Quaternion (0,0,0,0) signifies what

math rotation quaternions
Srinivasan Krishnan picture Srinivasan Krishnan · Dec 15, 2016 · Viewed 11k times · Source

After performing quaternion multiplication I am getting (0,0,0,0). Could anyone let me know what it signifies.

(1 0 0 0) - Identity quaternion, no rotation,
(0 1 0 0) - 180° turn around X axis,
(0 0 1 0) - 180° turn around Y axis,
(0 0 0 1) - 180° turn around Z axis,

Likewise what could be the explanation for (0,0,0,0)

Answer

Gilles-Philippe Paillé picture Gilles-Philippe Paillé · Apr 1, 2019

As mentioned by John Coleman, the (0,0,0,0) quaternion is the zero element. The only way to obtain this result using multiplications is to multiply by (0,0,0,0). Since we don't not much about the context, we cannot be more specific about the origin of the problem.

About the meaning of the (0,0,0,0): geometrically, a quaternion encodes a rotation AND a scale transformation: q = s*u, where 'q' is the quaternion, 's' is a scaling factor (a factor 's' leads to a s^2 scaling), and 'u' is a unit quaternion (a rotation). Since 'u' is non-zero by definition, the only way to obtain (0,0,0,0) is to have a scaling factor of zero combined with an undefined rotation.

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