Plotting functions
6 Plotting functions
One of the most exciting uses of MATLAB is its ability to easily
create the graph of a function. Suppose that we wish to plot the
graph of the parabola
y=
x^{2} over the interval 2
£ x £ 2.
How might we do this?
If you wanted to plot this on a piece of paper, you might generate a
table of numbers such as
x 
2 
1 
0 
1 
2 
y 
4 
1 
0 
1 
4 
Then you would plot each point (
x,
y) and connect the values with
a curve which seemed appropriate  in this case a parabola. Let's
call this way of plotting ``
x vs.
y''.
Another way you might want to plot is to simply tell the computer to
plot the function ``
x^{2}''. The command to plot a
symbolic function
will be
ezplot
.
MATLAB knows of other types of plots as well:
 Parametric plots: these allow you to plot x versus y only,
these are
parameterized by a third variable say t for time. Here's an example of
plotting the circle:
x(t) = cos(t), y(t)=sin(t); 2 £ t £ 2.
>> t =linspace(0,2*pi);
>> x = cos(t);y=sin(t);
>> plot(x,y); % notice we define x and y interms of
% t, but we plot x vs y
 Polar plots: to plot in polar coordinates
 Threedimensional plots: plotting x, y and z.
You may be interested in some extensions to the basic MATLAB plotting
scheme.
 makemenus
: Adds nice menus to plotting window which
allow you to add text to graphs easily, to rotate axes, and other
things. You can read about it in this file
makemenu.README. The files are available on the
MATHWORKS
website, or on the math department site. At the math
department site the windows
files are in makemenu.exe and the
UNIX
files are here
makemenu.tar.
6.1 Plotting x versus y
We see here how to
plot
functions, by plotting a table of values for
x and
y=
f(
x).
Example: Cost of a used car
Suppose you were interested in buying a used car. You may want to
know the relationship between number of miles the car has and the
value of the car. Such numbers are available on the internet, for
example these numbers were found at
http://www.kbb.com. The price of a used
1996 Jeep Cherokee is figured according to the number of miles
given. Here is some sample data:
Mileage 
Estimated Price 
5,000 
23,225 
10,000 
23,050 
20,000 
22,900 
40,000 
19,900 
60,000 
17,600 
80,000 
16,800 
100,000 
16,500 
We want to understand the relationship between the two variables,
and from the table alone we have a hard time viewing the exact
one. It is clear that as the mileage increase the cost decreases,
but what is the relationship: is it linear, or exponential or
something else? One way to see is with a plot of the two
variables. To do this in MATLAB we need to put the two lists of
numbers into a plotting function. The commands to do this are given
below:
>> mileage = [5,10,20,40,60,80,100]; % skip the thousands
>> cost = [23.225, 23.050, 22.9, 19.9, 17.6, 16.8, 16.5]; % in thousands
>> plot(mileage,cost)
Figure 8: Plot of used car mileage versus cost
From the graph we can see an interesting relationship not obvious from
the table. For low, low mileage cars the graph is kind of flat
prsumably as people believe the car is practically new, but as the
mileage increases the cost decrease rapidly after a certain point.
This may be explained by the realization that people shouldn't have to
pay for the mileage already on the car, and the loss of warranty. The
graph is more or less linear here. This eventually tails off as the
mileage gets real high and the graph flattens out.
It is precisely the ability of plots or graphs to convey information
quickly and clearly that makes them so invaluable. In this section you
can learn how to create them.
6.1.1 Plotting lines
We all know that two points determine a line. What does this mean?
We'll use MATLAB to plot the graph of a line using just two points.
First you may want to recall some basic formulas to describe lines:
Concept: Equations for lines
Let's translate this into MATLAB commands:
Example:
For definiteness, we want to plot the line connecting (1,2) to
(5,7). First lets define the points. How should we do this? Lets
pair off the
x values and the
y values:
>> x=[1,5];y=[2,7];
Now we can use MATLAB to reference the individual components if we
need to. Notice how this is done:
>> x(1)
ans = 1
>> y(2)
ans = 7
So we could compute the slope by
m = ( y(2)  y(1) )/ ( x(2)  x(1) )
Or we could
plot
the line by
>> plot(x,y)
Figure 9: plot of line segment
Notice this draws a line between our two points. What if we wanted
to plot the line over a specified interval, say [0,5]. We have a
slope, and a range of
x values, and a point (1,2). Using the
pointslope form
we know we should use the
formula
y =
m (
x 
x_{1}) +
y_{1}. We know
m and
x_{1} and
y_{1},
what do we do with
x and
y?
When plotting, we need to make a table of values for
x and a corresponding table of values for
y. In MATLAB this is done
by letting
x be a list or
vector
or numbers and then
creating
y based on
x. To do this we can use the
linspace
command:
>> x = linspace(0,5); % 100 evenlyspace numbers between 0
% and 5
>> y = m * (x  x(1)) + y(1); % pointslope form
>> plot(x,y);
Example: plot of farenheit
Let's plot the relationship between farenheit and celsius. Recall
the formula is
F = 9/5
C + 32. The interesting range of values
might be for celsius between 0 and 100.
>> celsius = linspace(0,100); % the domain
>> farenheit = 9/5 * celsius + 32 % our formula
>> plot(celsius,farenheit) % the plot
>> hold on;
>> plot(farenheit,celsius) % the inverse bunction
6.1.2 Plotting functions
Suppose that we wish to plot the graph of the parabola
y=
x^{2} over
the interval 2
£ x £ 2. In the absence of MATLAB, we could
choose a set of
x values, say,
x=2,1,0,1,2, then square each
x
value to determine the corresponding
y values,
y=4,1,0,1,4. We
then mark each corresponding (
x,
y) pair as a point on a Cartesian
coordinate system. These pairs are
{(2,4),(1,1),(0,0),(1,1),(2,4)}. Finally, we try to connect these
points smoothly to obtain a sketch of the parabola. To create a graph
of
y=
x^{2} using only the same 5 points as described above, we can
issue the following MATLAB commands.
>> x=2:1:2; % creates the array x=[2 1 0 1 2]
>> y=x.^2; % creates the array y=[ 4 1 0 1 4]; note the ``dot" after x
>> plot(x,y)
Figure 10: plot of y=x^{2}, not enough points
A brief explanation is in order. The first line defines
x to be the
list
(or row
vector
) of values starting with 2,
continuing in steps of 1, and ending at 2. (This uses the
colon
operator
.) The second line defines
y
as the array of values which are the squares of the
x values. That
is, the
y list is obtained by squaring the
x list
elementbyelement.
See a description
here
of the
dot operator
).
What you see should be a crude graph of the function
y=
x^{2}
consisting of a sequence of broken lines connecting the (x,y) points
calculated. To create the graph, MATLAB simply starts with the first
point, connects it with a
straight line to the second point,
and connects the second point with a
straight line to the
third point, and so on. Thus every graph in MATLAB consists of a
sequence of straight lines.
If you wish to obtain a smoother
graph, all you have to do is use more points. But this requires no more labor
on your part than using just 5 points. The following commands should create a
much smoother graph as they utilize 201 points to construct the graph. Although
it may no longer be evident, the graph still consists of a
sequence of straight lines!
>> x=2:0.01:2; % creates the array x=[2 1.9900 1.9800 ... 1.9900 2]
>> y=x.^2; % creates the array y=[ 4 3.9601 3.9201 ... 3.9601 4]
>> plot(x,y)
Figure 11: plot of y=x^{2}, more points
Graphing functions  more details
Here are a number of different examples of how we can use MATLAB to
plot functions.
 Continuous Functions
A function f(x) is a set of ordered pairs (x,y) such that
y=f(x). To create a graph of this function we first form two
lists x=[x_{1},x_{2},...,x_{n}], and
y=[y_{1},y_{2},...,y_{n}] where y_{i}=f(x_{i}), i=1,2,···,n and then
issue the MATLAB command
plot
.
Example: Plot of y=e^{x}
As an example, let us create a graph of the function y=e^{x}
describing each step in detail.
First decide the domain of the function and the desired
frequency of plot points. Suppose that we let x vary from 1
to +1 in steps of 0.2. This is accomplished by the command:
>> x = 1 : 0.2 : 1; % or use linspace(1,1,11)
This creates an array with 11 elements starting at x = 1,
increasing steps of .2 and ending at x = 1. If you do not type
the `;' at the end of the command line you can see the array
created as
x = [1, .8, .6, .4, .2, 0, .2, .4, .6, .8, 1]
Recall (Generating lists of data)
for the explanation of the
colon operator
. (that x=a:h:b
generates an array of values starting at x=a, increasing in
steps of `h' without exceeding x=b. Thus, this command will
divide the interval [a, b] into n equal parts
(n = (b  a)/h), thus sampling the domain at (n + 1) points
including the two end points.
 For each value of x, calculate the corresponding value of
y. This is accomplished by the command:
>> y = exp(x);
Note that the builtin function
exp(x)
is defined
such that if the argument x is an array, then it generates
an array y of function values corresponding to each of the
x values. Thus, y is now an array of 11 elements. If the
semicolon at the end of the line is omitted you will see this
array as:
y = [.3679, .4493, .5488, .8187, 1.0000,
1.2214, 1.4918, 1.8221, 2.2255, 2.7183]
 To obtain a continuous plot of e^{x} over the domain
[1,1], issue the command
>> plot(x,y)
Figure 12: plot of f(x)=e^{x}
The desired continuous graph will be created on the screen.
Here, continuous plot means that MATLAB marks
each ordered pair (x_{i},y_{i}), i=0,1,2,...,n on the graph and
then connects, by a straight line, the point
(x_{0},y_{0}) to (x_{1},y_{1}), the point (x_{1},y_{1}) to
(x_{2},y_{2}), and so on until the point (x_{n},y_{n}) is reached.
This graph created with 11 sample points is obviously not so
smooth. Thus to obtain a smooth looking curve one needs to take
sufficiently many x points depending on how rapidly the
function varies over its domain. The following three commands
may be used to obtain a smoother graph;
>> x = 1 : 0.01 : 1 ; y = exp(x) ; plot(x,y),grid
We have added a
grid
command at the end to produce a set
of grid lines on the graph. Note that we have used a smaller
step size of 0.01 giving us 201 (2/.01 = 200) sampled
points and therefore a much smoother graph.

Discrete plots
At times, instead of a continuous plot we may wish to
obtain a discrete plot or point plot whereby the
points are marked on the graph but they are not connected to each
other by straight lines. In that case we need to specify the symbol
we wish to use to mark each point. Supposing that the symbol is
`*'
, the plot command becomes
>> plot(x,y,`*')
Try this and see what happens.
MATLAB permits only a limited number of symbols to be used in
discrete
plot
s. These are the symbols
*, `.', `+',`x',`o'.
Example: Discrete Plots
To see the discrete points distinctly, you should use a reduced
number of sample points, by taking a larger step size:
>> x=1:0.2:1; y=exp(x); plot(x,y,`*'), grid
which will produce a discrete graph with exactly 11 points.
A convenient way to control the number of points on a graph
without calculating the corresponding step size over the domain of
definition is to use the builtin function
linspace
.
Using this function, the above graph can be obtained by entering
>> x=linspace(1,1,11); y=exp(x); plot(x,y,`*'), grid
More generally, the command x=linspace(a,b,n);
generates n
points equally spaced over the closed interval [a,b]. Note that if
you wish to divide an interval into 10 equal subintervals, you
need 11 points including the end points of the interval. If you
omit n
then the command linspace(a,b)
generates 100
equally spaced points over [a,b].
 GRAPHING MORE THAN ONE FUNCTION ON THE SAME GRAPH
You can plot more than one function at a time by using the plot
command in a extended way.
Example: Amplitude vs. Period
Let's investigate the relationship between the amplitude and the
period for the
cosine
function. Recall
Concept: the generic form of a cosine function
y = a + d cos(b x + c).

The value of a determines the shift up or down the
yaxis
 The value of d is the amplitude.
 The value of b determines the period by the formula T =
2p/b.
 The value of c determines the phase shift. (it
is not c, but rather c/b.
Plot the function y=4cos x and y=cos 4x together over the
interval 0£ x £ 2p.
>> x=0:pi/100:2*pi; y1=4*cos(x); y2=cos(4*x); plot(x,y1,x,y2), grid
Figure 13: 2 plots on same graph
By giving MATLAB data in this form it knows to graph both
functions. Note that MATLAB decides a frame which fits in all
function values, and then creates a plot of each function. If you
have a color monitor, different colors will be used for each
function.
Another way to achieve this is with the
hold
function:
>> x=0:pi/100:2*pi; y1=4*cos(x); y2=cos(4*x);
>> hold on; % prevents second graph
>> plot(x,y1), grid % from overwriting the
>> plot(x,y2) % first
The hold
command has two uses hold on or
hold off. This toggles whether or not MATLAB will try to
draw the next graph without erasing the previous one.
Example: Secant line example
Concept: Definition of the secant
line
The secant line is the beginning of the study of derivatives in
calculus. It involves lines, and their slopes. The fundamental
thing to know is the following definition:
The limit of the slope of the secant line (if it exists) is
the derivative of the function.
Let y=f(x) be a function and let x_{1},x_{2} be two points in its
domain and consider the secant line connecting the two
points P_{1}=(x_{1},f(x_{1})) and P_{2}=(x_{2},f(x_{2})) on the graph of
this function. The
slope
of this secant
line is given by
m=(f(x_{2})f(x_{1}))/(x_{2}x_{1}).
This represents the average slope of the function f(x) on the
interval [x_{1}, x_{2}].
Another way we see this written is to let h = x_{2}  x_{1} be the
difference between the two points x_{2} and x_{1}. Then the
formula for the slope becomes
m=(f(x_{1}+h)f(x_{1}))/h,
and the
derivative
of f(x) at the point x_{1} is given
by
f'(x_{1}) = 

(f(x_{1}+h)f(x_{1}))/h.

To see the secant line and the function on the same graph, we need
to
plot
both functions simultaneously. This is done via the
hold
command: Let f(x) = sin(x), and let x_{1} = p/4,
and x_{2} = x_{1} + h where h = p/8. We'll plot the secant line
and the function between 0 and p/2.
>> x1=pi/4;h=pi/8;x=linspace(0,pi/2); % assign the constants
>> m = (sin(x1+h)  sin(x1))/h; % find the slope
>> ysin = sin(x); % the y values for f(x)
>> yline = m*(xx1) + sin(x1) % pointslope form of a line
>> hold on; % turn on hold
>> plot(x,ysin) % plots the function
>> plot(x,xline) % plots the line
You should see both plots on the graph.
 GRAPHING FUNCTIONS OVER DOMAINS WITH DELETED POINT(S)
When we do not have a
continuous function then we have
to do more work to plot it with MATLAB.
Example: Deleted points in the domain
Plot f(x) =1/(x^{2}1) over [0,2]: Notice the function
f(x) is a
discontinuous function at
x=1. First try typing:
>> x = 0 : 0.05 : 2; y = (1)./(x.^21);^ plot(x,y), grid
What does the graph look like?
The function is undefined at x = 1. In processing you
can avoid that point by dividing the domain into two parts. Notice
we avoid the point x=1.
>> x1 = 0 : 0.05 : 0.95; y1 = (1)./(x1.^21);
>> x2 = 1.05 : 0.05 : 2; y2 = (1)./(x2.^21);
>> plot(x1,y1,x2,y2),grid
Mathematically, we plotted the following function:
f(x) =

ì í î 
1/(x^{2}1) 
0 £ x < 1 
1/(x^{2}1) 
1 < x £ 2 


f(x) = (x^{2} 1)^{1} if x ¹ 0, f(0)=0.
Figure 14:
 PLOTTING FUNCTIONS DEFINED BY MORE THAN ONE EQUATION
Many functions in Mathematics need to be defined in a piecebypiece
fashion. For example the
absolute value
function, or the
greatestinteger function. To plot these we have to use MATLAB in a
piece by piece fashion as well
Example: The sign function
Plot the following function, sometimes called the, sign
function, over the interval [3,3] defined as follows
f(x) =

ì í î 
x / x 
if x ¹ 0, 
0 
if x = 0 


f(x) = x/x if x ¹ 0, f(0) = 0.
Define
>> x1=linspace(3,0); y1=abs(x1)./x1; % 3<x<0
>> x2=linspace(0,3); y2=abs(x2)./x2; % 0<x<3
>> plot(x1,y1,0,0,'*',x2,y2), grid
Figure 15: plot of sign function
Note that in the
plot
command, the single point at the
origin is being marked with a `*' to make it visible. This one
is not well suited for the
hold
command.
6.2 plotting with ezplot
6.3 Parametric plots
6.4 Polar plots
6.5 Threedimensional plots
MATLAB has some abilities to work with 3dimensional plots. In this
section you can learn how to plot
As well, you can plot 3d trajectories with the
mfiles
csimovie.m
You may find the
makemenus
mfiles
to be of use with
manipulating the graphing window. Among other things, these allow you
to use the mouse to rotate the viewing angle.
6.5.1 Threedimensional plotting functions
To plot with three dimensions we use the following builtin MATLAB
functions:
meshgrid
,
plot3
,
surf
,
view
,
sphere
,
cylinder
.
As well, we will define several short
mfiles
that facilitate
the plotting process. These use the MATLAB commands above to plot.
6.5.2 Plotting vectors
Plotting vectors is as easy as connecting two points with a
line. Recall in two dimensions, to connect two points we use the
plot
command. An example is given here
>> plot([1,5],[2,7]);
This plots the line between the points (1,2) and (5,7). In other
words, the command
plot(x,y) plots the list of numbers in
x versus those in
y connecting the points
(
x_{i},
y_{i}) to the points (
x_{i+1},
y_{i+1}). The
plot3
command does exactly the same thing, only it needs three coordinates
for a point as it plots threedimensional points. So to connect the
point (1,2,3) to the point (5,7,8) we could use the command
>> plot3([1,5],[2,7],[3,8]); % connects the two points with a line
Notice, you may have your points given in terms of a vector, say
v=
á 1,2,3
ñ to plot these you can access the
individual components as follows
>> v = [1,2,3]; plot3(v(1),v(2),v(3)); % plots the point associated to
% the vector v
The simple
mfiles
qvector.m will allow you to plot
a vector with the command
qvector(v)
6.5.3 Plotting planes
To plot a line in two dimensions you make values of
x and
corresponding values of
y and plot the pair of lists. For
example this will plot a line
>> m = 5; b = 2; % y = mx + b
>> x = linspace(5,10); % plot the line between 5 and 10
>> y = m*x+b;plot(x,y); % make the plot
We need to do exactly the same thing to plot a plane in MATLAB. So we
need to generalize the linspace command and go from there.
Concept: equation of a plane
Recall the equation of a plane which is normal to the vector
v, and goes through the point
P=(
x_{0},
y_{0},
z_{0}) is given by
n · á x  x_{0}, y  y_{0} , z  z_{0} ñ = 0
or solving, if
n =
á a,
b,
cñ then one has
a x + by + cz = d = n · (P) = ax_{0} + by_{0} + c z_{0}.
if
c is not 0 then we can solve to get
z = (
d 
ax 
by)/
c.
So to plot a plane we first generate a mesh of values for
x
and
y, then we find
z and then we plot using the
surf
command. Here is an example
>> n = [1,2,3];p=[3,2,1]; % normal to n, through p
>> [x,y] = meshgrid(1:.1:1, 2,.1:1); % meshgrid like linspace.
>> z = (dot(n,p)  n(1) * x  n(2) * y)/n(3); % n(3) non zero
>> surf(x,y,z); % plots the surface
The
mfiles
qplane.m will automate this for you, and
plot the vector as well.
An important command for viewing planes is the
view
command. This allows you to change perspective.
>> view(n); % called with a vector. What is the
% output?
>> view([3,0,1]); % a vector parallel to plane. Where did
% the plane go?
>> view([1,1,1]) % view from the point (1,1,1)
6.5.4 Plotting Cylinders
Concept: Plotting Cylinders
In Calculus, a cylinder is defined to be all the points which lie on
lines that are parallel to a given vector, and go through a given
curve. For example, the usual cylinder we think of is made up of all
points on the lines parallel to the
z
axis, or the vector
k, that go through the curve given by
x^{2}+
y^{2}=1.
To plot a cylinder then we could simply shift the curve in the
direction of our vector and then trace out the curve, repeating this
several times. Here is an example
>> t = (0:25)*pi/25; % or linspace(0,pi,25)
>> x = t; y = sin(t); % parameterize the sine curve
>> z = zeros(size(x)); % make z a list of 0's, the same size
% as x
>> v=[1,2,3]; % our vector
>> plot3(x,y,z);
>> hold on;
>> for k=(0:10)/10 % loop between 0 and 1 10 times
plot3(x + k*v(1),y + k*v(2),z + k*v(3)); % plot the curve shifted
end
This is automated by the
mfiles
qcylindr.m
(notice the silly spelling). (This is different than the built in
MATLAB command
cylinder
which plots a surface of revolution
despite its name.)
To use the
qcylinder command, we need to trace out a
parameterized curve in the
x,
yplane, and pick a vector. Here are some
examples
>> t = linspace(0,2*pi);x = cos(t);y=sin(t);
>> qcylindr(x,y,[0,0,1]) % parallel to zaxis
>> qcylindr(x,y,[0,1,1]) % parallel to the vector [0,1,1]
>> x = linspace(0,6*pi);y = sin(x); % a sine wave cylinder
>> qcylindr(x,y,[0,1,1]) % parallel to the vector [0,1,1]
6.5.5 Plotting surfaces of revolution
Concept: Surfaces of revolution
Surfaces of revolution are surfaces associated with equations of
the form
x^{2} + y^{2} = [f(z)]^{2}
or any permutations of the three variables. The one above is a
surface of revolution about the
zaxis. Notice for a fixed value
of
z. the curve is a circle with radius 
f(
z).
To plot a surface of revolution there is the MATLAB command cylinder.
(A cylinder is a surface of revolution, as well as a mathematical
cylinder.) If you don't like the language cylinder for a surface of
revolution, you can use the
mfiles
qsurfrev.m
instead. Here are some examples, first Gabriel's horn (what is its
volume? What is its surface area?)
>> z = linspace(1,100);r = (1)./z; % notice the dot
>> cylinder(r); % or qsurfrev(r)
Here is how a cylinder is a surface of revolution:
>> z = linspace(1:10); r = ones(size(z)); % all ones??
>> cylinder(r); % a cylinder!
Here is cone:
>> z = linspace(1,10); m = 2; r = m*z; % cone with ``slope'' 2
>> cylinder(r); % or use qsurfrev
Here is a sphere:
>> z = 1:.1:1; r = sqrt(1  z.^2); % notice the dot
>> cylinder(r); % or use qsurfrev
6.5.6 Plotting vectorvalued functions
To plot a vectorvalued function we need to associate a vector with a
point. The point is the terminal point of the vector if its initial
point is at the origin. Thus is the vector
á 1,2,3
ñ
then the point associated to this vector is the point (1,2,3). This
is an easy concept to grasp, but is also very easy to get confused.
A vectorvalued function that we can plot should be a function of a
single variable, returning a vector in 2 or 3 dimensions. For
concreteness, we will consider functions of the type
f(
t) =
á x(
t),
y(
t),
z(
y)
ñ. That is, the function returns a
threedimensional vector.
To plot, we simply associate the point with the vector, then this
becomes the same problem as drawing a parameterized curve in three
dimensions.
This will hopefully become clear with some examples:
Here is a helix: The function we are graphing is
f(
t) =
á cos(
t), sin(
t),
tñ.
>> t = linspace(0,4*pi);
>> x = cos(t);y=sin(t);z=t;
>> plot3(x,y,z); % plots the parameterized curve
Here is a straight line given by a point and a vector:
>> p = [1,2,3]; v = [0,1,3]; % a point and a vector
>> t = linspace(3,3);
>> x = p(1) + t*v(1); y = p(2) + t*v(2); z = p(3) + t*v(3);
>> plot3(x,y,z); % plots the line. Use view to get
% different views
Here is the flight of a baseball to right center
>> t = linspace(0,5);
>> x = 100 * cos(pi/4) * cos(pi/6) t;
>> y = 100 * cos(pi/4) * sin(pi/6)*t;
>> z = 3 + 100 * sin(pi/4) * t  16 * t.^2; % notice the dot
>> plot3(x,y,z);
6.5.7 Plotting functions z=f(x,y)
The plot of a function
z =
f(
x,
y) is done by plotting the triples of
points (
x,
y,
f(
x,
y)), just as the plot of the function
y=
f(
x) is the
plot of the pairs of points (
x,
f(
x)). To do such a plot, we need to
define the values of
x and
y which is done with
meshgrid
and then find the corresponding
z values. This exactly what we needed to
do to plot and plane, and the idea is no different. Here are some
examples.
Here is the plot of the bell curve
>> temp = 3:.1:3;[x,y]=meshgrid(temp,temp);
>> z = (1/sqrt(2*pi)) * exp((x.^2+y.^2)/2); % the bell curve
>> surf(x,y,z); % use the surf command
Plot the egg carton
f(
x,
y) = sin(
x) * sin(
y):
>> temp = 3*pi:.1:3*pi;[x,y]=meshgrid(temp,temp);
>> z = sin(x) .* sin(y); % notice the ``dot''
>> surf(x,y,z)
Plot the function
f(
x,
y) = cos((
x^{2} + 2
y^{2})/4)
>> temp = pi:.1:pi; [x,y]=meshgrid(temp,temp);
>> z = cos((x.^2 + 2*y.^2)/4);
>> surf(x,y,z);
6.5.8 Plotting with csimovie.m
You can use the function
csimovie
top plot 3d
trajectories. Try the
help
command to find out more
information. The file
csimovie.m is installed on the CSI
network, or can be found here for you to install.