1. Superposition and Transposition
Chapter 9
Superposition and Transposition

2. Finding optimal Root mean square deviation

3. Process Degrees of freedom include Equivalenced elements Rotation
Translation (usually centroid)

4. HW Example 9.1
In two dimensions

5. Translation
In two dimensions
Shift Centroids to the origin

9. Example HW 9.2
In two dimensions
Rotation Matrix

10. The matrix in the book is just an angular rotation

11. The first step Transpose centroids to the origin
Foreach angular displacement in x
Foreach angular displacement in y
Calculate RMSD
If this RMSD is less than current minimum, save it

12. But, how did we get the equivalenced elements?
First seed the problem with an initial equivalence E0
Then find the Transformation that results in a minimum RMSD
Use this Transformation to find a better equivalence

13. Alternating Superposition and Alignment

14. Example The best rotation and translation is then found and a new
alignment is generated