Graphics Reference
In-Depth Information
obtained by subtracting the corresponding tail coordinates from the head coordinates: 3
−
1
=
2,
and its vertical component is obtained by subtracting 2
1.
From the mid-19th to mid-20th centuries, two methods appeared to combine the x
(horizontal) and y (vertical) components: one technique places the components as an ordered
pair as xy , and the other places them as
y
.
The former is called a
row vector
, while the
latter is known as a
column vector
. In this text, we employ column vectors. However, when a
column vector is referred to within a block of text, it is written as
xy
T
, which depicts a
transposed row vector
, i.e., a column vector, which saves space on the printed page.
No restrictions are placed upon vectors — they can be any length and point in any direction.
However, as vectors are often computed from other vectors, it is possible to create a vector
with no length — such a vector is called a
null
or
zero vector
. Figure 2.2 shows four vectors
labeled
a
b
c
, and
d
, and Table 2.1 summarises their head and tail coordinates and x and y
components.
−
1
=
Y
3
a
b
2
c
d
1
1
2
3
4
X
Figure 2.2.
Table 2.1
Vector
Head coordinates
Tail coordinates
x
component
y
component
−
−
a
02
33
3
1
b
43
22
2
1
c
12
10
0
2
d
31
21
1
0
Thus, the vectors are
−
2
1
0
2
1
0
3
a
=
b
=
c
=
d
=
−
1
