Graphics Reference
In-Depth Information
where
s
x
and
s
y
are the factors of scaling in the
x
-axis and
y
-axis directions, re-
spectively. We represent this scaling operation as
V
as
=
V
a
S
(
s
x
,
s
y
)=
V
a
S
.
=
Figure 8.5 shows an example where the scaling operator has scale factors of
s
x
3
=
.
and
s
y
0
5, or
Y-a
xis
S
(
s
x
,
s
y
)=
S
(
3
,
0
.
5
)
,
S(3,0.5)
V
a
(3,8)
operating on the point
V
a
:
V
as
(9,4)
V
a
=
x
a
y
a
=
38
X-axis
Origin
and
resizing
the point to the new position
V
as
:
Figure 8.5.
The scale
operator.
V
as
=
x
as
y
as
=
V
a
S
(
s
x
,
s
y
)
=
x
a
×
s
y
s
x
y
a
×
=
3
5
×
38
×
0
.
94
=
.
Notice that we can work with the
x
and the
y
scaling factors independently: the
amount of size change in the
x
-axis direction is defined solely by the
s
x
parameter
and is unrelated to
s
y
in any way. Typically, scaling factors are positive floating-
point numbers.
0 has the effect of
stretching
a
point in the positive direction of the corresponding axis, whereas a factor less
than 1
A scaling factor greater than 1
.
Y-axis
0 has the effect of compressing a point toward the origin. From Figure 8.5,
we see that
s
x
.
=
3 stretches
x
a
(the
x
-component of
V
a
) from
x
=
3to
x
=
9,
S(3,0.5)
)
will push
all
input points to the origin. As in the case of the translation operator,
the scaling operator repositions a point relative to the point's initial position, and
this operation is independent of any other points.
=
.
=
=
(
,
whereas
s
y
0
5 compresses
y
a
from
y
8to
y
4. Scaling factors of
S
0
0
V
c
=
(1,5)
V
cs
=(3
,
2.5)
X-axis
Origin
Figure 8.6.
Scaling two
points with
S
(
3
,
0
.
5
)
.
As we saw in the case of translation, this property allows us to apply the same
operator on any number of points. Figure 8.6 shows that we can apply the same
S
(
,
.
)
3
0
5
operator on the point
V
c
:
V
c
=
x
c
y
c
=
15
,
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