Piotr created MATH-1634:
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Summary: Quaternion representation of Rotation is incorrect
Key: MATH-1634
URL: https://issues.apache.org/jira/browse/MATH-1634
Project: Commons Math
Issue Type: Bug
Affects Versions: 3.6
Reporter: Piotr
Attachments: image-2021-10-22-13-12-53-900.png
Rotation is internally represented using quaternions. This representation is
not correct in terms of quaternion values, though aparently the Rotation object
behave correctly when it is constructed using angles or axes.
For example, consider following rotation:
Rotation r2 = {color:#000080}new {color}Rotation({color:#000080}new
{color}Vector3D({color:#0000ff}0{color},{color:#0000ff}0{color},{color:#0000ff}1{color}),
Math.{color:#660e7a}PI{color}/{color:#0000ff}2{color},
{color:#660e7a}VECTOR_OPERATOR{color});
It describes a counter-clockwise rotation around Z axis by 90 degrees, similar
to the example given here:
[https://commons.apache.org/proper/commons-math/javadocs/api-3.6/org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html#VECTOR_OPERATOR]
Such rotation should transform vector (0,0,1) into (0,1,0).
The values of quaternions for this rotation are:
!image-2021-10-22-13-12-53-900.png!
(recall that 0.7071 is approximately sqrt(2)/2)
Performing the rotation using quaternion algebra, corresponds to:
p = (1,0,0) = i
f(p) = q p q^(1) = (q0 + q3*k)*i*(q0 - q3*k) = -j = (0, -1, 0)--
where, i, j, k are imaginary unit vectors corresponding to axes x,y,z
respectively.
You can visualize quaternions here:
[https://eater.net/quaternions/video/intro]
to see that in fact these quaternion values would produce rotation by - 90
degrees around Z axis.
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