From Quaternion to 3D Rotation
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Any nonzero quaternion has a corresponding unitary (length one) quaternion in the same direction as . Unitary quaternions are an elegant and efficient way to formalize 3D rotations.
Contributed by: Isabelle Cattiaux-Huillard and Gudrun Albrecht (April 2018)
Snapshots
Details
A quaternion can be interpreted in terms of a geometric transformation. Consider the quaternion with magnitude ; then the unitary quaternion of is .
The unitary quaternion can be expressed in the form , where is real and is a 3D vector.
Consider the rotation around the axis with direction through the angle . The image of a vector can be calculated from the quaternion using the formula , where is the conjugate of .
Reference
[1] R. T. Farouki, Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, Berlin: Springer, 2008.
Permanent Citation
"From Quaternion to 3D Rotation
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http://demonstrations.wolfram.com/FromQuaternionTo3DRotation/
Wolfram Demonstrations Project
Published: April 22 2018