Graphics Reference
In-Depth Information
so that the person in the photo occupies about the same visual area as your friend.
Is this in fact the distance at which you are likely to view the photo? Try to explain
what your brain might be doing when it views such a photo at a distance other than
this “ideal.”
Exercise 13.8:
(a) Fixate on a point on a wall in front of you, and place your
arms outstretched to either side. Wiggle your fingers, and move your arms forward
until you can
just
detect, in your peripheral vision, the motion on both sides, while
remaining fixated on the point in front of you. Have a friend measure the angle
subtended by your two arms, at your eyepoint. This gives you some idea of your
actual field of view, at least for motion detection.
(b) Have a friend stand behind you, holding his hands out in place of yours, but
showing either one, two, or three fingers on each hand. Ask him to move them
forward until you can tell how many fingers he's holding up on each hand (while
still fixating on the wall). Measure the angle subtended by his hands at your eyes
to get a sense of your field of view for nonmoving object comprehension.
Exercise 13.9:
We said that the unhinging transform in the
zw
-plane was
uniquely determined by three properties: The plane
z
=
f
transforms to
z
=
0;
the eye, at
(
z
,
w
)=(
0, 1
)
, transforms to a point with
w
=
0; and the plane
z
=
−
/
n
1
remains fixed. In this exercise, you'll prove this. Restricting to the
x
=
y
=
0
plane, this last constraint says that the point
(
z
,
w
)=(
−
−
1, 1
)
transforms to itself.
To start with, the matrix we seek is unknown:
M
=
ab
cd
.
(a) Show that the condition on the transformation of the eyepoint implies that
d
=
0.
(b) Now setting
d
=
0, show that the third condition implies that
c
=
−
1 and
a
=
b
+
1.
(c) Finally, show that the first condition implies
b
=
n
/
(
f
−
n
)
, and solve for
a
as
well.
