3D Object Scrolling Panel

Hello,

I'm trying to do a 3D menu with 3D texts and objects, and everything was good until I needed to accomplish a Scrolling Panel.

My idea is:

I have a 3D tablet with buttons inside a Scrolling Panel, and I need to make this buttons' mesh disappear gradually when the player scrolls and a button reaches the border of the tablet. I can't just hide the button behind the border of the tablet because the border is thinner than the button. I need to make it's mesh/material (don't know which) gradually disappear.

I saw a similar effect with NGUI and its clipping shader, but I don't want to use GUI and really don't know how to apply it to 3D objects.

Does anybody have any idea how this could be accomplished?

Thanks in advance.