Make a physical Escher print by cutting different parts of a tessellation in different materials.
Step 1: Get Image
Get a digital copy of your favorite tessellation either by scanning a paper copy of searching the web.
I chose reptiles.
Step 2: Create CAD File
Convert the image to a vector format.
I converted the jpeg to a tiff and then used Adobe Streamline to convert it from a raster image to a dxf. The dxf was really messy, so I cleaned it up by hand using AutoCAD and cut out everything but a single repeating tile.
Both the raw and cleaned dxfs are in the files section.
Step 3: Remove Excess Points
Streamline generated too many points, but could not be trusted make good vector files at lower point densities. Knowing that 8 billion points at every corner of the drawing would only slow down the cutting process (or worse, overload the tool's limited memory), I deleted extra points by hand. When three points form a line, delete the middle point. Use your judgement and remove points that are beyond the resolution of the tool.
Step 4: Customize the CAD for Your Tools and Materials
This is the hard part. Customize your CAD so that it works with your materials and your tools. I wanted the first layer cut out of aluminum by an abrasive jet machining center and the second and third layers cut from acrylic by a laser cutter.
I put each of the three lizards on a different layer in the dxf, and copied this base tesselation into an array. Since the lizards in one layer did not touch one another, I connected them with a thin strip of material that followed the outline of the lizards in the other layers.
The software on the Omax abrasive jet does automatic kerf correction. This mean it generates the tool path to follow a line just outside of our drawing, so you get the proper dimensions. In this type of work, this is both a blessing and a curse. Some of the lines on the lizards are not closed polygons, so I changed their type so the jet followed them directly. There was also a fair amount of tweaking the dxf so that the path generating software didn't get "stuck."
The laser cutter doesn't care about its kerf. So, while the lines down the backs of the lizards were fine, I had to use an outline tool in AutoCAD to draw lines around the lizards. I measured the kerf in the acrylic I was using, outlined the lizards by half this distance, and deleted the interior shape. Notice the differences between the lizards' toes in the picture of the dxf meant for aluminum and the picture of the dxf meant for acrylic.
Step 5: Cut the First Layer Out of Aluminum
I cut the first layer out of 1/8 thick aluminum. The abrasive jet's computer could only handle half of the file at once, so I had to cut it in half.
Step 6: Cut the Second and Third Layers
Cut the second and third layers from acrylic.
I chose 1/8 thick acrylic and cut with the protective paper still on. While this prevents burn marks on the finished piece, it does lead to the second most maddening step of this project: removing the paper. Carefully pull the paper off without breaking the fragile acrylic. Cut at least two copies, so when you break one, you won't be too upset.
Step 7: Assemble the Layers Together
Assemble the layers together with nuts and bolts. Seperate the layers by approximately 0.5 using stand-offs or multiple nuts.
Step 8: Hang and Enjoy
The light and shadows that come through the print are gorgeous.