Graphics Programs Reference
In-Depth Information
T
T
S
E
NE
SW
N
E
N
S
B
B
B
W
W
(b)
(c)
(a)
Figure 4.30: Cubic Panoramic Projection.
Figure 4.31a shows two faces (we'll call them panels) of a cube viewed from the
positive
z
direction. Each face of the cube is 2
k
units long, and we see the two panels
located at
x
=
k
and
y
=
k
. Figure 4.31b shows the two panels after they have been
rotated to stand side by side, and we look at their outside surfaces. To best visualize
this, imagine that there are hinges between the two panels, so they look like a folding
closet door (notice the direction of the
x
axis). The figure indicates that the
x
=
k
panel is parallel to the
yz
plane, which is why all points on it have coordinates of the
form (
k, y, z
), while the
y
=
k
panel is parallel to the
xz
plane and all its points are of
the form (
x, k, z
).
P
2
y
P
0
z
z
L
(
t
)
P
*
2
P
*
0
P
*
2
y
=
k
P
*
0
1/2
y
x
P
*
1
P
*
1
P
*
1
P
1
x
z
x
=
k
y
=
k
x
=
k
(b)
(a)
Figure 4.31: Cubic Projection of a Straight Segment.
We arbitrarily select the two points
P
1
=(4
k, k/
2
,
0) and
P
2
=(
k/
2
,
2
k,
1). The
former is projected to the
x
=
k
panel,wherepointshavecoordinates(
k, y, z
), which
is why it is projected to
P
1
=(
k, k/
8
,
0). The latter is projected to the
y
=
k
panel,
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