Chain of connected points and rotation matrices?

While I'm a bit confused, I will take a stab at it. It sounds like you have a set of points and want to reorient them while fixing some in certain locations and preserving the spatial relationships of the group. If you know the coordinates of 4 points in the starting location and their coordinates in the destination location, you can just put those points (x,y,z,1) as columns in a 4x4 matrix S.

You put the destination coordinates in another matrix D. Then you solve D = MS where D is the destination, S is the source, and M will be the transformation that takes you from S to D. So we right-multiply by S~ (inverse) to get M = DS~.

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