I don't see how this would help. Visvalingam selects a subset of the inverted points, so when inverting back, I'll still end up with a subset of my original points. So the algorithm still cuts corners instead of adding areas.
If you add a midpoint along each edge Visvalingam creates, invert the reduced poly then remove the original points, you'll get a containing polygon. I think. But we're heading rapidly into hackish bodge territory :-)
This doesn't work. Consider a polygon with all points on the unit circle - your transformation is the identity (both before and after Visvalingam's algorithm is applied).
