Revision 5b3ef302f54bcc77cff98bd05018d873621812c1 (click the page title to view the current version)
3D Mathematics
Reading Ma (2004) Chapter 2 + Appendix A
Briefing
- Recap Change of Basis
- New Representations of 3D Motion
- (More on 3D Motion)
Exercises
Note. Exercises in parentheses are optional. Please skip these unless you have a lot of time.
All exercises are from Ma 2004 page 38ff
- Exercise 2.1 a+d (b+c). (See Definition A.12 page 446.)
- (Exercise 2.2) (See Definition A.7 page 444 and A.29 page 454)
- Exercise 2.3. (See Definition A.13 page 447.)
- ?? Exercise 2.4.
- Exercise 2.5.
Exercise 2.6.
If you prefer, you can consider transformations in 3D instead, with the matrices \[ R_1= \begin{bmatrix} \cos\theta & -\sin\theta & 0 \\ \sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \quad R_2= \begin{bmatrix} \sin\theta & \cos\theta & 0 \\ \cos\theta & -\sin\theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \] The relationship between the two matrices will be the same in 2D and 3D.- Exercise 2.7.
Exercise 2.10.
TODO From the textbook
Debrief
Continue on 3D Mathematics