The applet:

This applet allows you to run the embedding algorithm on outer-planar graphs that you construct.  Specifically, the input graphs are 2-connected, but they do not have to be maximal.  If you input a graph that is not 2-connected, the applet will use only the block (maximal 2-connected component) that includes xmin and its clockwise neighbour on the outer face.

The graph is input in the left side of the applet, and the point set is input in the right side after the graph is finished.

Graph input:

Point set input:
Running the algorithm: