• You can bend around obstacles in a number of ways, including parabolas, 1/x, and exponential equations, but one way I saw someone else using involved combining terms of this format: “a•((x-k)+abs(x-k))” (I’m using • because HN is swallowing asterisks). k is the x-value at which your equation curves, and a is the slope afterwards. Each term like this adds another point at which your equation can change direction. It works because abs() is math’s equivalent to the “if-else” – with enough convolutions, you can make equations conditional on almost anything. However, I think with this technique, you have to change parts of previous terms to account for the new term – I haven’t figured out how yet.
• Add k•sin(99•x) to your equation to give yourself a “beam” k high.
I'm tempted to write a program that can create an equation of piecewise line segments to fire. The inputs would be a list of x-values of the segment boundaries and angles for each segment. I probably won’t get around to it, but someone else, feel free to.
> I'm tempted to write a program that can create an equation of piecewise line segments to fire.
I was also tempted to do that. I wanted to give it a graphical user interface, too, as that's what would be best for a human for this task: the user could click points on the screen, and the program would construct a piecewise function to connect them. (This would probably make the task trivial. But I'd want it done anyway--I like seeing this sort of thing demonstrated.)
Definitely an interesting idea, I can now apply all those functions I learned from calculus ages ago!
One suggestion, provide a list of "standard" functions, on a normal 4-quadrant Cartesian plane, showing how they look on the graph. It'd definitely lower the barrier to entry.
I think it'd be more fun if you could move around. Maybe having the choice to skip a turn and move a unit around?
Also maybe having a preview of what your equation looks like? It'd make the game easier and you'd still have to think about what kind of equation to use.
Ever since I played DOS games like Scorched Earth and the Gorillas game that came with DOS 5.0's Qbasic, I've wanted to take the concept further and use it to teach kids math in a fast-paced video game setting.
I haven't played this particular game due to the Java requirement, but I do like the idea.
• You can bend around obstacles in a number of ways, including parabolas, 1/x, and exponential equations, but one way I saw someone else using involved combining terms of this format: “a•((x-k)+abs(x-k))” (I’m using • because HN is swallowing asterisks). k is the x-value at which your equation curves, and a is the slope afterwards. Each term like this adds another point at which your equation can change direction. It works because abs() is math’s equivalent to the “if-else” – with enough convolutions, you can make equations conditional on almost anything. However, I think with this technique, you have to change parts of previous terms to account for the new term – I haven’t figured out how yet.
• Add k•sin(99•x) to your equation to give yourself a “beam” k high.
I'm tempted to write a program that can create an equation of piecewise line segments to fire. The inputs would be a list of x-values of the segment boundaries and angles for each segment. I probably won’t get around to it, but someone else, feel free to.