The Mathematics Behind Anamorphic Art

Hi, my name is Juha Kim, and I go to Concordia International School in Shanghai. For our AP Precalculus 2024 project, we were given Transformational Art as our theme. I decided to work on anamorphic art using a bendable mirror.

What is anamorphic art?

Anamorphosis is a cool perspective technique that gives a distorted image of the subject represented in a normal picture when you see it from a particular angle or reflected in a curved mirror. The distorted image disappears and the picture appears normal.

Anamorphosis originated from the Greek prefix ana, meaning again or back—the word morphe, meaning shape or form. I bought a bendable mirror and made a cylinder shape myself. Mirror anamorphic images are created in a flat horizontal plane. A reflective surface is then placed at a specific location on the horizontal plane so that the image in the horizontal plane can be reflected onto the surface to reveal the normal image.

Here are some other examples of anamorphic art that doesn’t require a mirror, but a specific angle to make it appear in a particular form.

For me, I wanted to make this project meaningful. Since I lived in Tokyo, Osaka, Seoul, Taipei, and Shanghai, I decided to design this project with signature landmarks in each city.

Seoul — Namsan Tower Tokyo — Tokyo Tower Taipei — Taipei 101 Shanghai — Oriental Pearl TV Tower

I was born in Seoul, Korea, and lived there for 4 years. I moved to Japan Tokyo when I was 5 and stayed there for a year. I moved back to Korea and stayed there until I was 10. I moved to Japan and lived there for 3 years, starting from 5th grade to 7th grade. I moved to Taiwan and lived there for 3 years, starting from 7th grade to 10th grade. Now, I have been living in China Shanghai since 10th grade. I am planning to graduate here at Concordia International School.

Here is the model I made for my final project.

I started by designing the images. I printed them out and colored them using colored pencils. After cutting the images, I placed them on a pink board with the mirror.

The cylindrical anamorphic art form involves making an image that only appears “correct” when viewed as a reflection.

I used the grid map to shape it correctly

Here is the formula for cylinder anamorphosis formula.

Rausch, K. (2012). The Mathematics Behind Anamorphic Art. The Mathematics behind Anamorphic Art. https://archive.bridgesmathart.org/2012/bridges2012-513.pdf