Efficient Vector Rotation Matrix Routine

Efficient Method to Determine a Matrix Needed to Rotate One Vector to Another
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Updated 23 Apr 2014

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Suppose you have a unit vector described by f = [ai bj ck] and you would like to rotate f such that its result is t = [di ej fk]. This routine will find R(f,t) such that R(f,t)*f’ = t’. Where R(f,t) is known as the 3 x 3 transformation matrix needed to rotate f into t.
This MATLAB routine was based on a published article titled “Efficiently Building a Matrix to Rotate One Vector to Another” written by Tomas Moller and John Hughes in 1999.

This method features no square roots or trigonometric function calls and is reported to be faster than any other vector rotation matrix method tested by Moller and Hughes. In fact, the Goldman method (fastest method tested) was 50% slower than this routine in conversion speed tests.

Working Example:

Unit Vector f:
>> f = rand(1,3);
>> f = f./norm(f);

Unit Vector t:
>> t = rand(1,3);
>> t = t./norm(t);

The transformation matrix R(f,t) is found:
>> R = vecRotMat(f,t);

Now, test that R*f’= t’
>> R*f’

Cite As

Darin Koblick (2024). Efficient Vector Rotation Matrix Routine (https://www.mathworks.com/matlabcentral/fileexchange/37597-efficient-vector-rotation-matrix-routine), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2012a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.1.0.0

Added robustness to parallel vector check. Added extra check to account for vectors that are parallel and have two or more identical values. Rotation error was found to be on the order of 1e-15.

1.0.0.0