He's still computing cross(z, d) and dot(z, d) separately. that looks like a code smell to me. with quaternions this would be easier: just calculate the quotient between z and d and take the square root (which means adding 1 and renormalising). the square root is necessary if one is dealing with vectors, which live in a kind of square-y space. finding the rotation between two spinors is even simpler: it's just the quotient of the the spinors as quaternions. unfortunately hamilton's view that quaternions are the quotient of vectors has never been quite abandoned. it's much more natural to think of them as quotients of spinors.

▲

BenoitP an hour ago | parent [-]

> He's still computing cross(z, d) and dot(z, d) separately. that looks like a code smell to me. with quaternions ...

Fair point, but I think you misspelled Projective Geometric Algebra

	▲	aap_ 19 minutes ago \| parent [-]
		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.