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Comment by tsarakoye_selo | Hacker News Reader

What happens if rotation is zero? Won't (ai +bj+ ck) get multiplied by zero then, and the orientation information is lost?

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If you click through to the interactive example, you can try it! You'll see that the if the above equations are `q`, then full formula to rotate a vector `v` is `v' = q * v * q^-1`

Sorry, what you have stated is not very clear. If you use cos(theta) + sin(theta)*(ai + bj + ck) representation as you mentioned, what does happen to the orientation information when sin(theta) becomes zero

When theta=0, you have

  q = cos(0) + sin(0)*(ai+bj+ck) = 1 + 0 = 1

That means applying the "rotation" to the vector gives

  v' = q * v * q^-1 = 1 * v * 1^-1 = v

So the output ("rotated") vector is the same as the input, as you would expect for a rotation by 0.

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