I want to extrapolate the positions and rotations of some object for a game mechanic I want to try out in where a NPC predicts what is going to happen in the near future. I know there are several extrapolation formulas used for multiplayer networking and that these formulas are used in economics. But I want to utilize this in my game design and therefor I thought I would be handy to get some information about the subject first. What has been done in this field and does anyone know any formulas that can predict a point in space based on a sequence (between maybe 10 and 20 frames or so) of positions. If I can apply it for positions I can probably also apply it for rotations.
Any ideas?