This is the best I could do with inkscape.

I duplicated the inner shape after tracing the bitmap, then dragged out each node to its respective location on the larger shape so all the node counts and orientations matched.
Click image for larger version. 

Name:	inkscape_interp.png 
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This was a 30 item interpolate, with a 0.5% blur applied to smooth it out.

-Rob A>