My mind boggles thinking about implementing a mechanic like this, especially in 4 days. Amazing work!
91 days ago (+1)
Thank you for playing and sharing your thoughts! It quite helped me realize what the players generally missed (which seems to be able to utilize the transformations to their full extent since I provided no demonstration through tutorial levels!). Stuff like this for e.g. as I noticed you tend to try drawing with just the plain grid.
I want to say I really appreciated your inquisitiveness into both details regarding the math involved in the game as well as to my research :P. In fact, I originally intended this game to have some educational value and I think you were the only one who displayed some interest in that side! So here is one resource that might help: https://xaktly.com/Matrix2Dtransformation.html . If you try multiply Kx * Ky, it’ll turn out to not be equal to Ky * Kx! Scaling on the other hand (like stretching the whole grid) would commute, because they can be written as diagonal matrices.
I guess this is not extremely satisfying tbh, more of an empirical way to justify it. A deeper understanding can somehow be understood by learning more about group theory and in particular the group of 2D transformations on euclidean space. It involves rather abstract ideas but incredibly generalized results. I’m sorry for the exposition xP this stuff gets me quite excited!