I'm currently studying the math involved with rotating vertices around an arbitrary axis in 3D space. For this, I have found the following page to be very helpful:

Conceptually, I get everything, however, when I try to multiply Txz-1, Tz-1, Rz(θ), Tz and Txz together, I can't get the result shown for the first matrix in 5.1.

The matrix for Txz is as follows:

enter image description here

The matrix for Tz is as follows:

enter image description here

And the matrix for Rz(θ) is as follows:

enter image description here

While not shown on the page, the matrices for Txz-1 and Tz-1 are easy enough to generate, but with all that said, could someone please give me some advice on how the author of the page is able to multiply those five matrices together and get the following result?

enter image description here

Thank you very much.

  • $\begingroup$ Maybe, this will be helpful. $\endgroup$ Apr 27, 2014 at 3:15
  • $\begingroup$ Felix, I looked at that link, but honestly cannot understand it. Could you please explain how that is beneficial in answering the question I asked? Thanks. $\endgroup$
    – HartleySan
    Apr 30, 2014 at 23:05


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