Compute Translation, Rotation in SE(3) with Chasles Theorem

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Discussion Overview

The discussion revolves around computing translation and rotation in the Special Euclidean group SE(3) using Chasles' theorem. Participants are exploring how to derive the axis, length of translation, angle of rotation, and radius of rotation, with a focus on algorithmic approaches.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the computation of translation and rotation parameters in SE(3) as described by Chasles' theorem.
  • Another participant shares a link to a lemma that may provide relevant information but does not confirm its applicability.
  • A participant expresses a desire for an algorithmic method to compute the required parameters.
  • One participant notes the dependence of algorithm development on the precise definition of input and admits unfamiliarity with Chasles' theorem, mentioning other related formulations such as Euler's theorem.
  • There is a mention of a resource found in another language that contains extensive text with few formulas, indicating a potential challenge in finding concise information.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best approach to compute the parameters in question, and multiple competing views and uncertainties remain regarding the definitions and applicability of Chasles' theorem.

Contextual Notes

Limitations include the lack of clarity on the definitions of inputs needed for algorithm development and the varying familiarity with Chasles' theorem among participants.

hunt_mat
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Suppose I have an element of SE(3)[\itex]. I know this can be thought of as a translation along an axis and rotation about that axis due to Chasles theorem.<br /> <br /> My question is simple: How do I go about computing the axis, length of the translation, angle of the rotation and radius of the rotation?<br /> <br /> It sounds as if it could be rather algorithmic but for the life of me I can&#039;t seem to find much information on it.
 
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Sort of. I will have a look. What I wanted ideally was something which would give me an algorithm to computing them.
 
An algorithm heavily depends on an accurate definition of the input.
To be honest I haven't found and don't know about the Chasles' theorem. There have been several related formulations and connected theorems (e.g. Euler). The only advantage I might have had is to search in an additional language. E.g. I found an article from Zurich but it was plenty of wording and only few formulas.
 

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