If I am required to compute the full transformation matrix compromising of the following sequence of

Quintin Stafford 2022-06-26 Answered
If I am required to compute the full transformation matrix compromising of the following sequence of operations:
rotation by 30 degrees about x-axis
translation by 1, -1, 4 in x, y and z, respectively
rotation by 45 degrees about y axis
Can I compute the rotation, translation and rotation matrix or would I be required to compute the rotation, rotation and translation matrix?
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Answers (1)

hildiadau0o
Answered 2022-06-27 Author has 21 answers
Since this question has been lingering for a long time, I decided to create an answer. I had to make some assumptions since you were not completely specific as to the directions of your rotations. In your case we have (using affine 4 × 4 matrices acting on the left of column vectors)
[ 1 0 0 0 0 3 / 2 1 / 2 0 0 1 / 2 3 / 2 0 0 0 0 1 ] (counterclockwise 30 degrees around x)
[ 1 0 0 1 0 1 0 1 0 0 1 4 0 0 0 1 ] (add (1,-1,4) to the x,y,z components)
[ 2 / 2 0 2 / 2 0 0 1 0 0 2 / 2 0 2 / 2 0 0 0 0 1 ] (counterclockwise rotation around y)
Multiplying them in the order they are applied, (if the matrices above are A,B,C, then that order is CBA in my notation) that makes a final transformation of
[ 2 / 2 2 / 4 6 / 4 3 2 / 2 0 3 / 2 1 / 2 1 2 / 2 2 / 4 6 / 4 5 2 / 2 0 0 0 1 ]
With the same matrices, one can see that changing the order of multiplication changes this final transformation.

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