Generate square "skin" around a line for icon solidifying

Question

I'm quite new to blender/modelling, and though I have made a few successful pieces previously, I'm having an issue in generating an object for 3d printing.

I am essentially creating a series icons, made up of straight lines. Here's an example of one:

The idea is that the black lines will be basically a square rod, and all connected to make up the icon. This square rod needs to have the faces aligned with the plane the object sits on... Like this:

I've traced the icon in blender using simple vertices linked together with straight lines.

The issue I'm having now is when I try and give the shape some volume. This is a very basic and out-of-proportion idea of what I'm trying to get as a final product:

Here, I've thrown this together by extruding the points up, creating faces an then insetting them, but the icon doesn't really have any physical volume, as it has no inner side wall or bottom face. Plus, the lines are all inset, instead of being equal on both sides of the line I really need to make it so that the lines all basically have a square tube around them all.

I've heard of people using bezier curves, and then beveling the lines to add thickness. This gives me several issues.

Firstly, the bevel comes out as a diamond, rather than a square, where the faces are all at 45 degrees to the plane the object sits on:

Secondly, the lines are all different thicknesses and appear to taper along their length, which I have no idea how it happens:

Finally, the corners of the shape have open ends, and I'm hoping to make it so that the object has sharp corners.

Any help with this issue would be much appreciated.

Answer 1

There seems to be some sort of screwiness that goes on in the mesh when you create it from vertices. To combat this, after I traced the image using vertices, I converted it to a poly curve (Alt+C). I set the curve extrude function to "0.1".

Then I converted the curve back into a mesh (Alt+C) again, and Removed Doubles in edit mode.

When I added the Solidify modifier this time it worked perfectly as long as "Even Thickness" was checked.

Here is my finished product. The blend file is included below, feel free to use it for your project.