I found this picture of the door before it had the "skin" on it. Hopefully, it'll shed a little light on how I made it:
Basically, the wall is built with a curve to it, ranging from about 4 inches at the bottom to about 18 at the top (over a 4 foot span). You should be able to adjust this to your specs.
Since I have 8 pie wedges, each of my sections has a 22.5 degree side. I think you said yours has 10 sections -- if, so then yours are probably at about 20 degrees, right? Whatever they are, these curved vertical risers are built so that they plug into one section of the pie. You then make 2 identically curved sections that you can put at the opposite angle from the outside -- that is, if your sides are at 20 degrees out, your door cut out vertical risers are at 20 degrees in. The beauty of this design is that you only have to find one curve, instead of making a different one for the cut outs.
I put a flat door piece at the back of the door cut out to make it 90 degrees again (since the door is at 90 degrees). A trapezoid-shaped header goes in at the top of the door cut out. And a "doorskin" or 1/16th inch MDF skin goes over the curved wall. I would think on yours, you wouldn't have to make the curve go all the way to the floor -- maybe about 3 feet off the ground up to the ceiling would be good.
Here's a quick sketch -- hopefully, it'll make sense!