Swinging with trigonometry- 3 mins
As a result of commuting, I’ve found myself back playing mobile phone and web games on the train. It’s a nice pass time, but I recently came around a game that although seems remarkably simple, it’s actually a ton of fun to play (plus it gets really challenging). Handulum + is a physics based game where you can “catch” a falling ball and swing it along a pendulum. I got decently far, but wanted to see what it would take to actually recreate this sort of physics engine. I’m not really a game developer, but I’ve been really interested in developing more low level graphics for creative side projects and though this would be a good place to start. Check out Handulum + below though, its miles beyond anything I could create!
The first thing I did was choose my ecosystem. Since my day job mostly revolves around Python, I quickly found myself reading into PyGame. The syntax was brief enough and it could draw circles and lines, which was more than enough on the graphics side for me. My main goal here was to recreate the physics involved, not spend too much time trying to make it pretty (although that might be a fun extension to this project). A few tutorials later, I now had a bouncing ball that somewhat emulated gravity.
But this game obviously required a bit more than bouncing. I needed to figure out how to get the ball to move in circle, and even more, observe some conservation of momentum as it attached and released from the pendulum. This was certainly more challenging than I had initially thought, and quickly found myself lost in Google searches and endless equations describing motion in “simple” pendulums (not so simple for me!).
When I first started, I simply tried to do everything via code, but I quickly found the ball moving in all sorts of crazy ways, and not getting and progress. In the end, I found it best to just draw it out, and pull out some handy-dandy trigonometry. What’s not shown below are the 10+ other pages of scribbles that I threw away along the process.
I realized were two key aspects that I had to consider:
- Converting forces in x and y directions to an angular direction via trigonometry (thanks to SOH-CAH-TOA).
- Understanding that angular velocity can be represented as linear velocity (in x and y direction) via the angle of the tangent, which luckily enough is also calculable via trigonometric equations.
Overall, this took me quite a bit longer than I expected, but I did end up learning a lot and brushing up on some mathematics that I had long forgotten. Doing this in Python made this project a lot easier as I was very comfortable code organization and structuring everything in an object oriented manner. Take a look at the prototype below:
If you’re even more curious, feel free to fork the repo and try running it yourself. Let me know what you think.