My Project and Reflection

My Reflection
In my Project I used a lot of different graphs to create my face. I think I used the parabola the most because it was easy for me to manipulate the graphs by doing translations and expansion/compressions so it would turn out the way I wanted. The parabola was very useful for places where it wasn’t pin straight, but it had a little, tiny curve like the sides of my face. The most difficult functions to use for me were the new ones we got taught ellipses, circles and hyperbola. After a while I did get the hang of translating them and creating the correct radii, but in the beginning, I would use a lot of sliders to help especially for the hyperbolas.
Now I am going through an explanation of what graphs I used for where and why.
For my nose I used a hyperbola, and this was the first graph I started with, and it took quite some time to make sure it looked good. I used ellipses for the nostrils and a cosine graph for the tip of my nose and I really like how it turned out. I also used restricted circles for the sides of my nose.
For the eyes I used a radical for the inner corners and used multiple parabolas to create my eye shape and I used a crazy number of logarithms to create my eyelashes and I created a type of pattern so that the distance between each eyelash was the same. Doing the restrictions for my eyelash was probably the most tedious job I had to do for my drawing.
For my lips I used 6 parabolas with a different expansion/compression and used restrictions to use parts of the parabola I wanted too.
For my eyebrows I used some exponential, linear, and parabolic functions.
For the structure of my face shape, I use a log for the jaw line and a parabola for my chin. For the sides I used some parabolas that has a function of ‘y’ and finished the little details with linear functions.
For my hair I used mostly parabolas except for the curtain bangs which I used cubic functions and for my middle part I used a part of a hyperbola.
For the necklace I used a hyperbola (with a line of symmetry on the x-axis) to create the chain. Then I used another hyperbola for the attachment of the flower to the necklace. For the actual flower necklace structure, I used ellipses and circles. Then I used more hyperbolas for a nice design
For the arms of my light blue sweater, I used restricted logarithmic functions and for the middle I used a hyperbola. I used a parabola to create a shirt underneath and created a button with an ellipse and some circles. I also created a small buttonhole on the other side of the sweater with half of a hyperbola.
Lastly, I made my initials “NJ” just for fun!
Now I am going to talk about what techniques I used to make it look even better!
I used restrictions on all my graphs except a few circles or ellipses where I didn’t need to.
There wasn’t a wide variety of options for colors, so I used a website called “free eyedropper tool” where you can upload a photo and it will give you the correct coordinates for any color on your photo that you place your mouse on. I searched on YouTube, and I found a way to create the colour on demos(I’m not going to go in detail because it would take some while to explain) So I used these colours for my skin, eyebrows, hair, lips, sweater and necklace. I found a photo online of a gold and silver necklace, so I used that to help me get the colours I wanted for my necklace.
The most difficult part for me was the shading. I found out myself and with friends and on YouTube some different ways you can use shading, but they wouldn’t on every function
1) You can use inequalities
2) You can make a letter equal a function then: H<y<J for example but this would only work for functions that had the ‘x’ restricted not the ‘y’ so I had to go back and change the restrictions for some of them which was frustrating. Other problems were that if I wanted to make a letter equal to the equation to for graphs like hyperbolas, ellipses, circles, and parabola that is a function on the ‘y’ I had to SOLVE the function for ‘y’ and sometimes it wouldn’t work because when you take the square root you get + and – but it doesn’t have that option. So, if I was LUCKY and only used the positive or negative side ONLY it would work!
Other problems was that sometimes it just wouldn’t work, and the shadings would overlap so for some functions I had divide it into TWO-FOUR different parts and restrict all differently.
For one section of my hair (under my curtain bangs) I added some more complex shading to make it look more realistic.
One other issue was when I started to run out of letters in the alphabet for sliders so what I did was for the functions I didn’t want to change any more I would plug in the actual number so I can delete the sliders. I also so a YouTube video of a guy who used capital letters and that helped a lot.
The only place my face was symmetrical was for my eyes and eyelashes so I copied the functions, so it flips over the y axis and changed the restrictions but for the rest of my face I did each side separately because my face isn’t fully symmetrical especially my eyebrows, so I made sure I did this, so it looked more realistic.
The last details I did were the thickness of my lines and the darkness of the shading. For example, for my eyes I used full shading while for my lips I did lighter shading. Also, for my necklace I used different thickness so it would look more realistic, and I did that for my clothing too.