1
Assignment 2 (NonProgramming & Programming)
Worth:
5 points
Due Date and Time:
Before class begins at 12:20 pm on 06/12/2007. Copy zipped
programming submission to CS250 web page. Place your stapled nonprogramming
submission in CS250 submission box in front office.
Topics
•
Introduction to Graphics Pipe
•
Transforms: Scaling, Rotation, Translation, and View
NonProgramming Section: Statement (Worth 50 points)
•
Part 1: First, solve all three parts of exercise 5.15 from the text. The first part of
exercise 5.15 is to derive the transformation matrix that rotates by an angle
θ
about
u
ˆ
. The matrix is to be derived by composing the matrix that rotates
u
ˆ
into the
−
Z
axis (call this
M
) with a rotation transform
(
)
z
R
, then composing this result
with
1
M
−
.
The
resultant
matrix
is
written
as:
( )
( ) ( )
( )
( )
( )
( ) ( )
( )
−
+
+
−
−
−
−
−
−
+
+
−
+
−
−
−
−
+
1
0
0
0
0
1
cos
sin
cos
1
sin
cos
1
0
sin
cos
1
1
cos
sin
cos
1
0
sin
cos
1
sin
cos
1
1
cos
2
2
2
2
2
2
z
z
x
z
y
y
x
z
x
z
y
y
y
z
y
x
y
x
z
z
y
x
x
x
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
The second part is to verify that, if
u
ˆ
is a principal axis, the matrix reduces to
x
R
,
y
R
, or
z
R
. Finally, explain why negating
u
ˆ
and
leaves the result unchanged.
•
Part 2: Assume that we wish to align
p
ˆ
to
q
ˆ
by rotation in a plane containing both.
As explained in class, alignment from
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 Spring '07
 Ghali
 Computer Graphics, Rotation, Englishlanguage films

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