Computes an RQ decomposition of 3x3 matrices

[R,Q] = cv.RQDecomp3x3(M)
[R,Q,S] = cv.RQDecomp3x3(M)

Input

• M 3x3 input matrix.

Output

• R 3x3 upper-triangular matrix.
• Q 3x3 orthogonal matrix.
• S Optional output struct with the following fields:
  • Qx 3x3 rotation matrix around x-axis.
  • Qy 3x3 rotation matrix around y-axis.
  • Qz 3x3 rotation matrix around z-axis.
  • eulerAngles 3-element vector containing three Euler angles of rotation in degrees.

The function computes a RQ decomposition using the given rotations. This function is used in cv.decomposeProjectionMatrix to decompose the left 3x3 submatrix of a projection matrix into a camera and a rotation matrix.

It optionally returns three rotation matrices, one for each axis, and the three Euler angles (as the return value) that could be used in OpenGL. Note, there is always more than one sequence of rotations about the three principle axes that results in the same orientation of an object, eg. see [Slabaugh]. Returned tree rotation matrices and corresponding three Euler angules are only one of the possible solutions.

References

[Slabaugh]:

Gregory G Slabaugh. "Computing euler angles from a rotation matrix". Retrieved on August, 6:2000, 1999.