# teaching machines

## Hollowed Box

In my recent status report for Madeup, I shared a picture of an H-shaped box that I designed in Madeup and printed. I actually had to print two, because when I showed my friend Heather, she wanted one too. Maybe you want one? But what if your name doesn’t start with H? Well, I offer here a general recipe for making hollowed boxes of any shape that doesn’t have holes in it. Our example will use the letter “I” because of its simplicity.

The core idea is that we need a function that walks the outline of our box’s guiding shape. For a blocky I, that shape is a plain old rectangle:

The guiding shape of our I-box.

Now, we’re going to need to draw this shape several times at different locations and with different dimensions. We drop it into a function:

Moving the guiding shape into a parameterized function.

Now we draw the shape four times:

1. At the box’s base along its outer wall.
2. At the box’s top along its outer wall.
3. At the box’s top along its inner wall.
4. At the box’s “almost base” along its inner wall, leaving some room for a solid floor.

For steps 3 and 4, we inset to the inner wall by moving our starting location in by the thickness of our wall, and we shrink the width and height by two wall thickness. The end result is four contours:

Tracing out the box’s four contours.

Now we use the surface solidifier, which will connect each vertex to its four neighbors: the two neighbors on its own contour, the corresponding neighbor on the previous contour, and the corresponding neighbor on the next contour. We tell surface how wide and high our grid of neighbors is and check out the result:

Looking up through the box’s unfilled bottom.

Almost great. The surface solidifier isn’t smart enough to fill in the floors. We can do that manually by walking the floor contours again and running the polygon solidifier. Which side of a 3D polygon is intended to face out is not something an algorithm can figure out, so we check the default direction and then flip as needed:

The completed box with polygon floors.

There we go! We’ve got a watertight model with the floors facing opposite directions.

Making the H is very similar, but the guiding shape has more turns and a few more parameters because of its concavities. The horizontal bridge between the verticals actually gets longer on the inner wall.

A similar process can be used to create a lid. An inset will help secure it in place, but make sure you inset by a bit more than the wall thickness to allow for expansion of your material. 0.5 mm works on my MakerBot Replicator 2X.

If your box is radially symmetric, it’s probably easier to revolve it.