What Are the Steps to Calculate Euler's Angles for Rotating a Vector?

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SUMMARY

This discussion focuses on calculating Euler's angles for rotating a vector using quaternion conversion methods. The user seeks to determine the angles alpha, theta, and gamma for a vector originating from (0,0,15) and rotating to (3,-12,15) using the zyz rotation sequence. The conversation emphasizes the importance of disregarding scaling factors and concentrating solely on orientation. Several resources are provided for further exploration of quaternion to Euler angle conversions.

PREREQUISITES
  • Understanding of Euler's angles and their applications in 3D rotations.
  • Familiarity with quaternion mathematics and their role in rotation calculations.
  • Knowledge of rotation matrices, specifically the zyz rotation sequence.
  • Basic vector mathematics, including vector representation in 3D space.
NEXT STEPS
  • Research "Quaternion to Euler angle conversion algorithms" for practical implementation.
  • Explore "Rotation matrices and their applications in 3D graphics" for deeper insights.
  • Learn about "Euler angle singularities and how to avoid them" to enhance rotation stability.
  • Investigate "3D vector rotation techniques in computer graphics" for broader applications.
USEFUL FOR

This discussion is beneficial for computer graphics developers, robotics engineers, and anyone involved in 3D modeling or simulations requiring precise vector rotations.

theboss2012
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Hello,

I have read about Euler's angles and matrices, including zxz,zyz, etc . I am not obliged to use a specific rotation but rather I want to figure out what angles I need to use for alpha,theta, gamma in the specific matrix. For example, I have a vector from the centre with vertex x,y,z of (0,0,15), I want to rotate it to (3,-12,15), what angles should I use or how can I obtain these angles ?

If let's say I choose zyz, i am finding difficulties finding the corresponding angles after the first x-y plane rotation.

Please disregard the scaling factor and just consider the orientation.

Look forward to hearing from you
 
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