# dcm2angle

Create rotation angles from direction cosine matrix

## Syntax

[r1 r2 r3] = dcm2angle(n)
[r1 r2 r3] = dcm2angle(n, s)
[r1 r2 r3] = dcm2angle(n, s, lim)

## Description

[r1 r2 r3] = dcm2angle(n) calculates the set of rotation angles, r1, r2, r3, for a given direction cosine matrix, n. n is a 3-by-3-by-m matrix containing m direction cosine matrices. r1 returns an m array of first rotation angles. r2 returns an m array of second rotation angles. r3 returns an m array of third rotation angles. Rotation angles are output in radians.

[r1 r2 r3] = dcm2angle(n, s) calculates the set of rotation angles, r1, r2, r3, for a given direction cosine matrix, n, and a specified rotation sequence, s.

The default rotation sequence is 'ZYX', where r1 is z-axis rotation, r2 is y-axis rotation, and r3 is x-axis rotation.

Supported rotation sequence strings are 'ZYX', 'ZYZ', 'ZXY', 'ZXZ', 'YXZ', 'YXY', 'YZX', 'YZY', 'XYZ', 'XYX', 'XZY', and 'XZX'.

[r1 r2 r3] = dcm2angle(n, s, lim) calculates the set of rotation angles, r1, r2, r3, for a given direction cosine matrix, n, a specified rotation sequence, s, and a specified angle constraint, lim. lim is a string specifying either 'Default' or 'ZeroR3'. See Assumptions and Limitations for full definitions of angle constraints.

## Examples

Determine the rotation angles from direction cosine matrix:

dcm = [1 0 0; 0 1 0; 0 0 1];
[yaw, pitch, roll] = dcm2angle( dcm )
yaw =

0

pitch =

0

roll =

0

Determine the rotation angles from multiple direction cosine matrices:

dcm        = [ 1 0 0; 0 1 0; 0 0 1];
dcm(:,:,2) = [ 0.85253103550038   0.47703040785184  -0.21361840626067; ...
-0.43212157513194   0.87319830445628   0.22537893734811; ...
0.29404383655186  -0.09983341664683   0.95056378592206];
[pitch, roll, yaw] = dcm2angle( dcm, 'YXZ' )

pitch =

0
0.3000

roll =

0
0.1000

yaw =

0
0.5000

## Assumptions and Limitations

The 'Default' limitations for the 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' implementations generate an r2 angle that lies between ±90 degrees, and r1 and r3 angles that lie between ±180 degrees.

The 'Default' limitations for the 'ZYZ', 'ZXZ', 'YXY', 'YZY', 'XYX', and 'XZX' implementations generate an r2 angle that lies between 0 and 180 degrees, and r1 and r3 angles that lie between ±180 degrees.

The 'ZeroR3' limitations for the 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' implementations generate an r2 angle that lies between ±90 degrees, and r1 and r3 angles that lie between ±180 degrees. However, when r2 is ±90 degrees, r3 is set to 0 degrees.

The 'ZeroR3' limitations for the 'ZYZ', 'ZXZ', 'YXY', 'YZY', 'XYX', and 'XZX' implementations generate an r2 angle that lies between 0 and 180 degrees, and r1 and r3 angles that lie between ±180 degrees. However, when r2 is 0 or ±180 degrees, r3 is set to 0 degrees.