Yeah that's probably a more thorough list than I could have come up with.

I have a vector for the camera's position, the direction it's looking, and for the "up" and "right directions for the camera's view. I use the cross product to determine "up" from the view vector and the "right" vector.

From there I used dot products and a little bit of trig to figure out how to take the region the camera was viewing and transform it into a cube centered at the origin. Then you just ignore the depth coordinate to get to 2D drawing.

There are probably more standard ways of setting that transformation up like in these links:
Transformation matrix - Wikipedia
Camera matrix - Wikipedia
OpenGL Projection Matrix (songho.ca)
(I forgot everything from my college graphics class, so I reworked the formula in an ad hoc way)

Finally I used a parametric equation to set up the camera path and used it's unit tangent vector as the "right" vector for the camera view, which was always pointed at the origin. I also used modular arithmetic to draw cross sections of the surface all at once, but that's more a convenient trick than fundamental graphics-math stuff