Superposition and Transposition Chapter 9 Superposition and Transposition

Finding optimal Root mean square deviation

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

HW Example 9.1 In two dimensions

Translation In two dimensions Shift Centroids to the origin

Example HW 9.2 In two dimensions Rotation Matrix

The matrix in the book is just an angular rotation

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

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

Alternating Superposition and Alignment

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