This Instructable will show how to carve a continuous two-sided sculptural surface out of a solid block of material, without creating any waste material. In the photo above, the surface was created using a block of foam identical to the one shown! Transforming a block into a sculptural surface is a subtractive process, typically involving carving the block with a chisel, router, or similar tool. Carving produces a lot of dust, a lot of waste, and takes a lot of time. The process shown uses slicing geometry to quickly build a surface with minimal waste and dust.

This example of a zero-waste surface uses a hand held hotwire cutter to to cut XPS foam, but the technique could be applied to many other materials (such as wood or stone) and tools (such as a CNC hotwire cutter, or a robotic arm with a hotwire end effector). My goal was to make this Instructable accessible to people with limited tools or skills.

This Instructable is highly customizable, so make sure you read through to the end to see some ideas for where you can take it!

To complete this Instructable as shown you will need:

Block of foam (XPS foam, 3"x6"x12")
Hot wire foam cutter (hand held)
Chipboard (approximately 1/8" thick)
Small clamps
Hot glue gun
Sand paper (100 and 200 grit)

Step 1: Understanding the Concept

The quickest way to understand this process is to cut some slices from a block of cheese. Every time I make a cut, I'm simultaneously creating the "back" of one slice, and the "front" of the next; so no wasted cheese. I can cut straight through to make a flat slice, or I can twist the blade as I'm cutting to create a more irregular slice.

If I had to describe the geometry of my cut, I would say that even though the surface may look complex, it was really just a straight line (the blade) swept through space. In geometry this is known as a ruled surface. If I needed to give instructions for how to precisely slice the cheese, all I would really need is a profile line describing the movement of the tip of the blade, and another profile line describing the base of the blade.

If I lined up all my cheese slices side-by-side, they would create a mini zero-waste cheese-wall with interesting sculptural surfaces on each side. All I need to do now is to find a way to align the end of one cheese slice with the beginning of the next cheese slice, in order to create a continuous surface.

Now we just need to substitute a block of foam for cheese, a hotwire cutter for the knife, and find a way to control the slicing geometry.

Step 2: Create Slicing Geometry

To create your basic slicing geometry, you can draw a series of profile lines on an elevation of the block. In this example, I'm slicing a 3"x6"x12" block of XPS foam into a series of 3"x12" slices. This means that my profile lines (defined by the two ends of the hot wire) will be drawn on a 6"12" rectangle. You can draw these profile lines drawing software such as AutoCAD or Adobe Illustrator, or you could draw them by hand. Profile lines can be curvilinear, straight, zigzagged, etc. Keep in mind that the more lines you draw, the more slices you'll make, and the thinner they'll be--if you leave 1/2" between two lines, your sliced surface will be 1/2" thick.

Separate these profile lines out into a series of closed shapes, each extending to the "back" of the block (to the left in this drawing). You might find it helpful to number these shapes to keep them straight.

Step 3: Make Slicing Jigs

Now, translate your slicing geometry into a series of jigs that you will use to guide the hotwire cutter. I did this by lasercutting 1/8" thick chipboard, but you could also tape a printout of your drawing over the chipboard and cut by hand.

Step 4: Make a Foam Slice

Place jig 1 on one side of the foam block, and jig 2 on the other side. It doesn't matter which goes on the "front" or the "back" of the block, as long as you're consistent with every slice. Make sure the straight edges of the jigs are even with the edge of the block, and lightly clamp them in place. Use the edges of the jig to guide the hotwire through the foam, moving nice and slow--if you go too fast, the wire will drag and create surface imperfections.

Step 5: Finish Slicing and Arrange

To cut the next slice, replace jig 1 with jig 2, and replace jig 2 with jig 3. Clamp and cut, following this pattern (3+4, 4+5, etc.) until finished. By re-using each jig for consecutive slices, you create identical edges from one slice to the next.

As you cut the slices, re-stack them or lay them out in a row to keep them organized. You should notice that the edges of adjacent slices align.

Step 6: Assemble Foam Slices

A hot glue gun works well on XPS foam: it cures quickly, holds strong, and doesn't melt the foam (it may melt EPS foam). Apply a thick bead of glue to the edge of a slice, and align it with edge of the following slice. You may find it helpful to use the table top to align the top and bottom edges.

Step 7: Sand Foam Assembly

Sand the assembly to smooth over minor surface imperfections, and conceal the seams between slices. You can start with rougher paper (100 grit) if needed, then use smoother paper (200 grit) for finishing.

Step 8: Customize It!

You can get a huge variety of surface types by modifying the profile lines in your initial template. For example, using straight, jagged lines will result in visible creases in the surface. If you add more profile lines to the template, the surface gets thinner, and longer. If you overlap two profile lines in your template, it will create openings in the final surface. Remember that no material is wasted in this process, so by creating an opening in one part of the surface you also create a bulge next to it.

The alternate surfaces here were generated digitally using a script I developed in Rhinoceros and Grasshopper. It allows me to quickly visualize the final surface just by modifying the original profile lines, and test out different design options.

I'm excited to see what other people can do with this! Try out different designs, different materials, and different tools let me know when you've "made It!"