Calculating Collisions
I had my midterm exams this entire week, so naturally I ended up wasting a lot of time on YouTube. Something interesting happens during exams — I procrastinate more and do everything except study, even productive things. Human psychology I guess. And I know I am not the only one; I know full well that all of my friends share the exact same laissez faire attitude during exam season. Or maybe it’s true that birds of a feather flock together.
I was binge-watching clips of The Office, and came across the scene where everyone is eagerly waiting for a DVD logo to hit a corner. And that made me curious — how many collisions does it actually take? So I quickly wrote a basic function to count the number of collisions for some initial coordinates and some given aspect ratio for the bounding box. I added two more lines of code to visualize the collisions as well. And got this:
Initial Y: 0.0000
Aspect ratio: 3.0000
Collisions: 5
You also can try specific aspect ratios: Most screens will usually have an aspect ratio of either 4:3 or 16:9. Anyway, I think there are some interesting insights. The collisions will either be infinite or finite depending on the initial conditions. It is finite whenever the ‘criss-crosses overlap’ — for lack of a proper definition/description. Note that it may not seem that way because the canvas has a finite precision, so if the Y position is off by even half a pixel, it will not register as hitting the corner.
Designing the function for collisions made it obvious why it has to be that way: Collisions are symmetric and the bounding box is a rectangle. So if the rhombic tiles are coming close to each other, it means the ray elsewhere is experiencing two close collisions — somewhere near a corner. As the tiling patterns overlap, that collision difference reaches zero which means the ray has to hit a corner. It also means that other initial conditions result in an infinite loop. That DVD square will never reach a corner. Sad.
As for other things, The Plan™ got derailed. Of course, it did. But to be fair, I did have my midterms all week. And while I did procrastinate a lot, I did learn other things — mostly about rotary positional embeddings. This post here explains it pretty well. Anyhow, I’ll try to start The Plan™ this week. For real. (If the lab exams don’t ruin my schedule.)
Cya next week.