I got an email today from a student looking for an interpolation technique to create smooth curves from a series of points. The reason he was after this was that he was making a game. His problem was that the technique looked a bit complicated and hard to implement on the target platform.
My advice in these situations is always “don’t sweat the complexity”. The simplest way to do this kind of thing is as a series of straight line segments. These are easy and quick to implement and should let you get something working really quickly. If the gameplay works OK, just stick with that technique and work with it. Remember that the player enjoying the game doesn’t know that you originally wanted to add curves. Only put the curves in if your game needs it.
If it turns out that lines would not be appropriate for your game theme, just change the game to one where lines do make sense. Remember that games are like “The Twilight Zone”. You control the horizontal and the vertical. The player is entering your universe, so you can define it as you like. Straight lines or curves, it’s all up to you. But start simple.