© 2001 by CRC Press LLC
3. Construct a (2
⊗
(
n
+ 1) matrix, the
G
matrix, where the elements
of the Frst row consist of the ordered (
n
+ 1)-tuplet, (
x
1
,
x
2
,
x
3
, …,
x
n
,
x
1
), and those of the second row consists of the corresponding
y
coordinates (
n
+ 1)-tuplet.
4. Plot the second row of
G
as function of its Frst row.
Example 9.1
Plot the trapezoid whose vertices are located at the points (2, 1), (6, 1), (5, 3),
and (3, 3).
Solution:
Enter and execute the following commands:
G=[2 6 5 3 2; 1 1 3 3 1];
plot(G(1,:),G(2,:))
To ensure that the exact geometrical shape is properly reproduced, remember
to instruct your computer to choose the axes such that you have equal
x
-range and
y
-range and an aspect ratio of 1. If you would like to add any text
anywhere in the Fgure, use the command
gtext
.
9.1.2
Inversion about the Origin and Refection about the Coordinate
Axes
We concern ourselves here with inversion with respect to the origin and with
re±ection about the
x-
or
y
-axis. Inversion about other points or re±ection
about other than the coordinate axes can be deduced from a composition of
the present transformations and those discussed later.
• The inversion about the origin changes the coordinates as follows:
(9.1)
In matrix form, this transformation can be represented by:
(9.2)
• ²or the re±ection about the
x
-axis, denoted by
P
x
, and the re±ection
about the
y
-axis, denoted by
P
y
, the transformation matrices are
given by:
′=−
xx
yy
P
=
−
−
10
01