I have a connected, sparse, graph (a molecule to be specific) and I'm interested in associating 3D coordinates with the vertices. Here's the kicker: I already have coordinates for none/some/all vertices which are not to be changed. The case of no coordinates I can solve with e.g. MDS, and the case where I have all coordinates is trivial.

In addition, I have a length associated with every edge which should be respected (but some distortion is fine). If it helps, I also have information about some (not all) angles and dihedral angles. Finally, all vertices should be separated as much as possible from one another. If need be, you may assume a maximum degree of ~6.

I don't expect a fully worked solution, but any pointers to literature would already be greatly appreciated!