Graphics Reference
In-Depth Information
4.16
E
XERCISES
Section 4.2
4.2.1
Prove equation (4.3).
4.2.2
Find the world-to-camera coordinates transformation T in two dimensions given the
following data: the camera is at (1,4) looking in direction (-1,-3) with the view “plane”
(a line) a distance
10
in front of the camera.
4.2.3
Find the world-to-camera coordinates transformation T in three dimensions given that
the camera is at (2,3,5) looking in direction (-1,2,1) with the view plane a distance 7 in
front of the camera.
Section 4.3
4.3.1
A camera is situated at the origin looking in direction
v
. Find the vanishing points of
the view defined by lines parallel to the standard unit cube when
(a)
v
= (2,0,3)
(b)
v
= (0,3,0)
(c)
v
= (3,1,2)
Section 4.5
4.5.1
With regard to Figure 4.11 show that the regions below are mapped as indicated:
-
<
zw
< -
1
Æ <
1
zw
< +•
-<
1
zw
<
0
Æ -•<
zw
<
0
0
<
zw
< + •Æ <
0
zw
< +
1
Note that z/w denotes the “real” z coordinate of a projective point (x,y,z,w).
4.5.2
Assume that the near and far planes for a camera are z = 2 and z = 51, respectively, in
camera coordinates. If the view plane is z = 5, find the matrix M
hcamÆhclip
.
Section 4.7
4.7.1
Explain how the case (0,0,0,0) can occur.
Section 4.9
4.9.1
Prove Proposition 4.9.1.
Compute the parallel projection of
R
3
onto the x-y plane in the direction
v
= (2,1,5).
4.9.2
Compute the parallel projection of
R
3
4.9.3
onto the plane x - 2y + 3z = 1 in the direction
v
= (2,1,-3).
