Graphics Reference
In-Depth Information
Applying the
R
(
45
◦
)
operator on four points.
Figure 8.15.
Now, if we examine the distance
d
acr
between the two output points
V
ar
and
V
cr
,
we have
d
acr
=
(
x
ar
−
x
cr
)
2
+(
y
ar
−
y
cr
)
2
2
2
≈
(
2
.
8
−
2
.
1
)
+(
8
.
5
−
4
.
9
)
≈
3
.
6
.
From this example, we see that although
V
a
and
V
c
are rotated along the circum-
Rotation operator.
Maintains
the size and shape of an object,
but not the orientation.
ferences of circles with different radii (
C
a
and
C
c
), and the orientation of output
points (
V
ar
and
V
cr
) appear to be very different from that of the input points, the
distance between points remains constant. In general, this property of constant
distance (size) is true for any rotation.
Figure 8.15 shows the effect of applying
45
◦
)
the
R
(
operator on four vertices that form a rectangle:
⎧
⎨
V
a
=(
8
,
4
)
,
V
b
=(
5
,
4
)
,
Input points :
⎩
V
c
=(
5
,
2
)
,
V
d
=(
,
)
.
8
2
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