How to find transformation matrix aligning two lines?
Given two points in 3D space, A and B, I get a line segment LS. Given two new points A' and B' yielding the line segment LS', I need to find the transformation matrix that transforms LS into LS'. The length of the line segments is assumed to be equal.

I have a theory on how to calculate the matrix, but I would really like some feedback from you excellent folks on whether it is a good theory or if there exists some better approach.

Here's my algorithm:

 1. Let L and L' be the lines parallel to LS and LS'
 2. Find the point P where L intersects L'
 3. Find the angle V between L and L'
 4. The final transformation matrix will be:

 
    translate(-P) * rotate(V) * translate(p)



Some background for the curious: I'm building this in XNA, though the math problem should be quite general. The line segment is part of a larger structure of connected segments. For each segment I will pre-calculate a transformation matrix per animation frame.
How to find transformation matrix aligning two lines?
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Given two points in 3D space, A and B, I get a line segment LS. Given two new points A' and B' yielding the line segment LS', I need to find the transformation matrix that transforms LS into LS'. The length of the line segments is assumed to be equal.

I have a theory on how to calculate the matrix, but I would really like some feedback from you excellent folks on whether it is a good theory or if there exists some better approach.

Here's my algorithm:

 1. Let L and L' be the lines parallel to LS and LS'
 2. Find the point P where L intersects L'
 3. Find the angle V between L and L'
 4. The final transformation matrix will be:

 
    translate(-P) * rotate(V) * translate(p)



Some background for the curious: I'm building this in XNA, though the math problem should be quite general. The line segment is part of a larger structure of connected segments. For each segment I will pre-calculate a transformation matrix per animation frame.