Chapter 5 - Plotting

Matlab for Engineers
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Plotting
Chapter 5
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A bargraph of vector x
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A bargraph of matrix y
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A three dimensional bargraph
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A pie chart of x

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In this chapter we’ll cover
• Creating and labeling two
dimensional plots
• Adjusting the appearance of your
plots
• Using subplots
• Creating three dimensional plots
• Using the interactive plotting tools

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Section 5.1
Two Dimensional Plots
• The xy plot is the most commonly
used plot by engineers
• The independent variable is
usually called x
• The dependent variable is usually
called y

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Consider this xy data
time, sec Distance, Ft
0 0
2 0.33
4 4.13
6 6.29
8 6.85
10 11.19
12 13.19
14 13.96
16 16.33
18 18.17
Time is the
independent
variable and
distance is the
dependent
variable

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Define x and y and call the
plot function
You can use any variable name that is convenient
for the dependent and independent variables

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Engineers always add …
• Title
• X axis label, complete with units
• Y axis label, complete with units
• Often it is useful to add a grid

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Creating multiple plots
• Matlab overwrites the figure
window every time you request a
new plot
• To open a new figure window use
the figure function – for example
figure(2)

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Plots with multiple lines
• hold on
• Freezes the current plot, so that an
additional plot can be overlaid
• When you use this approach the
additional line is drawn in blue –
the default drawing color

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The first plot is drawn in blue

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The hold on command
freezes the plot
The second
line is also
drawn in blue,
on top of the
original plot
To unfreeze the plot
use the hold off
command

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You can also create multiple lines
on a single graph with one
command
• Using this approach each line
defaults to a different color

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Each set of
ordered pairs will
produce a new
line

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Variations
• If you use the plot command with
a single matrix, Matlab plots the
values versus the index number
• Usually this type of data is plotted
on a bar graph
• When plotted on an xy grid, it is
often called a line graph

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If you want to create multiple plots,
all with the same x value you can…
• Use alternating sets of ordered
pairs
• plot(x,y1,x,y2,x,y3,x,y4)
• Or group the y values into a
matrix
• z=[y1,y2,y3,y4]
• plot(x,z)

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Alternating sets
of ordered pairs
Matrix of Y
values

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The peaks(100)
function creates
a 100x100 array
of values. Since
this is a plot of a
single variable,
we get 100
different line plots

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Plots of Complex Arrays
• If the input to the plot command is
a single array of complex
numbers, Matlab plots the real
component on the x-axis and the
imaginary component on the y-
axis

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Multiple arrays of complex
numbers
• If you try to use two arrays of
complex numbers in the plot
function, the imaginary
components are ignored

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Line, Color and Mark Style
• You can change the appearance of
your plots by selecting user defined
• line styles
• color
• mark styles
• Try using
help plot
for a list of available styles

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Available choices
Table 5. 2 Line, Mark and Color Options
Line Type Indicator Point Type Indicator Color Indicator
solid - point . blue b
dotted : circle o green g
dash-dot -. x-mark x red r
dashed -- plus + cyan c
star * magenta m
square s yellow y
diamond d black k
triangle down v
triangle up ^
triangle left <
triangle right >
pentagram p
hexagram h

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Specify your choices in a
string
• For example
• plot(x,y,':ok')
• strings are identified with a tick mark
• if you don’t specify style, a default is
used
• line style – none
• mark style – none
• color - blue

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plot(x,y,':ok')
• In this command
• the : means use a dotted line
• the o means use a circle to mark
each point
• the letter k indicates that the graph
should be drawn in black
• (b indicates blue)

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dotted line
circles
black

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specify the
drawing
parameters for
each line after
the ordered pairs
that define the
line

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Axis scaling
• Matlab automatically scales each
plot to completely fill the graph
• If you want to specify a different
axis – use the axis command
axis([xmin,xmax,ymin,ymax])
• Lets change the axes on the
graph we just looked at

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Use the axis
function to
override the
automatic
scaling

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Annotating Your Plots
• You can also add
• legends
• textbox
• Of course you should always add
• title
• axis labels

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Improving your labels
You can use Greek letters in your labels by
putting a backslash () before the name of the
letter. For example:
title(‘alpha beta gamma’)
creates the plot title
α β γ
To create a superscript use curly brackets
title(‘x^{2}’)
gives
x2
2
x

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Tex Markup Language
• These label improvements use
the Tex Markup Language
• Use the Help feature to find out
more!!

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Section 5.2
Subplots
• The subplot command allows
you to subdivide the graphing
window into a grid of m rows and
n columns
• subplot(m,n,p)
rows columns location

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subplot(2,2,1)
2 rows
2 columns
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x
Peaks
y

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2 rows and 1
column

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Section 5.3
Other Types of 2-D Plots
• Polar Plots
• Logarithmic Plots
• Bar Graphs
• Pie Charts
• Histograms
• X-Y graphs with 2 y axes
• Function Plots

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Polar Plots
• Some functions are easier to
specify using polar coordinates
than by using rectangular
coordinates
• For example the equation of a
circle is
• y=sin(x)
in polar coordinates

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Practice Exercise 5.3
• Try these exercises to create
some interesting shapes
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2
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5
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210
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270
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180 0
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2
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180 0
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2
3
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5
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180 0
0.2
0.4
0.6
0.8
1
30
210
60
240
90
270
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180 0

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Logarithmic Plots
• A logarithmic scale (base 10) is
convenient when
• a variable ranges over many orders
of magnitude, because the wide
range of values can be graphed,
without compressing the smaller
values.
• data varies exponentially.

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• plot – uses a linear scale on both
axes
• semilogy – uses a log10 scale on
the y axis
• semilogx – uses a log10 scale on
the x axis
• loglog – use a log10 scale on both
axes

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x-y plot – linear on
both axes
semilogx – log scale
on the x axis
semilogy – log scale
on the y axis
loglog – log scale on
both axes

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Bar Graphs and Pie Charts
• Matlab includes a whole family of
bar graphs and pie charts
• bar(x) – vertical bar graph
• barh(x) – horizontal bar graph
• bar3(x) – 3-D vertical bar graph
• bar3h(x) – 3-D horizontal bar graph
• pie(x) – pie chart
• pie3(x) – 3-D pie chart

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Histograms
• A histogram is a plot showing the
distribution of a set of values

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Defaults to
10 bins

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X-Y Graphs with Two Y
Axes
• Sometimes it is useful to overlay
two x-y plots onto the same
figure. However, if the order of
magnitude of the y values are
quite different, it may be difficult to
see how the data behave.

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For example

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Scaling Depends on the
largest value plotted
• Its difficult to see how the blue line behaves, because
the scale isn’t appropriate

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The plotyy
function allows
you to use two
scales on a
single graph

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Function Plots
• Function plots allow you to use a
function as input to a plot
command, instead of a set of
ordered pairs of x-y values
• fplot('sin(x)',[-2*pi,2*pi])
function input as a
string
range of the independent
variable – in this case x

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Section 5.4
Three Dimensional Plotting
• Line plots
• Surface plots
• Contour plots

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Three Dimensional Line
Plots
• These plots require a set of order
triples ( x-y-z values) as input
The z-axis is labeled
the same way the x
and y axes are labeled

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Matlab uses a
coordinate
system
consistent with
the right hand
rule

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Just for fun
• try the comet3 function, which
draws the graph in an animation
sequence
• comet3(x,y,z)
• If your animation draws too
slowly, add more data points
• For 2-D line graphs use the
comet function

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Surface Plots
• Represent x-y-z data as a surface
• mesh - meshplot
• surf – surface plot

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Both Mesh and Surf
• Can be used to good effect with a
single two dimensional matrix

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The x and y coordinates
are the matrix index
numbers

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Using mesh with 3 variables
• If we know the values of x and y
that correspond to our z values,
we can plot against those values
instead of the index numbers

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Surf plots
• surf plots are similar to mesh
plots
• they create a 3-D colored surface
instead of an open mesh
• syntax is the same

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Shading
• There are several shading options
• shading interp
• shading flat
• faceted flat is the default
• You can also adjust the color
scheme with the color map
function

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Colormaps
autumn bone hot
spring colorcube hsv
summer cool pink
winter copper prism
jet (default) flag white

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Contour Plots
• Contour plots use the same input
syntax as mesh and surf plots
• They create graphs that look like
the familiar contour maps used by
hikers

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To demonstrate these functions lets
use a more interesting example
• A more complicated surface can be
created by calculating the values of
z, instead of just defining them
• We’ll need to use the meshgrid
function to create 2-D input arrays –
which will then be used to create a
2-D result

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Pseudo Color Plots
• Similar to contour plots
• Instead of lines, a 2-D shaded map
is created
• Uses the same syntax
• The following example uses the
built-in Matlab demonstration
function peaks

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Section 5.5
Editing Plots from the Menu Bar
• In addition to controlling the way
your plots look by using Matlab
commands, you can also edit a
plot once you’ve created it using
the menu bar
• Another demonstration function
built into Matlab is
sphere

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Once you’ve created a plot you can
adjust it using the menu bar
• In this picture the
insert menu has
been selected
• Notice you can
use it to add
labels, legends,
a title and other
annotations

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Select
Edit-> Axis
Properties from the
menu tool bar
Select Inspector
from the
Property Editor
Change the
Aspect Ratio
Explore the
property editor to
see some of the
other ways you
can adjust your
plot interactively

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• If you adjust a figure interactively,
you’ll lose your improvements
when you rerun your program

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Creating plots from the
workspace

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Matlab will suggest plotting options
and create the plot for you

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Saving your plots
• Rerun your M-file to recreate a plot
• Save the figure from the file menu
using the save as… option
• You’ll be presented with several choices of
file format such as
• jpeg
• emg (enhanced metafile) etc
• Right-click on the figure and select
copy – then paste it into another
document

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Summary
• The x-y plot is the most common
used in engineering
• Graphs should always include
titles and axis labels. Labels
should include units.
• Matlab includes extensive options
for controlling the appearance of
your plot

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• Multiple plots can be displayed in
the same figure window
• Most common plot types are
supported by Matlab including
• polar plots
• bar graphs
• pie charts
• histograms

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• Matlab supports 3-D plotting
• line plots
• surface plots
• You can modify plots interactively
from the menu bar
• You can create plots interactively
from the workspace window

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• Figures created in Matlab can be
stored using a number of different
file formats

Chapter 5 - Plotting

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Chapter 5 - Plotting