Step 2: Case Design
I don't really know anything about bending acrylic, but I have glued some before. For this sign, I just used a box made out of layers of 1/8 inch acrylic to create a space to fit all the LEDs and have the light bounce around a bit. In the final version the layers are so, from front to back:
* white border around front to hold next layer
* single-side frosted clear (translucent acrylic causes the pattern to be too blurry), with opaque white border on three sides to hold this layer in place
* white with the pattern cut out
* mirror with the pattern cut out (this layer is not entirely necessary, since it only serves to reduce the light leakage through the layer before it)
* translucent white to diffuse the LED light, I believe it's 60% transmission
* about 8 layers forming the wall of the sign (one of these layers holds captive nuts for the screws that hold the back on)
* mirror acrylic
* white spacer layer
* white layer with wall-mounting holes
it may be possible to sand the sides flat, but I like the rough layered look, so I left it as-is.
The layers are almost all glued together with acrylic glue, except for a gap before the last mirror layer, which is so the back of the sign can be removed.