A mate has designed a cupboard for an odd-shaped alcove and asked me to build it for him.
The front of the cupboard isn't parallel to the back -- it's at 45 degrees.
Plan view here:
He doesn't want the hinge visible on the outside and it seems to me that, unless there's some weird hinge out there that first pushes the door forward, the side of the cupboard will obstruct the rotation of the door.