$(x,y)$ points extrapolation

My process is generating $x,y$ points. The points are result of tracking movement of an object so its a bit inertial. The tracked object can't change direction rapidly. I need to extrapolate data between 2 points. I have an advantage that I know points before missing points and after missing points. There is a picture for a better understanding. Dotted line need to be extrapolated and I know how many points are missing.

• One method that will give a smooth curve is making a spline of the points you got and using the results to get the missing points (for example a qubic spline). – Winther Apr 19 '15 at 14:23