The functions I selected in drafting my self portrait were useful because they very accurately traced and followed the lines of my facial structure and could easily be used to depict my facial features. One function I used very consistently were a regular linear line graph and a parabola. Although I utilized many other graphs I made use of these two an exceptional amount of times. I used it for my chin along with my lips and top of my head. I used the line graph for my eyebrows and for certain small portions of my hair. In terms of unique functions I used two tangent graphs to perfectly sculpt the edges of my nose paired with circles graphs to get the extra curl at the bottom. The lips were a challenging portion as I couldn’t figure out how to properly shape my lips and what graphs to use. In the end I used a restricted ellipse along with two restricted widened parabola to form the top lip. To make the dip in the middle I used to separate lines and linked them. I also added a bit of a wrinkle to the end of my mouth by using some circles I cut in half.

I believe I’ve achieved an extending on this project for many reasons. To start the graphs I chose to make my self portrait are easily recognizable as facial features. I also experimented heavily with different graphs testing which shapes fit best for the given features and even figured out how to alter formulas in order to tilt ellipses. I also researched and tried many different shapes with complex formulas that may help in the construction of my portrait. Along the entire process I restricted the domain and range to aid in the shaping of my face and make proper cuts to provide a more seamless transition between lines. I used sliders to change the positioning of graphs that contained more than one of the same variables. I also used colour to distinguish between my face and air. To create an extremely pleasing composition I did the best I could to smoothen the lines and make it seem as if the graphs appeared as one solid one. When selecting graphs I took alot into consideration based on my needs. For something like the hairline it would be more more ideal to use something like a parabola which is significantly simpler to restrict and also type than a hyperbola.