1. Photogrammetry V: Dr. Gamal Hassan Seedahmed Dept. of Surveying Eng.
3D Rotation Matrix: Euler Representation
Dr. Gamal Hassan Seedahmed
Dept. of Surveying Eng.
Faculty of Eng.
University of Khartoum

2. 2D Rotation Matrix
It is a 2 x 2 matrix

3. 2D Rotation Matrix: Rotation by 30 degrees
MATLAB Code
MATLAB Results

4. 3D Rotation Angles

6. Rotation Matrix Around The X-Axis

7. Rx :Rotation by 30 deg
MATLAB Code
MATLAB Results

8. 3D Point Rotated By Rx

9. 3D Point Rotated By Rx (30 deg)

10. Derivative for Rx with respect to Omega

11. Rotation Matrix Around The Y-Axis

12. Rotation Matrix Around The Z-Axis

13. Closer Look to the structure of the 3 rotation matrices

14. Simultaneous Rotation By The 3 Angles

15. 3D Point Rotation by R

16. Properties of R
It is true for the transpose of R

17. Orthogonality Property of R
And similarly true for the other rows and columns

18. Rotation by an Angle Theta About an arbitrary Axis Containing the Origin and having Unit Length Direction W=(wo , w1 , w2 )

19. Example No. 1

20. Example No. 1: Results

21. Example No. 2

22. Example No. 2: Results

23. Example No. 3

24. Example No. 3: Results

25. Example No. 4

26. Example No. 4: Results

27. Major Properties of Rotation Matrix
The rotation matrix depends only on:
The rotation axis direction (w).
And the rotation angle.

28. General Representation of the 3D Rotation Matrix

29. How to compute theta from R?

30. How to compute S from R?