Graphics Reference
In-Depth Information
V
a
b
Rectangle:
R
i
c
T(-1,-5)
d
Rectangle:
R
t
S(3,0.5)
V
at
V
bt
V
ats
V
bts
V
dt
V
cts
V
dts
Edge:
e
bct
Edge:
e
cdt
V
ct
Rectangle:
R
ts
Figure 9.5.
Combining translate and scale operators on a rectangle.
values. Now, if a vertex has 0 for its
x
-coordinate value (e.g.,
V
bt
and
V
ct
),
then the scaling in the
x
-direction will not affect these vertices. Notice that
this has the effect of keeping the left side of the rectangle stationary while
stretching the right side of the rectangle by
s
x
. As a result, the scaling oper-
ation will change the size of the rectangle by a factor of
s
x
. Because the left
side of the rectangle does not move under the scaling operation, we have
eliminated the horizontal component of the moving side effect.
•
Edge
e
cdt
.
This edge resides on the
x
-axis. Similar to the reason given
above for
e
bct
, since the vertices (i.e.,
V
bt
and
V
ct
) that define this edge have
0for
y
-coordinate values, these vertices are not affected by
s
y
. As a result,
when applying the scaling factor
s
y
, we press down the edge
e
cdt
and com-
press the other vertices along the
y
-axis direction. This has the effect of
keeping the bottom edge of the rectangle stationary when stretching/com-
pressing the top edge of the rectangle by a factor of
s
y
. Once again, because
the bottom edge of the rectangle does not move, we have eliminated the ver-
tical component of the moving side effect.
•
Vertex
V
ct
.
This vertex is at the origin and is not affected by any scaling
operation.
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