This preview shows page 1. Sign up to view the full content.
CS480/CS680 Problem Set 1
Due in class Tuesday, February 12 at the beginning of lecture.
Please prepare the answers to these questions, neatly written or typed, on separate paper.
1. (a) (3 points) Write a
4
×
4
homogeneous transform matrix
M
that when applied to a point
(
x,y,z,
1)
yields
(
x
0
,y
0
,z
0
,w
0
)
where
x
0
=

1
√
2
x

1
√
2
z
+
a
y
0
=

2
y
z
0
=
1
√
2
z

1
√
2
x
+
a
w
0
=
1
(b) (12 points)In words
, what four basic computer graphics transforms occur when we apply
M
to a 3D point? Give a homogeneous transform matrix for each, and show the order in
which they are multiplied.
2. (15 points) We have a unit cube centered at the point
c
= (1
.
5
,
0
.
5
,
2
.
5)
. Derive the ho
mogeneous transformation matrix that will rotate the cube by angle
θ
around a vector in the
direction
v
= (1,0,1). The pivot point for the rotation is the cube’s center
c
.
3. Use quaternions in your answers to the following.
•
(5 points) Prove that in general two 3D rotations about different rotation axes do not
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Sclaroff

Click to edit the document details