Enumerating all objects in the Git object store

Hi, I'd like to visualize the objects in a Git repository using Graphviz and "dot". I'd like to see commits as circles, trees as triangles, blobs as rectangles, and have arrows linking these objects showing how they reference each other in the Git DAG. For small repositories this may be a useful way to visualize how Git objects work.

I could not find a pre-existing script to do this so I am considering writing one. Is there a way to enumerate all the objects in the Git object store, and for each one figure out its type (commit, tree, or blob) and obtain a list of the objects it references? If not, is there a way to do this for a single object at a time? (I can then simply recurse through the whole structure.)