Corner building flat

If it's rural, how about a barn? Get some junk Plasticville farm building parts.....kitbash and add extra styrene....then paint.

What about a rusted shed with corrugated aluminum siding.....you can get styrene and paint/rust /weather it... or, you can use cardboard which comes as packing material.....here's a picture of a factory I made out of cardboard over 20 years ago. My technique is much better now, but you can get the idea.

I made these somewhere between 94-97.

Peter

Here ya go:

This happens to be an ammo warehouse in Massachusetts.

All you need is some red brick patterned paper if nothing else, maybe add that grayish front entrance to one side.

Ameri-Towne building kits or separate walls.  Walls may be stacked as tall as you desire.  Two walls of a complete kit could be used for the corner pictured and the other two as shown in Peter's second picture. 

Several other kits are available.

 John in Lansing, ILL

If it were me, I would not attempt a structure there. It is more likely to attract attention to the corner than to deemphasize it. Rather, I would simulate a rock escarpment. It is very easy to make flats that accomplish this by using thin strips of broken ceiling tile. Two such flats will do the trick. But, do not have them meet at right angles. Instead, position them at the least acute angle you have room for. Make the meeting edge as irregular as possible, to deemphasize the existing angle--you want it to look natural, not "built".  Then, put lots of foliage around the "stone". Work hard to avoid symmetry. 

Here are a few scenes from my layout that use this technique (although none on a convex corner):

I think Pete is right in suggesting a road escarpment if you are able to continue it further and end it naturally in either side. If you're really set on a building flat, you might consider an escarpment on the right hand side since you have depth to the wall and continue it around the corner on the left where a building flat would be surrounded by the escarpment. For the flat, a very inexpensive way to do it would be to Google O scale building flats and you'll see two sellers that offer mounted pictures (on 1/4" foam) of real buildings of all types and sizes. It's very easy to add sides and a narrow roof of cardboard or foam board (let's say about 1" deep or so) so it sticks out from the wall and the escarpment could go around and over it so the building appears to be set in the mountain. Adding a few 3-D details like roof vents, a billboard, etc. adds to the effect.  

Fellas...he says he's got "outside" corners, not inside.  Frankly, there's almost nothing that will absolutely hide such a corner.

It's a wall, put some brick pattern material on it and make it look like a brick wall.

I definitely agree that scenery, in the form of a rock cut or hillside, would look better and conceal the corner better than building-flats. Also, the footprint of the rock cut/hillside should be curved and remain equidistant (about one inch) from the edge of the cork and extend for some distance (maybe ten inches) along that curve on both sides of the corner. I generally stack and carve pieces of extruded pink foam to create hillsides and elevated terrain. You can then place a small shack atop the hillside and a billboard directly in front of the corner.

MELGAR

How about a barn with a silo covering the outside corner?  Think about a piece material curved into an arc where the absolute corner the wall is touching the inside of the arc.  Make it as tall as you want and make it resemble whatever material you want (sheet metal versus concrete versus wood)  Then place a barn flat next to it.

The Shadow

There does not seem to be a lot of clearance from the corner to the inside curve. The O.P. needs to watch the clearence.... Clarence! Rodger Rodger...

Lots of creative ideas.  Thank you.  Pete and Jerr tie for the gold star sticker.  I bumped out the shelf at that point to provide real estate for building a short tunnel through a steep ceiling height spine  back mountain ridge.

I also agree w/ Pete's scenery suggestion above.  A mountain cut as shown above or like those shown in many of Norm Charbonneau's layout videos would be my choice.  Mountain cuts are very prototypical and do not create a potential limited service or derail access as does a tunnel.