Lecture 3 Supplement

1
Lecture 3 Supplement

• Prof. Hsien-Hsin Sean Lee
• School of Electrical and Computer Engineering
• Georgia Institute of Technology

2
Rotation Along an Arbitrary Axis

• Transform the axis to cross origin (0,0,0)
• Transform the axis around X onto the XZ plane
• Transform the axis around Y onto the Z axis
• Perform Rotation (angle?)
• Inverse Transform of 3.
• Inverse Transform of 2.
• Inverse Transform of 1.

3
Step 1 Translate to (0, 0, 0)
Rotating axis

• For easier viewing, I use RHS.

4
Step 2 Rotate around X, project to XZ
y
(a, b, c)
b
?
z
x (into the screen)
c

• Lets pick up a random point (a, b, c) on the
  axis to figure out cos?

5
Step 3 Transform around Y onto the Z axis
y
a
x
y (into the screen)
?
x
?
(a, 0, c)
z
z
6
Step 4 Perform Rotation (angle?) on Z
7
Combine all matrices with Step 5, 6, 7