How can I convert a closed path to a mesh?

I have a dynamically created 2D path that I want to convert into a solid object.

I managed to extrude the path using LinearExtrude and now want to find a way to create a bottom and top meshes to solidify the object.

Using DelaunayMesh i could create them, but it only works for convex paths and in my case the path might be concave.

I found this in the Blender manual http://wiki.blender.org/index.php/Doc:2.4/Tutorials/Modeling/Meshes/Fill_Faces

In a sense I want to fill the path with faces. And I’m looking for a way to do this in Away.

I’m quite new to 3D and Away3d and my googling has not provided solutions.
I’m using Away3D 4.1.1

I managed to solve this.

For anyone else looking for a solution here’s what I did:
I divided the shape to smaller concave shapes and then filled them using SkinExtrude to a point in the middle of the shape. DelaunayMesh produced few rendering errors for some reason.