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https://issues.apache.org/jira/browse/MATH-1634?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Piotr Gutkowski updated MATH-1634:
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Attachment: image-2021-10-25-10-20-22-202.png
> 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 Gutkowski
> Priority: Major
> Attachments: image-2021-10-22-13-12-53-900.png,
> image-2021-10-25-10-20-22-202.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 (1,0,0) 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
> -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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