How to transform angles to a transformation matrix?

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I'm working on an open source project. I need to transform three angles (X, Y, Z) to a matrix.

The matrix is a standard 4x3 homogeneous transformation matrix, where the right column describes the translation.

Angles are in input :

  • X : 20
  • Y : 20
  • Z : 0 (disabled)

Rotations are applied in this order : X, Y, Z.

The matrix in output is :

\begin{matrix} 0.993998507596972 & -0.041215528655313 & 0.101332359553377 & 0 \\ 0.0593914715688805 & 0.981226162107692 & -0.183488070185209 & 0 \\ -0.09186740444725 & 0.188405145877369 & 0.977785191648479 & 0 \\ \end{matrix}

How can I transform angles to this matrix ? And reverse this matrix to initial angles ?

Thanks for your help, and your explanation.

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Your question is a bit vague. However, I think it is related to Euler angles.