Hello!
This is the perfect opportunity to bring up something I’ve noticed that vastly differs from my experience studying mathematics. Two things: How to label the axes and orientation.
In 3D calculus, my experience has been that the Z-axis is always up. I made sense of this because all throughout simpler math classes, we drew the XY-place on a flat piece of paper on our desk. When adding a third dimension, the only place to go is out. Makes sense for math and taking notes. In Unity (and perhaps game development as a whole, I don’t have the experience to say that it is industry standard), the Z-axis is forward. It really threw me for a loop but I’ve now accepted it as a rule.
With respect to handedness, I bring up orientation. In my calculus experience and even my experience in physics, I was used to things a certain way. Never did I use the left-handed rule. Always, it was the right-handed rule that helped determine the correct or positive orientation of a surface. Placing the side of your right hand on a coordinate system, with the thumb ejecting outward representing a positive Z direction, your fingers curled in the direction of a positively orientated rotation (counter-clockwise). Putting your right hand on the underside of that surface would result in a Negative Z direction and a negative orientation for rotation.
It’s very interesting to see that we are working with a left-handed coordinate system and that it isn’t even inappropriate to do so. That might take a little more getting used to.
I suppose that’s just the way it goes when you learn something through one lens, and view it again with a different one. Nevertheless, I appreciate both perspectives.
GK