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> You absolutely need quaternions, You absolutely do not. Quaternions are (usually) the best solution, but they're not the only one. > And they probably shou
by bigbillheck 4y ago
> You absolutely need quaternions,
You absolutely do not. Quaternions are (usually) the best solution, but they're not the only one.
> And they probably shouldn't have
Geometric algebra may or may not be better in certain low-dimensional applications like CG, but there's a whole lot more to linear algebra than that.
- jacobolus 4y agoMatrix algebra and geometric algebra are two different languages for many of the same topics/structures. If you like you can embed either one in the other (though embedding geometric algebra into matrix algebra is extremely cumbersome, sort of like rewriting your Python programs in assembly language). Geometric algebra has a much richer geometrical structure, but in some contexts the more basic structure of linear transformations is all you need, and matrices work just fine. In geometric algebra, you can extend a linear transformation of vectors by "outermorphism" to act on arbitrary multivectors.