Waterproof doors for bathroom cupboard
 

Hi,

I'm currently redoing my bathroom.

Right next to the bath (which also has a power shower going into it)
is a heating cupboard. Previously there was an additional shower
curtain used to cover the cupboard double doors and keep water from
splashing onto them, but now I'd like a better solution.

I am tiling the whole bathroom, so I am toying with idea of tiling two
small sheets of ply to make seamless/invisible type cupboard doors. I
would also need some kind of white rubber (which would look like the
grout) round the edges and frame to seal the doors watertight. The
doors will be opening out the way (I thought about sliding doors but
they are not really feasible because of pipes).

What would be the best way of going about this? Doesn't matter too
much if it doesn't look perfect, my main concern is the waterproofing.

Mark.