The RIGIDTFORM function efficiently solves for the optimal rotation and translation between two sets of corresponding points in N dimensions. The solution minimizes the root mean squared deviation between the two sets of points. This is a generalization to N dimensions of the Kabsch algorithm using singular value decomposition. The technique is described for three dimensions here.

[R,T] = RIGIDTFORM(P1,P2) returns the rotation matrix, R, and translation vector, T, for the optimal rigid transform between two sets of corresponding N-dimensional points, P1 and P2. Each row of the equal-sized, real-valued floating point matrices P1 and P2 represents the N-dimensional coordinates of a point. The outputs, R and T, are N-by-N and 1-by-N arrays, respectively. The transform can be applied as P1(i,:)*R+T to rotate and translate P1 to P2 or as (P2(i,:)-T)*R' to go from P2 to P1.

[...] = RIGIDTFORM(P1,P2,DIM) optionally specifies which dimension the points are stored in of the two datasets, P1 and P2. The default is 1, i.e., each row represents the coordinates of a point. If DIM is 2, each column represents the coordinates of a point and the outputs R and T are transposed such that the transform can be applied as R*P1(:,i)+T to rotate and translate P1 to P2.

[R,T,ERR] = RIGIDTFORM(...) returns the root mean squared error between each corresponding point in the datasets P1 and P2 as a column vector. If DIM is 2, ERR is transposed.  

Andrew D. Horchler, horchler @ gmail . com, biorobots.case.edu
Created: 12-8-16, Revision: 1.0, 2-17-17

This version tested with Matlab 9.1.0.441655 (R2016b)
Mac OS X 10.12.3 (Build: 16D32), Java 1.7.0_75-b13
Compatibility maintained back through Matlab 8.3 (R2014a)
 

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