How to find rotation parameter in sphere?

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SUMMARY

This discussion focuses on determining rotation parameters on a sphere using Euler coordinates. The challenge arises when the axis of rotation is perpendicular to the circle, as this results in the circle rotating into itself, making it impossible to ascertain the rotation angle solely from the circle's position. The conversation also explores the implications of using curves, such as wave signals, instead of circles, suggesting that the complexity of the problem increases with non-circular shapes.

PREREQUISITES
  • Understanding of Euler angles and their application in 3D rotations
  • Familiarity with spherical coordinates and their mathematical representation
  • Knowledge of geometric transformations and their effects on shapes
  • Basic principles of signal processing, particularly in relation to waveforms
NEXT STEPS
  • Research the mathematical foundations of Euler angles and their computation
  • Explore algorithms for detecting rotation parameters in 3D space
  • Study the effects of different axes of rotation on geometric shapes
  • Investigate signal processing techniques for analyzing waveforms on spherical surfaces
USEFUL FOR

Mathematicians, computer graphics developers, and engineers working with 3D modeling and rotation analysis will benefit from this discussion.

rahman_f_t
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Suppose there is one circle ( signal shape ) on the sphere. then the sphere is rotate. By comparing these two circle, is it possible to find 3 rotation parameters or angles in Euler coordinate (or 2 rotation angle, sphere coordinate)?
Any idea?
Thanks
 
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One obvious difficulty is that, if the axis of rotation is perpendicular to the circle, the circle will rotate into itself. Clearly, just knowing the circle will not tell us the angle the sphere rotated.
 
HallsofIvy said:
One obvious difficulty is that, if the axis of rotation is perpendicular to the circle, the circle will rotate into itself. Clearly, just knowing the circle will not tell us the angle the sphere rotated.

Suppose it is not really circle, there are curve on it ( like as wave signal on the circle). how about this time?
 

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