LEGO currently has an incomplete selection of parts for corners. Plates and macaroni bricks allow for 2 and 4 stud radius corners. Finer detail can not be achieved unless one is very tricky with a 2x2 round plate. But even then gaps are apparent. Faceted corners fare a bit better with 1, 2, and 4 stud corners. However, matching plates are only available in 2 stud corners and higher.
This idea offers up three new parts. The first is for a plate with a 1 stud round corner. This would be a good matchup for the round 2x2 plate and especially the 2x2 macaroni bricks.
The second piece is a plate with a 1 stud faceted corner. This would be complementary to the 2x2 facet brick.
The third piece is based on the 2x2 corner panel. The corner has been rounded in this case.
If necessary, each plate could add a 1x2 wing to each side to allow for better connectivity to other round or facet pieces. The idea is to allow for each side of the corner to only be 2 studs deep. A 3x3 plate with the demonstrated corner shapes would not meet the intent in this case.
Matching tiles are encouraged.
This idea should be considered to be an idea in addition to others that have already been posted.