# Cylindrical Mirror Art

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Curved mirrors distort images because they send pieces of the image off in different directions that look strange to your eye; this is the basic principle behind funhouse mirrors. But if you send a distorted image into a mirror, then from a certain perspective the image will look correct to your eye! This kind of art is generically called "anamorphic art" and is commonly seen in the from of dramatic street art that looks three dimensional from certain perspectives.

You can play with "cylindrical anamorphoses" pretty easily at home. Constructed using a cylindrical mirror, cylindrical anamorphoses were a popular attraction at parties during the Victorian era, but you can still use them to impress your friends at dinner parties here in the 21st Century!

There are two ways to produce the reflected artwork --- one way is by hand (the classic way), and the other is with software like Photoshop. I'll outline how I do it by hand here, and in the last step describe how to do it with Photoshop.

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## Step 1: Materials

(1) Cylindrical Mirror -- I used a chromed sink extension tube I picked up at the hardware store

(2) Paper, Pencil, Ruler, Compass, Protractor

(4) Computer (optional)

## Step 2: Reference Art

The anamorphosis requires a piece of distorted art to reflect. To make the distorted art, print out the image you want to use, so you can work and write on it. The mirror reverses images left to right, so if you want your image to have the expected left-right appearance when reflected (for instance, words or recognizable symbols), flip the image horizontally before you print it.

## Step 3: Making Your Drawing Grid

The art is transferred to a distorted grid (the "drawing grid") that is made up of concentric circles and radial lines.

(a) In the center of a blank piece of paper, trace an outline of your cylindrical mirror.

(b) Using your compass, draw concentric circles around the mirror location, spaced by 1/4 inch.

(c) From the center of the mirror circle, draw radial lines outward, separated by an angle of 22.5 degrees.

(d) The resulting drawing grid is shown here. You can also make one up on the computer, so you can quickly print them off if you want to make a new piece of art. The disadvantage of the computer drawing grids is you cannot erase the grid lines once your art is transferred.

## Step 4: Check Your Drawing Grid

If you're worried your drawing grid didn't get drawn right, you can check it by putting your mirror down in the center.

You should see a perfect, square grid reflected in the mirror! This is the mirror correcting for the distortion of the curved mirror -- the same physics that will turn your distorted image into a something to look at!

There is still visible distortion where the mirror sits on the piece of paper; this is because the concentric circle and radial line grid is not exactly correct (mathematically) down near the contact point with the mirror. We will keep our art far from this distortion region.

## Step 5: Art Reference Grid

To transfer the art, we will use a modified version of the "grid transfer method" that many of us are taught in grade school.

(a) On the piece of art you would like to display in the mirror, draw a perfect square grid (the "art grid"). The number of vertical grid lines should match the number of radial lines you drew for the reflection, and the number of horizontal lines should match the number of circles you drew outside the mirror circle.

(b) It is helpful to label the drawing grid and the art grid. I use letters for the vertical lines (radial lines), and numbers for the horizontal lines (concentric circles). On the art grid, label the lines left to right, and bottom to top. On the drawing grid, label the radial lines clockwise, and the concentric circles from the center outward.

## Step 6: Transfer Sketching

To transfer your image, focus your attention on one square of the art grid at a time.

What is in it? Note where lines touch the edge of the square, and where details appear in the square (just left of center, etc.).

Note the letter and number of the square you are working with, and find the corresponding letter and number on the drawing grid.

The corresponding "square" on the drawing grid is not square at all! You must transfer what you see in the square grid to the cylinder grid by noting where details appear, and drawing them in their distorted locations.

You can check your progress at any time by simply putting the mirror in place. Some cylindrical mirror artists create their distorted images by simply sketching freehand while watching the reflection not their hands!

## Step 7: Finishing Up the Transfer

I sketch initially in pencil, so I can make adjustments and erase mistakes, then I go back over it with something more bold, like a Sharpie.

When you are done, clean up what you don't want to see with an eraser, and display your new art!

## Step 8: Making Distorted Art With a Computer

Modern graphics software often has the ability to distort images properly for display in a cylindrical mirror. This is particularly useful if you want to display a complex picture, or a picture in color.

In Photoshop, load your image up, flip it horizontally, and apply the filter called "Polar Coordinates" (Filter > Distort > Polar Coordinates).

This Superman logo was done in Photoshop. To get the distortion exactly the way you like, you may have to play around with the whitespace on the canvas, moving the image around before applying the filter.

## Step 9: SCIENCE 1: Flat Mirror Reflection

One of the fundamental laws in optics is the "law of reflection." It says that when light reflects off a surface, it bounces off at the same angle it entered.

To see how this works for a flat mirror, imagine a simple object, like a row of colored dice. Physicists think of light as travelling along straight lines called "rays" -- think of them as arrows that point the direction the light is going. Each of the dice has rays of light that your eye receives, telling you the color, location, and shape of the dice.

When a ray hits a mirrored surface, the law of reflection says if you measure the angle between the mirror and the incoming ray, the outgoing ray has exactly the same angle between it and the surface.

The consequence of this is that someone looking at the mirror, like Selene in our image, sees all the light from the row of dice arriving together and lined up just like it left the dice. The only oddity is that the image is reversed; if Abigail had looked directly at the row of dice, without seeing the reflection in the mirror, she sees the order reversed compared to Selene.

## Step 10: SCIENCE 2: Curved Mirror Reflection

Because our cylindrical mirror surface is curved, incoming rays from the row of dice get reflected off in different directions. That means light from an image doesn't stay together to reconstruct a compact image for your eye to see.

Each bit of light obeys the law of reflection, bouncing off at the same angle as the angle it hit the mirror. But each bit of light gets reflected in a slightly different direction because the surface is curved.

This distorts the image to an observer like Kate, who is looking at the mirror surface.

## Step 11: SCIENCE 3: Anamorphic Reflection

The cylindrical anamorphosis takes advantage of the law of reflection by thinking about the distortion in reverse.

The distorted image is drawn in such a way that when each bit of light hits the mirror, the result is the light is brought together so a viewer like Calvin sees an undistorted image.

By spreading the image out on the cylindrical grid, you are using the law of reflection backward. The mirror takes widely distributed bits of light and reassembles them into a compact form that your eye sees as an undistorted picture.

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## 32 Discussions

did anyone notice that the first drawing was of Hobbes from "Calvin and Hobbes"?

This is amazing!

Amazing idea :D

I have plenty of reflective balls from bearings lying around.

Can this be extended further for reflecting on a sphere? :)

2 replies

In a sense, the calculation is straightforward but messy. Take a ray from your eye to a point on the mirror. Now draw two rays: one will be the continuation of the original ray, find out where it intersects a given vertical plane (xi, 0, zi) (for convenience chosen to be the xz plane). Second should be the reflected ray from the mirror. Find out where it intersects the horizontal plane z = 0 (xo, yo, 0). Then, a point at (xo, yo, 0) after reflection will appear to be at (xi, 0, zi). So, to colour the pixel at (xo, yo, 0), find out what is the pixel at (xi, 0, zi) in your image.

You can do this for any shaped mirror: all you need to know is the equation of the normal to the mirror, this is required for finding the reflected ray.

Please let me know if anyone needs more details. I have been fascinated by anamorphic art!

Oh, that's a cool idea. It should absolutely be possible; the trick is figuring out how to make the drawing grid. I'm guessing you'll end up with two sets of curved lines somehow, without any straight lines; the trick will be figuring out how to draw them. I'll have to go think about it; maybe another Instructable eventually? :-)

I use reflective mylar coated on plastic (used for solar reflectors) pasted on PVC pipes. Works extremely well, as they are very reflective.

Prolonged exposure can lead to marks on the film, I have used standard thin lamination to get over the problem. Does reduce the reflectivity, but it is still great!

I didn't use a mirror at all --- I used a chrome drain pipe extension I found in the plumbing section at the hardware store. Anything reflective that could also be bent into a cylinder shape should work --- I can imagine taking a piece of silver mylar (like helium balloons are made of) and wrapping it around a soup can, though you'd have to work to get it smooth! Good luck -- let us know if you find a good alternative!

To adjust this for a sphere, wouldnt you just change the spacing of the concentric circles? This should account for the vertical curve in the same way that the angle of the radial lines accounts for the horizontal curve, right?

That was a very easy explanation of an art form which seemed very tough to me.
Thanks alot.
But, is there any measurements we have to follow in the drawing grid regarding the art grid.
& about the radial lines on drawing grid, do they particularly have to start and end on that point?

It kind of works. This is just me playing with it really quickly. You can see that the Polar to Rectangular "decodes" the image. It's split kind of funny, but the image seems readable.

3 replies

This is just Step 8 of the instructable, right? I used Filter>Distort>Polar Coordinates to make both the intro image with Hobbes and the Superman image. I hadn't thought about using Photoshop to "decode" a distorted image though, going Polar -> Rectangular. That's kind of a cool idea!

Sorry! Such an idiot. Thought this was all manually done. Didn't see how you used Photoshop.

Some of it WAS manually done; I'm tricky that way. :-) No worries though -- your question taught me something new, namely that Photoshop can do the inverse distortion too!

Wonder if you can use Photoshop's Polar Distort filter. Have you tried?

omg thanks you just sent my brain off on a photographic ramble involving light painting, mirrors LEDs and this tut :)

I wonder if there is software available to do this to stl files so you can print out a distorted 3d model that will look like a normal 3d model in the cylindrical mirror.