Desmos: Totoro

When it came to figuring out what exactly I was going to draw on a graphing calculator, I had a lot of trouble selecting an image to base my work off of. I considered doing rather complex flowers or characters, but their outlines were so irregularly illustrated that I spent half the class time on the first day searching for the right image. Finally, I just decided to stop looking for something “easy” and do something I actually like. I chose to draw Totoro, a mythical creature in the Ghibli Universe. He had curves and lines, edges and rounded corners, so I thought he’d be appropriate to show my skills in graphing.

In the first few lines I drew, I thought I’d try some guessing and testing, punch some numbers in, and check if it would fit. This method was very ineffective and inefficient, so I looked back on my note package and used some of the things we learned about prior to this project. Sure enough, efficiency went up!

For each of the body parts, I used the following equations and functions.

Nose+Mouth: Circle relation, linear equations

Whiskers: Linear equations

General body outline: Square root function, Reciprocal function, Quadratic equations, Cubic Equations

Feet: Reciprocal equations, linear equations

Eyes: Circle relations

Chest Marks (these took a lot of experimenting to do as they were all slightly different irregular shapes.): Linear equations, Circle relations, Quadratic Equations.

As for strategies, I had a few.

Because Totoro has seven chest marks, all of them slightly different in size and requiring two circles, I copy pasted circle relations in and just changed the variables that needed to be changed rather than plugging in new values to a skeleton equation every single time Totoro needed a circle.

Totoro is also symmetrical in some parts of his body. By copy pasting some equations and by adding a + or – in necessary places, I reflected some lines over the y-axis and saved a lot of time.

I also played around a bit with restrictions as well, using both > and < in them to have fun.

If someone were to ask me what I learned from doing this, I’d tell them I know how to draw things with math now.

That’s a joke –

In all seriousness, I familiarized myself with what different lines from different functions and relations look like. I also got to practice domain and range using restrictions and developed critical thinking every time I thought Hm, that didn’t work. What should I try next?

Overall, this was a very satisfying project. I have to say, after 80+ equations in desmos, one feels a great sense of accomplishment!