Graphwar -- Artillery game where you use mathematical functions
graphwar.com
graphwar.com
• 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 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.)
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.
You don't - everyone sees themselves and their teammates on the left side of the screen.
- a dot where x and y integers intersect ( like the intersections of the lines on a math notebook ).
- ability to preview the trajectory;
- larger font for the formula box
- ability to choose direction to shoot in
The concept is very interesting, and this could be quite useful for people who want to improve their knowledge of function graphs.
Also, really wish this were flash instead of a Java applet.
I haven't played this particular game due to the Java requirement, but I do like the idea.