In this project, I had to utilize different functions to represent the features of my face. I firstly used a reference photo where I could overlay the functions on top. Despite this daunting task, I decided to simplify it into shapes as visualizing it wholly made it quite difficult.

For the pupils, I used circles; however, due to the eyelids being curved (the top lid an ellipse and the bottom a parabola), I had to overlay two circles on top of each other and create restrictions so that the pupil wasn’t over the eyelid. Restrictions are something I utilized a lot in this project, especially when it came to the hair where I used parabolas, circles, ellipses, and cubic functions. I used these functions as each had a curve to the line which mimicked the slight curls of my hair. I also used inequalities to shade my pupils so that they were fully black.

I also used the radical function for my eyebrows and my double eyelids as their shape naturally curved in the beginning to soon flatten out slightly. For my nose, I used ellipses and absolute value function as it was able to capture both the sharp and rounder shape of it. I often used ellipses as I found it easier to manipulate as I could change the value of h, k, a, and b. This allowed me to translate it vertically and horizontally, but also expand and compress it. Furthermore, I could also create a larger radius which helped with the larger portions of my hair. Using the sliders too was very useful as inputting in every single number can get quite long, so having a shortcut way of doing it was efficient.

For my mouth, I used hyperbolas and linear functions. My mouth had a rounder shape on the bottom but turned sharper on the top (similar to my nose). I found that using hyperbolas were easier when it came to larger portions such as my clothing. I used two hyperbolas for the shirt I was wearing as the hyperbola allowed for a subtle ‘v’ shape that looked more natural than a straight line. For the straps of my shirt, I vertically translated the hyperbola high up so I could get a curved line and added restrictions around the center of the graph instead of inserting a bunch of linear equations.

For my shoulders, neck, and jaw, it was a combination of multiple functions. The cubic function came in handy for my shoulders as if I expanded the function, it would resemble the natural curve of a shoulder. I used another hyperbola for my chin as it was easier to transform as using a parabola ended up being a bit finicky for the shape I wanted. For the sides of my jaw and my neck, I used linear functions as they were good for sharper features.

Overall, I found that I utilized the quadratic function and ellipses the most in this project, finding them the easiest to manipulate as one I was very familiar with and the other having the shape that resembled the most to the features on my face. Working on this project improved my skills in restrictions as almost every single function contained a restriction. It allowed me to find creative ways to ensure that functions were lined up and parts of the function were hidden.