This project was a really long, winding process. I'm going to try to explain it the best I can here. It was originally written in Python as it was for a class project. I used the Pygame module as a graphics library, which I learned from a video by the YouTuber Clear Code. This project began once I finished my Fractal project around April 1st.

When I started this project, I set out to make a software simulation of physics for people early in an engineering or physics education or with a strictly art and design-based education. I've seen 2D dynamics sandboxes before (though actually when doing research for this project, I couldn't really find much). However, most of it blackboxes what's actually going on on the computer graphics side. I wanted to create some kind of sandbox that shows how soft and hard bodies interact. I figured some kind of changing cloth would be the best option for a soft body, particularly because cloth is EVERYWHERE in traditional and digital art. This was the simulation choice that would give the most bang for its buck. As I continued through this project, I thought more about what "cloth" can model. Hair, human skin clinging to its bone, waves, and more. Of course, I knew once I'd decided to do a cloth simulation that I'd likely be using a mass-spring model to track its movement as mass-spring models already work for just about everything.

To remedy this transparency issue, I retained the points between sticks in the cloth mesh and retained sliders that are analogs for the real-world forces. Why analogs? Well, initially, I created a cloth sim based on equations I had learned in physics class. Updating position based on first calculating acceleration from Newton's 2nd Law (using Hooke's Law for force), then integrating velocity, then integrating movement. However, the results I got, while somewhat accurate (the mesh slid down based on gravity but held up by "pins" up top) had difficulty remaining stable as the animation continued and also did not respond well to constraints I tried to apply. I couldn't tell if this was a software issue or a physics-knowledge issue.

This is when I had to start researching. I found an article on Pikuma about cloth simulation and Verlet integration. This is where I learned about Verlet integration of course, which is a form of integration position based on implicit velocity and not explicit velocity. Essentially, rather than calculating acceleration from force and velocity from acceleration, you calculate velocity as the rate of change from position. So, Verlet integration essentially is a position-based analog to regular physics-class integration of movement. Similarly, you do a position-based analog of Newton's 3rd law when you correct.

In a mass-spring model of cloth, the stretchiness of a fabric is modeled by the stiffness constant (k). Since most data for fabric stretchiness is given via Young's Modulus, you need to convert it first, which can be difficult but is still possible. Then, you calculate spring force from Hooke's Law and integrate velocity and movement from there. However, this does not lead to stable results. Instead, you do a position-based analog! Putting it crudely, spring force wants to expand or compress to go back to its rest length. Instead, we store the initial (rest) length of a stick initially by copying the distance between its two assigned points. Then, we correct the points back to bring the sticks back to their initial length. Effectively, this does the same thing. You wouldn't want to use it in a physics class because energy is not conserved correctly, but in a computer simulation with constraints, this is the best option.

I think, in the end, I ended up creating a tool that would be best suited for people learning computer graphics or digital art more so than traditional work. I'll need to keep thinking about what would be most helpful for traditional artists, but I think this gives me a good "jumping off point" to start with. I'm pretty happy with this project. It may not be the MOST impressive thing ever, but I really feel like I've learned a lot more in the direction I'm trying to dive more towards.

My First Cloth Sim!