How to implement semi-randomized level in iPhone game?

Question

I want to create a game with a level structure similar to iCopter or Canabalt, where each level has a randomized floor (and roof), but the height of the floor is never impossible to reach from the previous one. I am also unsure on how to continually increase difficulty. I have searched far and wide for a tutorial or something like that, but I couldn't find anything. Can anyone help?

Answer 1

It sounds like far too specific a need to be the subject of a tutorial, to be honest. I've played Canabalt but not iCopter so I'll talk about a game like the former.

There are all sorts of calculus equations you could use to calculate acceleration and gravity to work out precisely where a platform would have to be in order to be reachable, but I suspect you will do just as well with a simpler approximation. If all your platforms are of a minimum length, then you can make an assumption on the speed that it's reasonable to expect a player to be able to reach by the time they get to the end. That, in combination with however long your jump algorithm keeps someone in the air, dictates the maximum distance that another platform of the same height could possibly be and still be reachable.

The highest platform you can reach is usually dictated by your jump algorithm - that could be a constant height, or it could be proportional to the speed, but either way you can easily estimate the highest reasonable jump you can make at the end of any given platform. This gives you a maximum relative height that you can reach from there.

Assuming your physics are fairly realistic and you apply a constant downwards force while the player is in the air, the apex of the jump will be at around the half-way point. So a platform that is the maximum attainable height relative to the player needs to be half as distant as one on the same level would be. And to find reasonable relative height and distance combinations in between, you can linearly interpolate.

Platforms below you are obviously more lenient - they can be further away than one on the same level, again by a distance roughly proportional to the speed you're travelling.

A simple algorithm then would be to pick, at each stage, either a higher or lower platform, pick a relative height from within the attainable bounds, then find the distance it needs to be at.

To adjust difficulty, you can start with these relative height and distance values above, which represent the extremes of what is possible, and reduce them by a proportion to make the jumps easier to complete. I might start with 50% reductions, +/-10% (randomised) to provide a few tougher jumps. Then as the game progresses, I'd slowly ramp that 50% down towards 0, so the player has less and less margin for error.

EDIT: Since I posted this answer, I found another interesting source which may be of use: A Probabilistic Multi-Pass Level Generator. Although the game in question is different (one of the Mario games I don't recognise) many of the principles are similar, in terms of placing platforms at reasonable heights and distances. Java code is provided.

Answer 2

I'm not sure how comfortable you are with math, physics, etc. but, in my opinion, this is a pretty simple solution:

Using a formula to determine if a launched ball will clear a fence in the distance is a reasonable way to find an arc defining the possible farthest points the next platform could be. It's a standard formula you learn in physics when studying projectile motion. There's a fairly interactive example here that includes the equation.

I'd recommend determining the position for your next platform like this:

1. Randomly choose a horizontal distance X from the end of the current platform to the beginning of the next platform (determine a reasonable range for X however you want).
2. Use the fence problem to find a maximum value for height Y to make the platform reachable.
   • You may need to subtract a small amount from the maximum height to ensure the platform can be reached depending on how you have things implemented.
3. Choose a height Y that is no higher than the maximum (remember that you can and should allow negative values for Y).
4. Place the next platform past the current one at distance X and height Y