Jumping, launch velocities and rounding errors

The physics behind a jump in a platformer is pretty simple and something I must have written a thousand times, but having an AI player jump and land where it wants to is considerably trickier. My initial attempt was to string a bezier curve between the start and end points and just make it follow that - this is easy to do and very reliable (as it will always get to the exact end point) but produces unconvincing motion. It really needs to use the proper physics otherwise it looks out of place.

Continued at my new journal location...