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### Calculate roll, pitch and yaw between two coordinate systems

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```Hello everyone,

I would like to calculate the roll, pitch and yaw between two coordinate systems as seen in the following image:

http://img534.imageshack.us/i/coordinates.png/

The xyz axes are represented by the rgb colors respectively. I guess the first thing I have to do is to decide which type of rotation happens between the two coordinate systems (xyz, yxz, zxy, etc).

Is the fact that the x - axis passes from my two lines of interest important? In the end, I want to apply the same rotation to the black line so it covers the cyan line, by using the rotation matrices.

I know this can be done much easier with other ways, but later, I want to use some angle constraints on the rotation of the line.

So any ideas on how to calculate the angles for these transformations.

```
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