We have four points: $p_1, p_2, p_3$ and $p_4$. The goal is to compute the distance between $p_1$ and $p_4$.
What we know:
- The distances between $p1$ and $p2$ ($a$) , $p2$ and $p3$ ($b$), $p3$ and $p4$ ($c$)
- The angles $\alpha$ and $\beta$ between ($p1$,$p2$,$p3$) and ($p2$,$p3$,$p4$) respectively
- The dihedral (torsion) angle $\phi$ between the two planes of $p1$ and $p4$
We do not have any coordinates of any of these points.
How do we use this information to compute the distance between $p1$ and $p4$? I tried doing something like projecting $p1$ onto the plane of $p4$, but I ended up needing information that I do not have access to.