I am building a space sim and I'm having problems with my ship not smoothly transitioning between waypoints (or sometimes missing them entirely). The code I have been writing and re-writing and re-writing (many times) has yielded the same results. I have "TurnTo" code so that my ship will look at the waypoint it has targeted. I can accelerate and decelerate if it's a straight shot with 1 waypoint. The problem comes when I have more than one. I have been using simple linear vector math to accomplish these futile efforts.

Now I would like to try an approach I didn't want: Parabolic paths between my waypoints. Essentially, I am discarding any notion of laws of motion like momentum for a "fixed" path. I hope I'm explaining it correctly.....

Basically I want each of my waypoints to be the "axis of symmetry" of a parabolic equation. Of course, this needs to be 3D. I'm not sure where to start with this, so any help would be appreciated.