https://www.desmos.com/calculator/7nsmfuwhrg

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For my project, I used many different types of functions and equations. For my head, I used an ellipse for the top of my head, and hyperbolas for the shaping of my cheeks, jaw, and chin, my neck was made of two different squared lines. I chose these functions for the power I had to manipulate them and make them into the closest shape to my picture as possible. I could also change the direction of the hyperpolia’s easily, making my chin and cheeks an easy fix and flip over the x and y-axis. My hair might have been the hardest part of this whole process because I couldn’t find a way to emulate my hair without making it too straight or too curly. So, I made it in two parts with an ellipse and a wave function that I rotated so it had some dimension to my hair. My lips were made of two ellipses that I made the lines very large for. My nose was also really hard to make, it’s made of straight angled lines and three ellipses as they gave it the best shape that was easy to connect and make it look like a fluid body part.    

However, the thing that I am the proudest about this project is the research and learning I did to extend my knowledge in graphing ellipses. During this project, I really want to rotate the ellipses to create my eyes and eyebrows. And while I did make my pupils circles, I scoured the internet to find how to rotate ellipses and found it! https://www.youtube.com/watch?v=m4RHSzWHPdY, this video not only shows you how to write out the equation but also how it works and a little bit as to why. This is how I made my eyes and I am so proud of how they turned out, it also became easier to make my eyes not having to make them out of three or four parts while achieving the same results is very rewarding.  

Learning links  

Link to angled ellipses – https://www.youtube.com/watch?v=m4RHSzWHPdY 

Angled Ellipses– \left(\left(h+a\cos t\right)\left(\cos q\right)+\left(k+b\sin t\right)\left(-\sin q\right),\left(h+a\cos t\right)\left(\sin q\right)+\left(k+b\sin t\right)\left(\cos q\right)\right) 

How to create custom colours – https://www.youtube.com/watch?v=bdRsIeTvSnY 

Colour website – https://htmlcolorcodes.com/