hinge to open close minimal-clearance door

I want to put a door in a bath panel leading to a cupboard under the bath. I want the door clearances to be the same as the grout lines, i.e. 2 to 3 mm, and to have no visible hinge when shut (like a kitchen cabinet door) The door will be around 20mm thick (board plus tiles). Thus a normal hinge would foul the edges at some point however it was set. I need a mechanism that will bring the door directly outwards (like a drawer) before turning like a hinge. A drawer is not really suitable due to the irregular space under the bath. And a removable access panel is too fiddly to use for a regularly opened cupboard. Any ideas ? Cheers, Simon.