I am impressed at the number of people reacting with « Euler angles are fine » or « quaternions are fine, we always did this way ». Having worked extensively with them it is obvious that Euler angles are broken beyound repair (singularities, 12 competing variations...) and quaternion are too (they only work in 3D). This article is extremely interesting and absolutely true. If geometric algebra had been discovered earlier we would never have needed a lot of these unnatural constructs.
We already do! You seem to ignore the widespread use of projective geometry in all 3D engines. For me it shows that you don’t know enough about the topic to have a useful opinion on this.
We do 4D stuff in 3D engines because it leads to massively nicer and simpler math, like replacing extremely large trigonometric calculations with a few additions and multiplications. It is actually the right way to do things. And bonus fact: it actually makes logical/intuitive sense when you actually try to understand the math.
That's hilarious, because I've studied projective geometry for years. I am literally writing a paper based on projective geometry right now (applied to abstract algebra). Projective coordinates still gives you a three-dimensional object, because you identify vectors that are scalar multiples of each other.
