I’ve been working on a small game recently, the goal of which is to change your player’s color to match the colors of incoming lines so that you can pass through them. Detecting when the player crosses a line is at the core of the game.
Detecting which side of a 2D line a point is on is a pretty simple task. I’d wager most people have encountered the problem relatively early in their game development efforts (not allowing the player to move outside of the screen, for example). Nonetheless it’s probably something that people (including me) have solved in an inefficient or needlessly complex way. So I’m going to go over the problem and solution implemented in my game.
, and I said that there was room for improvement. I thought about it a little bit and found a couple things to speed it up.
has the information in there: there will always be more twos than fives. Counting from 1 to 10:
, a 16-bit (2-byte) integer has a max value of
, etc. In fact since any integer in a computer is made of bits it will have a maximum value of 
. The prime factorization of an n-bit integer is in the notation, it is n 2s all multiplied together. Like so: 
, 
. For example 
and 
. The 
. That’s a big number, over a googol. You can see the whole thing