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The article says
"Compared to rotation matrices they are more compact, more numerically stable, and more efficient"
However, quaternion rotation requires 24 add/mul operations but a 3x3 matrix requires only 15 add/mul operations. Also, the "more numerically stable" claim is unjustified and I cannot find a reference. — Preceding unsigned comment added by 80.47.47.163 ( talk) 15:22, 19 May 2020 (UTC)
The paragraph argued that usage of the Shuster convention is discouraged, as did the cited article "Why and How to Avoid the Flipped Quaternion Multiplication" by Sommer et. al. But the formulas in the paragraph are not clearly distinguished (except by red minus signs). These formulae are beginning to show up on Google Images out of context, creating a lot of confusion to students. I tried to add labelling "\qquad \text{alternative Convention, usage discouraged} to the right of the formulas but the edit got reverted by a anti-vandalism bot. If anyone (especially registered users) agree, please help with the edit. 184.147.40.19 ( talk) 04:04, 25 January 2022 (UTC)
Since quaternions are rotations about arbitrary axis, it makes sense as a matter of convention that the angle is always a non-negative number. Moreover, the angle must always be in the 1st and 2nd quadrant as all other quadrants have equivalent negative angles. If for example we want to represent a rotation of about the axis, this is entirely equivalent to a rotation of about the axis.
So indeed the formula to recover the rotation angle presented will indeed produce the correct answer, in the 1st and 2nd quadrants because thee first argument is always going to be positive, but it is un-necessarily complicated. I propose to recover the angle we simply use
which also produces results in the 1st and 2nd quadrants, Once the angle is recovered, then the axis is simply the vector part divided by the sine of the half angle
— Preceding unsigned comment added by Jalexiou ( talk • contribs) 16:26, 11 June 2022 (UTC)
Shouldn't that be the other way around? That is, one rotation has two representations – not that one matrix can represent two rotations. — Tamfang ( talk) 05:41, 2 August 2023 (UTC)
This is the
talk page for discussing improvements to the
Quaternions and spatial rotation article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Archives: 1, 2Auto-archiving period: 730 days |
This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to multiple WikiProjects. | |||||||||||
|
The article says
"Compared to rotation matrices they are more compact, more numerically stable, and more efficient"
However, quaternion rotation requires 24 add/mul operations but a 3x3 matrix requires only 15 add/mul operations. Also, the "more numerically stable" claim is unjustified and I cannot find a reference. — Preceding unsigned comment added by 80.47.47.163 ( talk) 15:22, 19 May 2020 (UTC)
The paragraph argued that usage of the Shuster convention is discouraged, as did the cited article "Why and How to Avoid the Flipped Quaternion Multiplication" by Sommer et. al. But the formulas in the paragraph are not clearly distinguished (except by red minus signs). These formulae are beginning to show up on Google Images out of context, creating a lot of confusion to students. I tried to add labelling "\qquad \text{alternative Convention, usage discouraged} to the right of the formulas but the edit got reverted by a anti-vandalism bot. If anyone (especially registered users) agree, please help with the edit. 184.147.40.19 ( talk) 04:04, 25 January 2022 (UTC)
Since quaternions are rotations about arbitrary axis, it makes sense as a matter of convention that the angle is always a non-negative number. Moreover, the angle must always be in the 1st and 2nd quadrant as all other quadrants have equivalent negative angles. If for example we want to represent a rotation of about the axis, this is entirely equivalent to a rotation of about the axis.
So indeed the formula to recover the rotation angle presented will indeed produce the correct answer, in the 1st and 2nd quadrants because thee first argument is always going to be positive, but it is un-necessarily complicated. I propose to recover the angle we simply use
which also produces results in the 1st and 2nd quadrants, Once the angle is recovered, then the axis is simply the vector part divided by the sine of the half angle
— Preceding unsigned comment added by Jalexiou ( talk • contribs) 16:26, 11 June 2022 (UTC)
Shouldn't that be the other way around? That is, one rotation has two representations – not that one matrix can represent two rotations. — Tamfang ( talk) 05:41, 2 August 2023 (UTC)