Planar Embedding with Some Nodes Constrained

I've read about basic planar-graph embedding and about embedding a planar graph onto a set of fixed points, but I was wondering how one might constrain the locations of some nodes—perhaps to a set of points—while allowing others complete freedom.

Is this achievable with a current popular algorithm, or with minor modification thereto? I guess the nature of the problem would lend itself better to grid-based embeddings, right?

I'm entirely new to graph theory, so it's possible the answer is obvious to those familiar with the field. I didn't see anything about it while searching.

With respect to grids, there are a couple of well known algorithms for drawing planar 3-connected graphs. One is Schnyder's algorithm (through the a Schnyder wood decomposition of the edges), and the canonical ordering algorithm (through a partition of the vertices of the graph). Both of these algorithms run in $O(n)$ time and produce drawings in an $O(n)\times O(n)$grid, where $n$ is the number of vertices of the input graph. At  you may find an overview of these two algorithms for the case of planar triangulations. You could even go to references  and  cited there for the original papers. It is worth noting that these algorithms have been generalized to work on 3-connected planar graphs as stated above.