Cylindrical Shadows

With this post, I continue to catch up on a multi-year hiatus documenting both old and new projects. In my last post I had described some recent experiments I did with my EggBot spherical pen plotter, making spherical designs whose shadows would be recognizable shapes, inspired by a 3D model of Henry Segerman. However, this wasn’t my first foray into thinking about shadows of distorted objects! Back in early 2020 I undertook a similar project with cylindrical designs.

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Cylinders have a huge advantage over spheres: you can unroll them. So, rather than having to create a design through 3D printing or using a special spherical pen plotter, you can use a much wider variety of tools to create flat things and roll them up: 2D pen plotters, laser cutters, or even just a traditional home computer printer, printing directly on to transparencies. Here’s the unrolled shadow design from above:

I didn’t own a pen plotter at the time, but I did have a laser cutter. Creating laser-cut designs for shadows has some significant advantages and disadvantages. Cutting out of a solid material means you have very distinct shadows. However, it also means you are essentially creating a stencil, which can’t have isolated “islands” because they’ll just fall apart. That really constrains design choices.

The fish design shown above was taken from a public source on the internet. That image was used as the desired shadow, and I used Rhino3D/Grasshopper to reverse-engineer the design that needed to be laser cut to give this shadow. More on that process toward the end of this post.

Here are a few other designs I tried. Of course, I had to do a Segerman-style projection of squares:

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And since I did squares, I did some circles, too:

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One of my go-to designs for experimenting with projections is the Mercator projection of the Earth (partly because I like the irony of projecting a projection). As with the spherical version I showed in my last post, one of the nicest features of this design is how unrecognizable it is when unrolled, while having an instantly recognizable shadow.

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The process to create all these designs isn’t difficult if you have just a little proficiency in Rhino/Grasshopper. The curves that define the desired shadow are placed in the xy-plane, along with a vertical cylinder.

Then, each curve is extruded to a point on the z-axis representing the light source.

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That shape is then intersected with the cylinder, and unrolled.

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If you try this on your own, one thing that you’ll quickly discover is that a rolled up piece of cut paper doesn’t create a very nice, round cylinder. I’m sure there are lots of solutions to this. I dealt with it by laser cutting a simple tab-and-slot design in a transparency, and 3D-printing two rings to insert at the top and bottom. Each laser-cut shadow design is then inserted between the rolled-up transparency and the rings, and they then hold their shape nicely.

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I’ll end this post with a personal appeal… When this blog went on a long hiatus I lost a lot of readers. If you’ve made it this far, please help me out by posting/reposting/liking on social media, emailing to anyone who you think might be interested, etc. You can also subscribe to this blog to get updates by mail when there are new entries. THANK YOU!!