Homework #1
Matrices, Vectors, and Transforms
Due Thursday, September 13 by the end of class
Question #1: (20 points)
For each of the following homogeneous coordinates,
(a) (6 pts) state whether it is a point or a vector.
(b) (6 pts) state whether it is normalized or not.
(c) (8 pts) if it is not normalized, please normalize it; if it is already normalized, do
nothing.
Question #2: (15 points)
(a) (5 pts) Solve the following dot product: =
(b) (5pts) Solve the following cross product: =
(c) (5pts) State the equation for the plane defined by the vector [1, 2, 3, 0]T and the point [3, 2, 1,
1]T. Your answer should be in the form ax + by + cz + d = 0.
Question #3: (35 points)
Part I:
Write out the following 4x4 matrices and label each with the following names:
• (4 pts) T0: Translate in x by 4 and in y by 3
• (4 pts) R: Rotate about the z axis by pi/4 (45 degrees)
• (4 pts) T1: Translate in x by -4 and in y by -3
• (4 pts) S: Scale in x by a factor of 2, and y by a factor of 4 (z is unchanged)
1
5
9
1
11
8
6
4
5
7
2
0
7
7
7
0
1/ 2
0
1/ 2
0
14
7
21
1
2
−1
5
⋅
3
8
10
4
1
9
×
2
8
1
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