Home > FR3DSource > zAngleOfRotation.m

# zAngleOfRotation

## PURPOSE zAngleOfRotation calculates the angle of rotation from a rotation matrix R

## SYNOPSIS function [alpha] = zAngleOfRotation(R)

## DESCRIPTION ``` zAngleOfRotation calculates the angle of rotation from a rotation matrix R
A good online reference is:
http://www.mathworks.com/access/helpdesk/help/toolbox/physmod/mech/mech_review7.html```

## CROSS-REFERENCE INFORMATION This function calls:
This function is called by:
• xDiscrepancyFast xDiscrepancy(Model,Cand) calculates the discrepancy between Model and

## SOURCE CODE ```0001 % zAngleOfRotation calculates the angle of rotation from a rotation matrix R
0002 % A good online reference is:
0003 % http://www.mathworks.com/access/helpdesk/help/toolbox/physmod/mech/mech_review7.html
0004
0005 function [alpha] = zAngleOfRotation(R)
0006
0007 alpha = 2*acos(min(1,sqrt(trace(R)+1)/2));
0008
0009 % occasionally trace(R) is slightly greater than 3, making alpha complex
0010 %[trace(R)-3]
0011 %[ sqrt(trace(R)+1)/2 alpha]```

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