User:DavidJCobb

I'm working on a Papyrus library for working with rotations. For now, this is my scratchpad. When the library's complete, I plan on posting it here. Searching for this information was a hellish task, and I'll gladly save others the trouble.

Scratchpad

• Import is unreliable, and I don't know what makes it break. It works in some cases, but in others, it completely fails to import global functions from the target file.
  • Errors will not be generated when compiling in the Creation Kit. You'll only be able to detect the problem by checking the Papyrus logs, which will contain something like
    Error: Method ImportedFunctionName not found on EntityThatHasAScriptThatImportsStuff. Aborting call and returning None
  • It's consistent: if it doesn't work for a file, then it will probably never work for that file (barring massive changes).
  • You can work around this by referencing all functions in the script to be imported as methods, e.g. ScriptToBeImported.FunctionName().

Progress made

• My code appears to be able to reliably convert Skyrim Euler rotations to rotation matrices and back again.
  • We don't handle an edge-case properly when converting back from matrices to Euler angles.
• My code appears to be able to reliably convert rotation matrices to axis-angles and back again.
• My code appears to be able to reliably convert axis-angles to quaternions, and to convert quaternions to rotation matrices.
• Thus, I can convert between all four rotation representations without getting too indirect.

Remaining tasks

• Successfully put the library to use.
  • Fix conversion from matrices to Euler in cases where cos(Y) == 0.
  • Fix quaternion multiplication.
  • Test quaternion conjugation, if necessary.
• Post the library here on the wiki, along with a tutorial on how to use it.
  • Tutorial idea: a Dibella Statue that sets itself to a random orientation, and then positions (using this code) and rotates (using my code) a Dragon Priest mask to cover the statue's face.
    • Step 1: Place a Dibella Statue at 0, 0, 0, unrotated.
    • Step 2: Place and rotate a Dragon Priest Mask as necessary to cover the statue's face.
    • Step 3: Note down the mask's position and rotation.
    • Step 4: Configure some sort of simple example script that I will provide, setting the mask position and rotation as properties.
    • Step 5: Slap the script down on the statue and test it!

Rotation resources

This page generates forumlae to convert from Euler angles (in any convention) to rotation matrices.

This page and this page together offer the information needed to convert from Euler angles (in any convention) to an axis-angle representation by way of rotation matrices. The axis you get won't be normalized.

This page describes how to pull right-handed Euler ZYX from a rotation matrix. It's easy to convert the math to left-handed if you use the matrix formula generator linked earlier and if you understand what atan2 does and why.

The process of converting from axis angle to quaternion (and vice versa) is one of the few rotation-related operations that Wikipedia explains in plain English. Ten bucks says a pack of PhDs will eventually come along and rewrite the article into gibberish, so that's a link to an archived version of the article as it existed when I found it.

In another rare instance of clarity, Wikipedia describes how to convert from axis-angle back to a rotation matrix. The article doesn't state whether it's working with extrinsic rotations, or what the handedness of the system is, but it seems to line up with the math at one of the previously-linked pages.

Converting any Euler sequence to a rotation matrix

Source: https://web.archive.org/web/20110721191940/http://cgafaq.info/wiki/Euler_angles_from_matrix

Corrected (Wikipedia-compatible) versions of that site's LaTeX are as follows:

"Symmetries" equation 1

  P = \begin{bmatrix} 0&1&0\\0&0&1\\1&0&0 \end{bmatrix}

"Symmetries" equation 2

  P = \begin{bmatrix} 0&0&1\\0&1&0\\1&0&0 \end{bmatrix}

"First merger" equation 1

\begin{align} {\mathrm rot}({\mathbf{xzy}_s},\theta_x,\theta_z,\theta_y) &= {\mathrm rot}(y,\theta_y)\,{\mathrm rot}(z,\theta_z)\,{\mathrm rot}(x,\theta_x) \\ &= \begin{bmatrix} c_y c_z & s_y s_x - c_y s_z c_x & s_y c_x + c_y s_z s_x \\ s_z & c_z c_x & -c_z s_x \\ -s_y c_z & c_y s_x + s_y s_z c_x & c_y c_x - s_y s_z s_x \end{bmatrix} \end{align}

"First merger" equation 2

\begin{align} {\mathrm rot}({\mathbf{xzx}_s},\theta_x,\theta_z,\theta_{x'}) &= {\mathrm rot}(x,\theta_{x'})\,{\mathrm rot}(z,\theta_z)\,{\mathrm rot}(x,\theta_x) \\ &= \begin{bmatrix} c_z & -s_z c_x & s_z s_x \\ c_{x'} s_z & c_{x'} c_z c_x - s_{x'} s_x & -s_{x'} c_x - c_{x'} c_z s_x \\ s_{x'} s_z & s_{x'} c_z c_x + c_{x'} s_x & c_{x'} c_x - s_{x'} c_z s_x \end{bmatrix} \end{align}

"First merger" equation 3

{\mathrm rot}(z,\theta_z)\,{\mathrm rot}(x,\theta_x) = \begin{bmatrix} c_z & -s_z c_x & s_z s_x \\ s_z & c_z c_x & -c_z s_x \\ 0 & s_x & c_x \end{bmatrix}