I want to be able to create a curved 4-sided polygon with equal perpendicular widths, like a thick bezier curve:

... but I want to do that with a shape, adding the curves, one at a time.

So, say I have "Curve 1". I want to create "curve 2" such that along any point on either curve, the perpendicular distance between the nearest point is equal.

You can't just copy and paste the same curve at a 45 degree angle, it bulges in the middle, like so:

The reason I want to do this is to create what is called a "sankey diagram", which shows quantitative flows, like the following image:

I want to be able to do a really nice one, like so:

http://www.wri.org/image/view/11147/_original
There is a decent sankey tutorial I found using the stacked column graph tool, but it doesn't seem to use curved lines.

http://www.nelsonelson.com/wiki/index.php?title=Sankey_Tutorial
Of course, I could approximate things by using bezier curves, but I can be much more exact by using separate curves.

Any help will be very greatly appreciated :)