
str2= ['The angle of the resultant force is ', num2str(angleMag), ' degrees.'];
disp(str2); 
% Plot Preparation
starts = zeros(3,2); % Origin for all 3 forces, 3x2 "zero" matrix
ends = [OA;OB;OC]; % End point for all 3 forces
vectors = horzcat(starts,ends); % Concatenate arrays horizontally
% Plot Forces on x-y Cartesian Coordinate System
% The following MATLAB function plots vectors as arrows 
% at the coordinates specified in each corresponding 
% pair of elements in x and y.
quiver( vectors( :,1 ), vectors( :,2 ), vectors( :,3 ), vectors( :,4 )); 
axis equal
grid
title('Forces on x-y Cartesian Coordinate System')
xlabel('x') % x-axis label
ylabel('y') % y-axis label
view(2) % setting view to 2-D

Output of quiver function.
Resultant1_Plot

Write an interactive script to calculate the resultant R of forces F1, F2 and F3 shown below and plot all four forces on x-y Cartesian coordinate system2.

An example for quiver3 plot.
resultant of  3 forces

clear
clc
disp('This script computes the resultant of three forces on x-y Cartesian coordinate system.')
f1=input('Enter the magnitude of first force in N: ');                                     
theta1=input('Enter the angle of first force in deg: ');
f2=input('Enter the magnitude of second force in N: ');                                     
theta2=input('Enter the angle of second force in deg: ');
f3=input('Enter the magnitude of third force in N: ');                                     
theta3=input('Enter the angle of third force in deg: ');
x1=f1*cos(theta1*pi/180); % The components of force
y1=f1*sin(theta1*pi/180); % The components of force
F1=[x1 y1];  % Force 1
x2=f2*cos(theta2*pi/180); % The components of force
y2=f2*sin(theta2*pi/180); % The components of force
F2=[x2 y2];  % Force 2
x3=f3*cos(theta3*pi/180); % The components of force
y3=f3*sin(theta3*pi/180); % The components of force
F3=[x3 y3];  % Force 3
R=F1+F2+F3;  % The resultant of F1, F2 and F3
magR=sqrt(sum(R.^2)); % The magnitude of resultant force R
angle=atan(R(2)/R(1))*180/pi; % Angle of R in degrees
disp(' ')                     % Display blank line
str1= ['The magnitude of the resultant force is ', num2str(magR), ' N.'];
disp(str1); 
str2= ['The angle of the resultant force is ', num2str(angle), ' degrees.'];
disp(str2); 
starts = zeros(4,3);
ends = [F1;F2;F3;R];
ends(3,3)=0; % inputs 0s for z components, making it 3D
vectors = horzcat(starts,ends); % Concatenate arrays horizontally
quiver3( vectors( :,1 ), vectors( :,2 ), vectors( :,3 ), vectors( :,4 ), vectors( :,5 ), vectors( :,6 )); % A three-dimensional quiver plot displays vectors with components (u,v,w) at the points (x,y,z), where u, v, w, x, y, and z all have real (non-complex) values.
axis equal
title('Forces on x-y Cartesian coordinate system')
xlabel('x') % x-axis label
ylabel('y') % y-axis label
view(2)

Output of quiver3 function.
quiver3 Example

Summary of Key Points

  1. plot(x, y) and plot3(X1,Y1,Y2) statements create 2- and 3-D graphs respectively,
  2. Plots at minimum should contain the following elements: title, xlabel, ylabel and legend,
  3. Annotated plots can be easily generated with GUI Plot Tools,
  4. quiver and quiver3 plots are useful for making vector diagrams.

Footnotes

  1. 1 Applied Engineering Mechanics by A. Jensen, H. Chenoweth McGraw-Hill Ryerson Limited © 1972, (p. 15)
  2. 2 Applied Engineering Mechanics by A. Jensen, H. Chenoweth McGraw-Hill Ryerson Limited © 1972, (p. 15)