> “It's fine to use a library that understands them and just continue making the important parts of your game.”
Oh that's indeed absolutely what a game dev should do.
A 3D engine dev however, might do well to eat the math leading to the understanding of quaternions, and by extension Clifford algebras (the underlying/original theoretical structure leading to geometric algebra). You get to understand how particular variations in n-dimensions of this structural framework are isomorphic to all numbers like R, C, H and much more. (hyperbolic! dual!)
It really paints a whole arch-picture, a meta-framework to unify all possibly kinds of numbers in one's mind (including the geometry of these numbers and ring operations, with a 1:1 equivalence between geom and algebra).
Note that this is why, I think, some strong proponents of GA (which I find myself agreeing with in that regard) would have it enshrined in K-12 education in lieu of linear algebra — because the intuition of GA is really great / second-to-none, and intuition is all that most math students in high school will ever retain afterwards (they won't do math again, ever, not really). The argument being that people who need more (from linear algebra for calculations notably) can learn that complicated and non-intuitive stuff later (university), building on top of a good base intuition nurtured in GA / Clifford.
So, the 3D engine maker, people in robotics, anyone working with spatial representations of any kind (even abstract, like research with multilinear models) would do themselves a fantastic favor for a lifetime to learn these topics. It's a no-brainer, really, from the other side.
Oh that's indeed absolutely what a game dev should do.
A 3D engine dev however, might do well to eat the math leading to the understanding of quaternions, and by extension Clifford algebras (the underlying/original theoretical structure leading to geometric algebra). You get to understand how particular variations in n-dimensions of this structural framework are isomorphic to all numbers like R, C, H and much more. (hyperbolic! dual!)
It really paints a whole arch-picture, a meta-framework to unify all possibly kinds of numbers in one's mind (including the geometry of these numbers and ring operations, with a 1:1 equivalence between geom and algebra).
Note that this is why, I think, some strong proponents of GA (which I find myself agreeing with in that regard) would have it enshrined in K-12 education in lieu of linear algebra — because the intuition of GA is really great / second-to-none, and intuition is all that most math students in high school will ever retain afterwards (they won't do math again, ever, not really). The argument being that people who need more (from linear algebra for calculations notably) can learn that complicated and non-intuitive stuff later (university), building on top of a good base intuition nurtured in GA / Clifford.
So, the 3D engine maker, people in robotics, anyone working with spatial representations of any kind (even abstract, like research with multilinear models) would do themselves a fantastic favor for a lifetime to learn these topics. It's a no-brainer, really, from the other side.
It's delicious math!