MATH + ART

For many, math and art seem like two completely separate worlds. Growing up, I always had the observation from others that math is often perceived as rigid and logical, while art is viewed as creative and expressive and as expressed in the lecture, the education system has fostered the idea that creativity is derived from the precision of our art-making skills. However, these two subjects have more in common and its intersection is becoming more recognized than ever. In my psychology course last quarter, we were taught about kaleidocycles, a ring of tetrahedra created by folding paper numeral times. This was created by Wallace Walker, an artist, who created 3D objects from paper and this creation had an impact on mathematics. 

Kaleidocycles

For me, both math and art have been my escape from the stresses of everyday life. I have a piece where I used both math and art extensively. In this video, I wanted to create a 3D “room,” and at first, it was tremendously difficult to keep track of each object’s location. It was only when I looked closely at the position values when I realized it follows the Cartesian coordinate system, which is recognized in 3D-graphics foundations. With this, I was able to move my objects at a more efficient rate and create a product that I envisioned.

3D Model in my video

I also encountered this intersection when I had this keen interest in creating facial filters that we commonly see in social media platforms like Snapchat and Tiktok. With this week’s material, I was inspired to research the math behind the filters extensively. While the process is long, I learned that facial recognition starts by using the Viola-Jones algorithm, which involves the conversion of an image to grayscale and the attribution of a numerical value to each pixel based on its tone, overall creating contrast. Facial marking is also done through Delaunay Triangulation/Voronoi Diagram to calculate the position of each facial point in 3D space based on the 2D image of the person's face, while also implementing Active Shape Model and the “golden ratio” of a face, which is defined as approximately 1.618. When these processes are combined, graphics and animations can be added to the precise points of the mesh model. Math and art worked together to create something that’s commonly used now!

Viola-Jones algorithm

Active Shape Model

The intersection of math and art is a fascinating and rich area of study that offers endless possibilities for creativity and innovation. Overall, the use of mathematical concepts and principles can enhance the beauty and aesthetics of artistic creations, while art can also provide a unique and engaging way to learn and explore mathematical concepts.

Sources

Text:

Köller, Jürgen. “What Is a Kaleidocycle?” Mathematische Basteleien, http://www.mathematische-basteleien.de/kaleidocycles.htm. Accessed 14 April 2023.

Maningas Cosmetic Surgery. “What Is the Golden Ratio of Facial Aesthetics?” Maningas Cosmetic Surgery, 2 Mar. 2023, https://mcosmeticsurgery.com/what-is-the-golden-ratio-of-facial-aesthetics/. Accessed 13 April 2023.

Philpot, Emily. “The Selfie Method: Exploring the Mathematics behind Your Favourite Snapchat Lenses.” Medium, Medium, 25 Mar. 2021, https://emilyphilpot.medium.com/the-selfie-method-exploring-the-mathematics-behind-your-favourite-snapchat-lenses-aa7d3ca8d2f6. Accessed 12 April 2023.

Slick, Justin. “3D Defined in Computer Graphics and Film.” Lifewire, Lifewire, 9 Dec. 2019, https://www.lifewire.com/what-is-3d-1951. Accessed 14 April 2023.

Vesna, Victoria. “Math + Art | Lectures.” DESMA9. https://bruinlearn.ucla.edu/courses/160989/pages/unit-2-view?module_item_id=5946322. Accessed 12 April 2023.

Xiao, Yi, and Hong Yan. "Facial Feature Location with Delaunay Triangulation/Voronoi Diagram Calculation." ACM International Conference Proceeding Series. Vol. 147. 2001.

Images:

Arcangel, Aubrey. “Active Shape Model.” DEV Community, 30 Jan. 2018, https://dev.to/aubreyarcangel/snapchat-filters-how-do-theywork-4c83. 

Payumo, Winzel. “Ariana Grande | OTW.” YouTube, YouTube, 20 Aug. 2018, https://www.youtube.com/watch?v=k7bV9BAfFUA. Accessed 14 April 2023

Philpot, Emily. “Viola-Jones Algorithm.” Medium, https://emilyphilpot.medium.com/the-selfie-method-exploring-the-mathematics-behind-your-favourite-snapchat-lenses-aa7d3ca8d2f6. Accessed 14 April 2023.