Construct a rotation matrix out of another rotation matrix

In summary, the problem is that the rotation and translation matrices were based on rotations around coordinate A, but the actual rotations took place around coordinate B. The speaker is seeking advice on how to adjust the matrices to account for rotations around B instead of A. They also ask for clarification on the use of 'K' in the explanation.
  • #1
TravelGirl
9
0
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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  • #2
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:
 
  • #3
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? )
 

FAQ: Construct a rotation matrix out of another rotation matrix

What is a rotation matrix?

A rotation matrix is a type of square matrix that is used to represent a rotation in a three-dimensional space. It is composed of a combination of cosine and sine values, and is used to transform points and vectors in a coordinate system.

How do you construct a rotation matrix out of another rotation matrix?

To construct a rotation matrix out of another rotation matrix, you can use matrix multiplication. Multiply the first rotation matrix by the second rotation matrix, and the result will be a combined rotation matrix that represents the combined effect of both rotations.

Can a rotation matrix be used to rotate objects in any direction?

Yes, a rotation matrix can be used to rotate objects in any direction in three-dimensional space. The direction and amount of rotation can be specified by the values within the matrix.

Are there any limitations to using rotation matrices?

One limitation of rotation matrices is that they can only represent rotations in three-dimensional space. They cannot be used to represent other types of transformations, such as scaling or shearing.

Can you construct a rotation matrix out of multiple rotations?

Yes, you can construct a rotation matrix out of multiple rotations by multiplying together the individual rotation matrices in the desired order. This will result in a single rotation matrix that represents the combined effect of all the rotations.

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