the dot/cross product are the same operation but expanded into coordinates. Maybe the quaternion (/geometric algebra) version is more compact but it's not like it's a different set of computations. Whereas their removal of the trig functions actually does skip a bunch of unnecessary steps.
reply> He's still computing cross(z, d) and dot(z, d) separately. that looks like a code smell to me. with quaternions ...
replyFair point, but I think you misspelled Projective Geometric Algebra
If you only care about rotations in 3d, quaternions do everything you need :) with all the added benefits of having a division algebra to play with (after all the cross product is a division-algebraic operation). PGA is absolutely great, but quite a bit more complex mathematically, and its spinors are not as obvious as quaternionic ones. in addition GA is commonly taught in a very vector-brained way, but i find spinors much easier to deal with.
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