MATLAB Laboratory 09/23/10 Lecture

Chapters 5 and 9: Plotting

Lisa A. Oberbroeckling

Loyola University Marylandloberbroeckling@loyola.edu

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 1 / 21

Examples of Plots used in Lectures

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y=1/x

y=−2x+2

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 2 / 21

Examples of Plots used in Lectures

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x=2y−y

x=y2−6y

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 3 / 21

Examples of Plots used in Lectures

−1

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xy

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L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 4 / 21

Examples of Plots used in Lectures

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Example 2

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L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 5 / 21

Plots

Where linspace(0,2*pi)

or 0:pi/60:2*pi (for example) comes in handy!

Also where ”dot operations” are needed

Look at plotEx# m-files on the H-drive

Basic commands:plot(x,y), plot3(x,y,z), surf(x,y,z), mesh(x,y,z).

Useful command: clf: clears the current figure

There are other ways to plot, like using fplot or ezplot

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 6 / 21

Plots

Where linspace(0,2*pi)

or 0:pi/60:2*pi (for example) comes in handy!

Also where ”dot operations” are needed

Look at plotEx# m-files on the H-drive

Basic commands:plot(x,y), plot3(x,y,z), surf(x,y,z), mesh(x,y,z).

Useful command: clf: clears the current figure

There are other ways to plot, like using fplot or ezplot

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 6 / 21

Plots

Where linspace(0,2*pi)

or 0:pi/60:2*pi (for example) comes in handy!

Also where ”dot operations” are needed

Look at plotEx# m-files on the H-drive

Basic commands:plot(x,y),

plot3(x,y,z), surf(x,y,z), mesh(x,y,z).

Useful command: clf: clears the current figure

There are other ways to plot, like using fplot or ezplot

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 6 / 21

Plots

Where linspace(0,2*pi)

or 0:pi/60:2*pi (for example) comes in handy!

Also where ”dot operations” are needed

Look at plotEx# m-files on the H-drive

Basic commands:plot(x,y), plot3(x,y,z),

surf(x,y,z), mesh(x,y,z).

Useful command: clf: clears the current figure

There are other ways to plot, like using fplot or ezplot

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 6 / 21

Plots

Where linspace(0,2*pi)

or 0:pi/60:2*pi (for example) comes in handy!

Also where ”dot operations” are needed

Look at plotEx# m-files on the H-drive

Basic commands:plot(x,y), plot3(x,y,z), surf(x,y,z),

mesh(x,y,z).

Useful command: clf: clears the current figure

There are other ways to plot, like using fplot or ezplot

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 6 / 21

Plots

Where linspace(0,2*pi)

or 0:pi/60:2*pi (for example) comes in handy!

Also where ”dot operations” are needed

Look at plotEx# m-files on the H-drive

Basic commands:plot(x,y), plot3(x,y,z), surf(x,y,z), mesh(x,y,z).

Useful command: clf: clears the current figure

There are other ways to plot, like using fplot or ezplot

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 6 / 21

Plots

Where linspace(0,2*pi)

or 0:pi/60:2*pi (for example) comes in handy!

Also where ”dot operations” are needed

Look at plotEx# m-files on the H-drive

Basic commands:plot(x,y), plot3(x,y,z), surf(x,y,z), mesh(x,y,z).

Useful command: clf: clears the current figure

There are other ways to plot, like using fplot or ezplot

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 6 / 21

Plots

Where linspace(0,2*pi)

or 0:pi/60:2*pi (for example) comes in handy!

Also where ”dot operations” are needed

Look at plotEx# m-files on the H-drive

Basic commands:plot(x,y), plot3(x,y,z), surf(x,y,z), mesh(x,y,z).

Useful command: clf: clears the current figure

There are other ways to plot, like using fplot or ezplot

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 6 / 21

Plotting

Plot commands basically ”connect-the-dots” and you have to tellMATLAB which dots to connect, and how to connect them.

Thus you have more control, so can make parametric plots, or plotswith x as a function of y, much easier than on graphing calculators orother packages.

−3 −2 −1 0 1 2 3−2.5

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−1.5

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−0.5

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0.5

1

1.5

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2.5

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 7 / 21

Plotting

Plot commands basically ”connect-the-dots” and you have to tellMATLAB which dots to connect, and how to connect them.

Thus you have more control, so can make parametric plots, or plotswith x as a function of y, much easier than on graphing calculators orother packages.

−3 −2 −1 0 1 2 3−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 7 / 21

Plotting

Plot commands basically ”connect-the-dots” and you have to tellMATLAB which dots to connect, and how to connect them.

Thus you have more control, so can make parametric plots, or plotswith x as a function of y, much easier than on graphing calculators orother packages.

−3 −2 −1 0 1 2 3−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 7 / 21

Basic Plot

Basic example: plotEx1a.mx=-2:2;

plot(x,x.^2)

What’s wrong with this plot?

Look at plotEx1aV2.m for better ways to define x

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 8 / 21

Basic Plot

Basic example: plotEx1a.mx=-2:2;

plot(x,x.^2)

What’s wrong with this plot?

Look at plotEx1aV2.m for better ways to define x

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 8 / 21

Basic Plot

Basic example: plotEx1a.mx=-2:2;

plot(x,x.^2)

What’s wrong with this plot?

Look at plotEx1aV2.m for better ways to define x

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 8 / 21

Formatting Plots

Line Specifiers (pages 121-123):

LineStyleLineColorMarkerType

More formatting in Chapter 5: LineWidth, MarkerSize, etc.

Look up and experiment with the different types!

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 9 / 21

More formatting

Good commandsaxis

grid

xlabel, etc.xlim, etc.title

text

legend

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 10 / 21

More formatting

Good commandsaxis

grid

xlabel, etc.xlim, etc.title

text

legend

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 10 / 21

More formatting

Good commandsaxis

grid

xlabel, etc.

xlim, etc.title

text

legend

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 10 / 21

More formatting

Good commandsaxis

grid

xlabel, etc.xlim, etc.

title

text

legend

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 10 / 21

More formatting

Good commandsaxis

grid

xlabel, etc.xlim, etc.title

text

legend

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 10 / 21

More formatting

Good commandsaxis

grid

xlabel, etc.xlim, etc.title

text

legend

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 10 / 21

More formatting

Good commandsaxis

grid

xlabel, etc.xlim, etc.title

text

legend

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 10 / 21

3D Plots

To plot a space curve

Example~r(t) = (3 cos t, 3 sin t, t)plot3(x,y,z) with x, y, z already defined as in 2D plotsORplot3(x,y,z, ’line specifiers’, ’Property Name’, prop

values)

Look at plotEx3a.m

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 11 / 21

3D Plots

To plot a space curve

Example~r(t) = (3 cos t, 3 sin t, t)plot3(x,y,z) with x, y, z already defined as in 2D plotsORplot3(x,y,z, ’line specifiers’, ’Property Name’, prop

values)

Look at plotEx3a.m

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 11 / 21

3D Plots (mesh/surface/contour, etc.)

To plot z = f(x, y), 4 main steps

1 establish the domain for x and y

2 create grid in xy-plane3 calculate z (z is calculated for each point in “grid”)4 make the mesh, surface plots, etc.

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 12 / 21

3D Plots (mesh/surface/contour, etc.)

To plot z = f(x, y), 4 main steps

1 establish the domain for x and y

2 create grid in xy-plane

3 calculate z (z is calculated for each point in “grid”)4 make the mesh, surface plots, etc.

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 12 / 21

3D Plots (mesh/surface/contour, etc.)

To plot z = f(x, y), 4 main steps

1 establish the domain for x and y

2 create grid in xy-plane3 calculate z (z is calculated for each point in “grid”)

4 make the mesh, surface plots, etc.

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 12 / 21

3D Plots (mesh/surface/contour, etc.)

To plot z = f(x, y), 4 main steps

1 establish the domain for x and y

2 create grid in xy-plane3 calculate z (z is calculated for each point in “grid”)4 make the mesh, surface plots, etc.

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 12 / 21

Creating the grid using meshgrid

ExampleDomain is −1 ≤ x ≤ 3, 1 ≤ y ≤ 4

u = -1:3;

v = 1:4;

[x, y] = meshgrid(u,v)

(can use whatever letters, names you want)

[x, y] are matrices of the x and y coords, respectively

(u,v) are the vectors for the domain of x and y (created throughlinspace, etc)

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 13 / 21

Creating the grid using meshgrid

ExampleDomain is −1 ≤ x ≤ 3, 1 ≤ y ≤ 4

u = -1:3;

v = 1:4;

[x, y] = meshgrid(u,v)

(can use whatever letters, names you want)

[x, y] are matrices of the x and y coords, respectively

(u,v) are the vectors for the domain of x and y (created throughlinspace, etc)

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 13 / 21

Creating the grid using meshgrid

ExampleDomain is −1 ≤ x ≤ 3, 1 ≤ y ≤ 4

u = -1:3;

v = 1:4;

[x, y] = meshgrid(u,v)

(can use whatever letters, names you want)

[x, y] are matrices of the x and y coords, respectively

(u,v) are the vectors for the domain of x and y (created throughlinspace, etc)

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 13 / 21

Creating the grid using meshgrid

ExampleDomain is −1 ≤ x ≤ 3, 1 ≤ y ≤ 4

u = -1:3;

v = 1:4;

[x, y] = meshgrid(u,v)

(can use whatever letters, names you want)

[x, y] are matrices of the x and y coords, respectively

(u,v) are the vectors for the domain of x and y (created throughlinspace, etc)

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 13 / 21

Creating the grid using meshgrid

ExampleDomain is −1 ≤ x ≤ 3, 1 ≤ y ≤ 4

u = -1:3;

v = 1:4;

[x, y] = meshgrid(u,v)

(can use whatever letters, names you want)

[x, y] are matrices of the x and y coords, respectively

(u,v) are the vectors for the domain of x and y (created throughlinspace, etc)

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 13 / 21

Calculating z

If you have already created a meshgrid using above example andletters and want to graph

z =3xy2 + 2

x2 + y2

z = (3*x.*y.^2+2)./(x.^2 + y.^2);

Then can usemesh(x,y,z) OR

surf(x,y,z)

(Those are the most common... there are others listed in the book)

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 14 / 21

Calculating z

If you have already created a meshgrid using above example andletters and want to graph

z =3xy2 + 2

x2 + y2

z = (3*x.*y.^2+2)./(x.^2 + y.^2);

Then can usemesh(x,y,z) OR

surf(x,y,z)

(Those are the most common... there are others listed in the book)

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 14 / 21

Calculating z

If you have already created a meshgrid using above example andletters and want to graph

z =3xy2 + 2

x2 + y2

z = (3*x.*y.^2+2)./(x.^2 + y.^2);

Then can usemesh(x,y,z)

OR

surf(x,y,z)

(Those are the most common... there are others listed in the book)

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 14 / 21

Calculating z

If you have already created a meshgrid using above example andletters and want to graph

z =3xy2 + 2

x2 + y2

z = (3*x.*y.^2+2)./(x.^2 + y.^2);

Then can usemesh(x,y,z) OR

surf(x,y,z)

(Those are the most common... there are others listed in the book)

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 14 / 21

Making the plots

Good: xlabel(’x’); ylabel(’y’); zlabel(’z’);

title(’title text’)

Notice the look: maybe should have had

u = linspace(-1,3); v = linspace(1,4);

Different plotsmesh, surfmeshz, meshcsurfc, surflwaterfallcontour, contour3

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 15 / 21

Making the plots

Good: xlabel(’x’); ylabel(’y’); zlabel(’z’);

title(’title text’)

Notice the look: maybe should have had

u = linspace(-1,3); v = linspace(1,4);

Different plotsmesh, surfmeshz, meshcsurfc, surflwaterfallcontour, contour3

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 15 / 21

Making the plots

Good: xlabel(’x’); ylabel(’y’); zlabel(’z’);

title(’title text’)

Notice the look: maybe should have had

u = linspace(-1,3); v = linspace(1,4);

Different plotsmesh, surfmeshz, meshcsurfc, surflwaterfallcontour, contour3

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 15 / 21

View command

view(az,el) OR view([az, el])az = azimuth: angle (in degrees) in xy-plane measured relative tonegative y-axis in COUNTERCLOCKWISE direction

el = elevation: elevation angle (in degrees) from xy-plane

DEFAULT: az = −37.5◦, el = 30◦

projection plane az elxy (top) 0 90xz (side) 0 0yz (side) 90 0

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 16 / 21

View command

view(az,el) OR view([az, el])az = azimuth: angle (in degrees) in xy-plane measured relative tonegative y-axis in COUNTERCLOCKWISE direction

el = elevation: elevation angle (in degrees) from xy-plane

DEFAULT: az = −37.5◦, el = 30◦

projection plane az elxy (top) 0 90xz (side) 0 0yz (side) 90 0

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 16 / 21

View command

view(az,el) OR view([az, el])az = azimuth: angle (in degrees) in xy-plane measured relative tonegative y-axis in COUNTERCLOCKWISE direction

el = elevation: elevation angle (in degrees) from xy-plane

DEFAULT: az = −37.5◦, el = 30◦

projection plane az elxy (top) 0 90xz (side) 0 0yz (side) 90 0

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 16 / 21

Contour Plots

If want to create contour lines:

contour(z,n)

n is the number of lines/levels you want

or

contour3(z,n) or contourf(z,n)

If you want the levels to be labeled:

[c, h] = contour(z, n); clabel(c, h);

MATLAB help: Contour plots... labeling

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 17 / 21

Contour Plots

If want to create contour lines:

contour(z,n)

n is the number of lines/levels you want

or

contour3(z,n) or contourf(z,n)

If you want the levels to be labeled:

[c, h] = contour(z, n); clabel(c, h);

MATLAB help: Contour plots... labeling

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 17 / 21

Contour Plots

If want to create contour lines:

contour(z,n)

n is the number of lines/levels you want

or

contour3(z,n) or contourf(z,n)

If you want the levels to be labeled:

[c, h] = contour(z, n); clabel(c, h);

MATLAB help: Contour plots... labeling

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 17 / 21

Contour Plots

If want to create contour lines:

contour(z,n)

n is the number of lines/levels you want

or

contour3(z,n) or contourf(z,n)

If you want the levels to be labeled:

[c, h] = contour(z, n); clabel(c, h);

MATLAB help: Contour plots... labeling

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 17 / 21

Basic Plot Examples

plotEx1a.m: Basic exampleplotEx1b.m: Basic fplot exampleplotEx1c.m: Lots of command examples to format plot

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 18 / 21

Multiple Plot Examples

plotEx2a.m: Basic multiple plot exampleplotEx2b.m: Using Line SpecifiersplotEx2c.m: Example of hold on, legends, etc.plotEx2d.m: Using fplot and adding pointsplotEx2e.m: More formatting, and adding manual axes

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 19 / 21

Using subplot

plotEx2f.m: Example of subplot using fplot

plotEx2g.m: Example where plot goes across cellsplotEx2h.m: Adding titles to subplotsplotEx2i.m: Example of subplot using plot and formatting the filefor better viewing and editing

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 20 / 21

3D Plot Examples

plotEx3a.m: Space curve examplesplotEx3b.m: 3D surface (and mesh) examples

L. Oberbroeckling (Loyola University) MATLAB 09/23/10 Lecture 21 / 21