Page 30 - Numerical Analysis Using MATLAB and Excel

Using MATLAB to Make Plots

The command plot3(x,y,z,'bd−') will display the plot in blue diamonds, connected with a solid
line.

In a three−dimensional plot, we can use the zlabel(‘string’) command in addition to the xla-
bel(‘string’) and ylabel(‘string’).

x
y
In a two−dimensional plot, we can set the limits of the − and − axes with the axis([xmin
xmax ymin ymax]) command. Likewise, in a three−dimensional plot we can set the limits of all
three axes with the axis([xmin xmax ymin ymax zmin zmax]) command. It must be placed
after the plot(x,y) or plot3(x,y,z) commands, or on the same line without first executing the plot
command. This must be done for each plot. The three−dimensional text(x,y,z,’string’) command
will place string beginning at the co−ordinate (xy z,, ) on the plot.

For three−dimensional plots, grid on and box off are the default states.
The mesh(x,y,z) command displays a three−dimensional plot. Another command, contour(Z,n),
draws contour lines for n levels. We can also use the mesh(x,y,z) command with two vector argu-
ments. These must be defined as length x() = n and length y() = m where
]
,
[ mn = size Z() . In this case, the vertices of the mesh lines are the triples x j() yi() Zi j,(,,{ ) . }
We observe that x corresponds to the columns of , and y corresponds to the rows of . Z
Z
,
(
To produce a mesh plot of a function of two variables, say z = f x y ) , we must first generate the
Y
X and matrices which consist of repeated rows and columns over the range of the variables x
Y
y
X
and . We can generate the matrices and with the [X,Y]=meshgrid(x,y) function which
X
creates the matrix whose rows are copies of the vector x, and the matrix whose columns are
Y
copies of the vector y.
Example 1.12
r
h
The volume of a right circular cone of radius and height is given by
V
--πr h
V = 1 2 (1.14)
3
≤≤
Plot the volume of the cone as and vary on the intervals 0 r 4 and 0h6≤ ≤ meters.
r
h
Solution:
(
h
,
r
The volume of the cone is a function of both the radius and the height , that is, V = f r h )
The three−dimensional plot is created with the following MATLAB script where, as in the previ-
ous example, in the second line we have used the dot multiplication, division, and exponentia-
tion. As mentioned in the footnote of the previous page, this topic will be explained in Section
1.8, Page 1−19.

Numerical Analysis Using MATLAB® and Excel®, Third Edition 1−17
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