The Mobius Panorama

April 10, 2008

A few months ago I hit on the idea of the mobius panorama. I can’t remember exactly why I thought about it, but it was an interesting idea, and I spent the next few hours thinking about how it could be done. There are a few things about the panorama that have to be true for it to be mobius-able. There has to be a weird kind of symmetry; the bottom left of the image has to work with the top middle. Not very many images will work for this. The best way to go about it is to start with a reflection panorama, where the top half is real and the bottom half is its reflection in a lake. It doesn’t have to be symmetrical across the length the entire way, you could have a mountain/lake reflection, then a wide open scene for 180 degrees, then another mountain/lake reflection that also is continuous with the first mountain/lake reflection, then another wide open scene for the other 180 degrees. I didn’t have that image readily available. I think it’ll take me a while to find. In the meantime, here’s my start:

There are two things to note about this image. First, it is symmetrical along its horizontal axis thanks to the lake reflection. Second, the panorama is continuous and the edges wrap together. I did this in photoshop by moving the image over by half and wrapping the other half around, then blending the seam with a little bit of photoshop magic.

The next step is to make a copy of this image and turn it into a cylinder with the inside offest by half the image. This way you get a straight panorama with the outside being what you would see if you were looking in, and the inside what you would see if you were looking out. It’s a little hard to explain, but the image does a good job. Here’s an example:

Now we get to take our regular cylinder and cut it at one of the seams (it shouldn’t matter which one you cut, but there are 2 available seams). Flip one of the sides over and reconnect to make your mobius strip. Like this:

The neat thing about the mobius panorama is that at some point the ground turns into the sky, but you can’t tell where. It’s tricky to find an image that will work for this kind of thing, and the image you do choose will very likely need some photoshopping to get it to work just right. Even after you do get it, it’s not like you can show it off or put it in a book easily.

As far as I can tell, nobody has yet thought of this, so nobody has tried to get it to work. I’m probably not the first, but whoever was first did a good job of hiding. It’s not a very valuable piece of knowledge; just a little curious.

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