Construct a rotation matrix out of another rotation matrix

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SUMMARY

This discussion focuses on adjusting a rotation matrix originally defined around point A (x1, y1, z1) to instead accommodate rotations around point B (x2, y2, z2). The user seeks to modify both the rotation and translation matrices to reflect this change in the center of rotation. Key concepts include the relationship between rotations along the line segment AB and the need to correct landmark positions accordingly. The discussion emphasizes the importance of understanding the geometric implications of rotation matrices in 3D space.

PREREQUISITES
  • Understanding of 3D rotation matrices
  • Familiarity with translation matrices in computer graphics
  • Knowledge of coordinate systems and transformations
  • Basic concepts of linear algebra
NEXT STEPS
  • Research how to derive a rotation matrix from two points in 3D space
  • Learn about the mathematical properties of rotation matrices
  • Explore the use of homogeneous coordinates for transformations
  • Investigate the application of quaternion rotations for smoother transitions
USEFUL FOR

This discussion is beneficial for computer graphics developers, robotics engineers, and anyone involved in 3D modeling or animation who needs to manipulate rotation matrices effectively.

TravelGirl
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The following is my problem: I have a rotation and rotation matrix, based on rotations around coordinate A(x1,y1,z1). But actually, the rotation found place around coordinate B(x2,y2,z2).

How can I adjust my rotation and translation matrix, so that it is adjusted for the rotations around coordinate B?
 
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Hi TravelGirl! :smile:

A rotation along AB is the same for both representations.

For rotations about axes AK and BK' perpendicular to AB, use σk'σk = … ? :wink:
 
Maybe I explained my problem incorrectly, I am sorry for that.

Based on the rotations around point A, I received landmarks of the object I rotated and also got a rotation and translation matrix.
Though, actually I should rotate around B, and correct the positions of my landmarks for this.

So how do I correct my matrices for rotating around B in stead of A.
(and what does 'K' mean in your explanation? )
 

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