I have two lines with known parametric equations and some number of distinct points along each line. I would like to rotate the points on $L_2$ some number of degrees $\theta$ along one and only one line $L_{map}$ s.t. that the set of points in $L_2$ can be translated to lie along $L_1$. Performing such a rotation on a set of points is straightforward, but how do I find $L_{map}$ and the rotation angle $\theta$ as a function of $L_1$ and $L_2$?
[1/3/2012] - To reduce the size of the solution set of lines satisfying the constraints for $L_{map}$, we can split $L_1$ and $L_2$ into two sets of parallel lines spaced the same distance apart, and ask for some line $L_{map}$ that allows one to overlay the two sets of parallel lines by translation.