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

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SUMMARY

The discussion focuses on computing translation and rotation in SE(3) using Chasles' theorem. Participants express the need for an algorithm that accurately defines the input parameters, specifically the axis of rotation, length of translation, angle of rotation, and radius of rotation. References to related theorems, such as Euler's theorem, indicate the complexity of the topic and the necessity for precise formulations. The lack of accessible algorithms and resources highlights a gap in available information for practitioners.

PREREQUISITES
  • Understanding of SE(3) transformations in robotics and computer graphics.
  • Familiarity with Chasles' theorem and its applications in motion analysis.
  • Knowledge of rotational matrices and translation vectors.
  • Basic proficiency in algorithm design and mathematical formulations.
NEXT STEPS
  • Research algorithms for computing transformations in SE(3).
  • Study Chasles' theorem in detail, including its mathematical proofs and applications.
  • Explore Euler's theorem and its relationship with rotation in three-dimensional space.
  • Examine existing libraries or frameworks that implement SE(3) transformations, such as ROS (Robot Operating System).
USEFUL FOR

Mathematicians, roboticists, computer graphics developers, and anyone involved in 3D motion analysis and transformation computations.

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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