GMod: Hovering cube with six thrusters, now functioning optimally

In this stream I demonstrate and reconstruct a control scheme for a cube with six thrusters. My setup is:
Garry's mod with:
- Wiremod
http://www.wiremod.com/
- Smartsnap (not necessary to build, just works well for precise easywelds)
https://steamcommunity.com/sharedfiles/filedetails/?id=104815552

In my original stream earlier this week, I walked through the problem of making a cube hover in various orientations. My previous solution used the Pitch and Roll angles of the cube, and the cosine of the Roll angle to scale the thruster on each face of the cube to balance the force needed to negate gravity. However, since the top and bottom thrusters accounted only for the roll (and not both the pitch and roll), it would thrust itself excessively in one direction. I recognized that I needed the cosine of the pitch+roll, a sum which is sort of unintuitive to work with and, as I realized, not the most elegant solution.

Throughout this week, I realized that I could find the cosine of that angle via the dot product. By comparing the top, right, and forward vectors of the object with the world gravity vector through the dot product, I was able to find the scale factor for each thruster to balance the forces, and achieved a hovering (although spinning) cube. Applications of this include working with similar devices thrust by fans.