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DonHopkins 2 days ago

Almost as annoying as Euler angles, which force you to choose an arbitrary ordering (XYZ, ZYX, ZXZ, …), while each choice is equally valid yet mutually incompatible, so there is no canonical “true” yaw-pitch-roll.

Not to mention gimbal-lock singularities, wrapping discontinuously at +/-PI, mapping one orientation to many triples, and forcing you to juggle trig identities just to compose two spins.

To pure mathematicians obsessed with elegant unambiguous coordinate-free clarity, Euler’s pick-any-order gimmick is like hammering tacky street signs onto the cosmos: a slapdash, brittle hack that smothers the true geometry while quaternions and rotation matrices sail by in elegant, unambiguous splendor.