Transformative Art — A Polygonal Shadow Self-Portrait at Angle

Transformative art was a field that I previously considered inaccessible to a beginner such as myself. I was presented a variety of transformational art forms as my AP Precalculus final project at Concordia International School Shanghai. My instructor, Before entering the world of transformative art, I decided to examine where my talents and interests meet the brand-new challenge of transformative art. My instructor, Dr. Tong, gave me inspiration to make the Shadow Face project but with a twist. I settled on this project as I feel like with my skillset it would be practical as well as interesting to do. I started out with a portrait of my morning face (depicted below) and made an artistic polygonal outline of the shadowed regions of my face in Blender. I would make a cardboard shadow cutout based on the shadow filter shape I designed in Blender, where I’m able to make sure the shadow projects correctly.

Fig 1A. Left, the base shape I came up with for the project; Fig 1B. Right, my actual face shape and the photograph I used as reference

But a simple shadow filter alone wouldn’t be much of a transformation, would it? I decided to add a catch. The shadow wouldn’t be correct to the image, except at one specific angle.

That way, the light source would have to be rotated in a specific direction — a transformation — which leads to transformative art. Here’s a brief explanation of why and how that works.

My face, now separated into thirds, joined by two parallel 30° plates. It doesn’t look exactly correct from the front, neither will the shadow. You’ll see why below.

The Math Behind the Shadows

Because of the addition of these 30° angled separation plates, transformations are now required to make the shadow project the correct face shape and proportions compared to my actual face in Fig 1B. The below image models what would happen if our light source was directly in front of the cardboard shadow cutout, and the beam in a direction perpendicular to the cutout.

As shown in the above diagram, when light is projected at an angle perpendicular to the parallel faces AB//CD//EF, which represent my actual face shape, it will result in an inaccurate lengthened shadow A1F1 (the entire shadow being A1B1C1D1E1F) that would significantly stretch certain parts of my face. In order for the shadow to be correct, we need to make sure that the shadow only displays the faces AB, CD, and EF, and that B1C1 and D1E1 are zero-length segments on the shadow. To do that, all we have to do is make sure that the light source direction is parallel to BC//DE, a setup which will be displayed in the diagram below.

As a result of the light source coming from a parallel angle to BC//DE, the shadow made by segments BC//DE on the wall [B2C2,D2E2] are zero-length, and without these segments, the face shape will be accurate. From this angle, the cardboard cutout would look like (left), and the actual cutout projected the shadow (right).

In addition, as a result of the shadow shape being proportional to the cardboard cutout shape as long as they are aligned along the same angle, the shadow face shape will always be correct regardless of distance as long as light direction is correct.

This means that it’s not that great of a challenge to get a nice shape out of this cardboard cutout, at any size. All the shapes will be proportional and accurate as longa s the light source and beam are parallel to the 30° segments CD and EF.

Final Result

Left, The cardboard cutout; Right, the correctly shaped shadow projected.

As you can see, with the light being projected at a correct angle, I was able to get a perfect shadow of my face (refer to Fig 1B, the image this was based off of). I had to jump through several hoops to turn blender into reality, however. Including UV-Mapping the 3d shape in blender on each side to construct and carve it out of cardboard.

Left, mask outline used to cut out cardboard pieces; Right, the cardboard after being carved out.

UV Map, exported from blender, 2d front view of the 3d shape used as cutting reference on cardboard.

Thoughts About This Project

After pulling off the Shadow Face project, I realized that transformative art may not be so out of reach, and even beginners like me can make interesting and unique pieces out of shadow art. I was also intrigued by the math behind it, and I was intrigued by the fact that the size of a shadow can be modeled just from ratios, like similar shapes being scaled up. Overall, I think transformative art is a great way to explore math, and it allows students of AP Precalculus to go beyond their curriculum to explore art that they’re passionate about. I’m very glad I was able to apply my passion in blender to this project, and I might consider making more complicated shapes in the future. After all, neither shadow art nor blender are limited to just my own face.