Graphics Reference
In-Depth Information
Center=(20,30)
R adius=5
Center=(22,32)
Radius=0 . 5
Cen te r=(18,32)
Radius=0. 5
C enter=(20,30)
W=2, H=1
Center=( 2 0,27 . 5)
W=5, H=1
Center=(21.25,27.75)
W=H =0.5
Center=(19.25,27.25)
W=H=0.5
Figure 10.11.
WC window of the face from Figure 10.10.
figure geometric person of Figure 10.10, we can choose a more convenient WC
space to specify the face of Figure 9.21. Figure 10.11 shows a Window into the
WC to illustrate the details of the new geometric face. In this case, the rectangular
WC window is bounded by
15
=(
,
)=(
,
) ,
center
cx wc
cy wc
20
30
x
25
WC window
=
35 =
width
=
W wc =
10
,
25
y
height
=
H wc =
10
.
Linearity of affine transfor-
mation. Recall that to trans-
form geometric contents be-
tween rectangular regions, we
can concentrate on construct-
ing the operator that trans-
forms between the rectangles
that surround the regions. The
contents inside the rectangles
will transform proportionally.
If we want to display the content of this WC window, we must construct an
appropriate M w 2 n operator. As we saw in Figure 10.8, as programmers of the
D3D graphics API, our goal is to construct the M w 2 n operator to transform the
WC window into D3D's internal coordinate system, i.e., the NDC. In turn, D3D
will automatically transform the content of the NDC to the drawing area on the
application window.
Figure 10.12 illustrates one way to construct the M w 2 n operator, where we
first move the center of the region to the origin and then scale the region into a
2
×
2 area, or
S 2
2
10
M w 2 n =
T
(
20
,−
30
)
10 ,
.
(10.7)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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