Graphics Programs Reference
In-Depth Information
where its
y
coordinate must be
k
, so it is projected to
P
2
=(
k/
4
,k,
1
/
2). We denote by
L
(
t
) the straight segment connecting
P
1
to
P
2
and compute it (from Equation (Ans.7))
as the weighted sum
L
(
t
)=(1
7
tk/
2
,k/
2+3
tk/
2
,t
). Next, we
determine the coordinates of point
P
0
on this segment. This point will be projected to
thecubecornerwhere
x
=
y
=
k
,soits
x
and
y
coordinates must be equal even before
it is projected. Since
P
0
is on segment
L
(
t
), it must equal
L
(
t
0
)forsome
t
0
.Thus,we
can compute
t
0
from the relation 4
k −
7
t
0
k/
2=
k/
2+3
t
0
k/
2, which yields
t
0
=7
/
10.
The coordinates of
P
0
are therefore
L
(
t
0
)=(
3
20
k,
3
20
k,
−
t
)
P
1
+
t
P
2
=(4
k
−
7
10
), and this is projected to
P
0
=(
k, k,
7
20
31
)=(
k, k,
14
/
31).
Once the
z
coordinate of
P
0
is known, we can compute the slopes of the two
segments that constitute the projection of
L
(
t
). On the
y
=
k
panel, the slope is
10
×
1
14
31
2
−
2
31
k
,
=
3
k
4
whereas on the
x
=
k
panel it is
14
31
−
0
16
31
k
.
=
7
k
8
The straight segment connecting
P
1
to
P
2
has been projected into two segments that
are straight but travel with different slopes on the two panels. Because of the symmetry
of a cube, there is no difference between horizontal and vertical lines and they all feature
the same discontinuity of slope between panels.
Exercise 4.12:
In what cases will the slopes be continuous across a panel boundary?
It is clear that a panorama made of six squares doesn't create a satisfying visual
sensation, and Figure 4.32 (courtesy of Shinji Araya) proves this claim. The figure
shows a beautiful scene, but the projection seems fractionated and unnatural. This
lack of artistic value is why the cubic panoramic projection was not seen much in
the past. Currently, however, cubic panoramas are very popular because version 5 of
the popular
QuickTime
software for the Macintosh computer can create this type of
panoramic projection and can also scroll it on the monitor screen such that the viewer
can eventually examine a field of view that encompasses 180
◦
vertically and a full 360
◦
horizontally. The main advantage of this scrolling is that it eliminates the discontinuities
of the slopes between panels. The image seems to flow smoothly on the screen without
any jumps or distortions. Such a panorama cannot be included in a topic, but many
can be found on the Internet by searching under “cubic panorama.”
MakeCubic is a simple OSX-ready app for creating cubic QTVR movies from six faces
or from equirectangular (a kind of sphere-to-rectangle projection which is used in some
java-based players and other places) images.
—From
http://developer.apple.com/quicktime/quicktimeintro/tools/
Search WWH ::
Custom Search