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Talk:Applications of dual quaternions to 2D geometry: Difference between revisions

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Revision as of 12:31, 10 September 2019 editIncnis Mrsi (talk | contribs)Extended confirmed users, Pending changes reviewers, Rollbackers11,646 edits →Unmotivated: in fact, misread what was said← Previous edit Revision as of 18:55, 12 September 2019 edit undoSvennik (talk | contribs)Extended confirmed users1,446 edits →UnmotivatedNext edit →
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:: @]: The article on ] is complicated enough as it is. I am against this. --] (]) 10:38, 10 September 2019 (UTC) :: @]: The article on ] is complicated enough as it is. I am against this. --] (]) 10:38, 10 September 2019 (UTC)
: The dual-complex numbers express all rigid-body motions as rotations about some point. If the point is ''at infinity'', then the rotations turn into translations. The complex number formalism that you gave instead represents rigid body motions as: rotations about a fixed origin, followed by a translation. This is a difference between the formalisms. Note that the way that the ] with its ] occur naturally in the ] should be of interest. Additionally, dual-complex numbers may have applications in ''linearly interpolating between two rigid-body motions'' using an algorithm similar to ]. The fact that taking a ] of a dual-complex number is so simple implies that ] can be adapted to it quite straightforwardly. One of the papers that I cited appears to do this in the context of image processing. --] (]) 11:47, 10 September 2019 (UTC) : The dual-complex numbers express all rigid-body motions as rotations about some point. If the point is ''at infinity'', then the rotations turn into translations. The complex number formalism that you gave instead represents rigid body motions as: rotations about a fixed origin, followed by a translation. This is a difference between the formalisms. Note that the way that the ] with its ] occur naturally in the ] should be of interest. Additionally, dual-complex numbers may have applications in ''linearly interpolating between two rigid-body motions'' using an algorithm similar to ]. The fact that taking a ] of a dual-complex number is so simple implies that ] can be adapted to it quite straightforwardly. One of the papers that I cited appears to do this in the context of image processing. --] (]) 11:47, 10 September 2019 (UTC)
Note: {{user|Svennik}} refactored the thread, removing my postings. The original can be seen on ]. ] (]) 12:07, 10 September 2019 (UTC)
: {{user|Incnis Mrsi}}, why is it that you don't accept people trying to tone a discussion down? Are you out for conflict? You do realise that I've invested time in this article? --] (]) 12:15, 10 September 2019 (UTC)

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Unmotivated

This article purports to provide a representation of Euclidean plane isometry with the dual-complex algebra (which has no published sources, only arXiv references). In fact, complex numbers are sufficient to represent such mappings as is shown at Euclidean plane isometry#Isometries in the complex plane. A blog article by Terence Tao also is cited but Tao’s results are not, and it is just a blog article, not WP:Reliable source. Is this worthy encyclopedia material ? — Rgdboer (talk) 22:27, 9 September 2019 (UTC)

BTW I doubt this should exist as a separate article at all. It is a subalgebra of dual quaternions and does not differ from it qualitatively. Merge to? Incnis Mrsi (talk) 04:43, 10 September 2019 (UTC)
@Incnis Mrsi: The article on dual quaternions is complicated enough as it is. I am against this. --Svennik (talk) 10:38, 10 September 2019 (UTC)
The dual-complex numbers express all rigid-body motions as rotations about some point. If the point is at infinity, then the rotations turn into translations. The complex number formalism that you gave instead represents rigid body motions as: rotations about a fixed origin, followed by a translation. This is a difference between the formalisms. Note that the way that the projective plane with its points at infinity occur naturally in the Dual-complex numbers should be of interest. Additionally, dual-complex numbers may have applications in linearly interpolating between two rigid-body motions using an algorithm similar to SLERP. The fact that taking a logarithm of a dual-complex number is so simple implies that SLERP can be adapted to it quite straightforwardly. One of the papers that I cited appears to do this in the context of image processing. --Svennik (talk) 11:47, 10 September 2019 (UTC)
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