I have managed to get the code working for the new design. The following is the new activity diagram for ConvertGeometry().

This includes two of the new objects, csColladaMesh and csColladaAccessor. Both of these objects have, at their core, a Process() function. The Process() function essentially parses the XML document and retrieves the necessary information. The activity diagram of csColladaMesh::Process() follows:

And the activity diagram for csColladaAccessor::Process():

The next stage will be to integrate a listing of polygons into the mesh object. This should be fairly straightforward, as before, and will be composed of yet another class, csColladaPolygon, which will have as sub-classes: csColladaSimplePolygon, csColladaTriangle, csColladaTriangleFan, csColladaTriangleStrip, csColladaLine, and csColladaLineStrip. I hope to have all of these converted and ready by this afternoon.
I have decided to go back and re-think the design of the library itself. In hindsight, I think that to make the code cleaner and more robust, it will be beneficial to add another couple of classes. Namely, what I added was a class representing the mesh itself. Ideally, I want to be able to process the COLLADA file in a single pass, without having to jump around looking for different elements in the document structure multiple times. To this end, I have decided to add a csColladaMesh class, which will effectively represent data stored in a mesh object. As of right now, this consists of just vertices. I will extend it in the near future. A new class diagram, with two new classes, is given below. I am currently working on redesign of the activity diagrams. They should be done tomorrow morning.
Note that I don't anticipate that this redesign will affect my schedule. I am merely doing this for my own ease of use.

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