After a week of evening programming I have a basic real time simulation with 3D visualizations, latitude/longitude coordinates, real units, a boat model with a rudder that can only be moved at a certain speed, current, a GPS model and the auto pilot itself.
The autopilot does not know which way the boat is pointing: it derives its course from recent GPS readings.
In the video the boat is travelling 30 MPH. The orange waypoint is approximately to the south. There's a side current of 6MPH - you can see how the boat has to travel somewhat sideways at the start.
Some planned improvements include adding a magnetic field sensor to make better actual course predictions, introduction of GPS inaccuracies and the ability to deal with them and the rotating effect of following seas.
And then finally porting this to a microcontroller and building the hardware.