I was recently using an algorithm for determining control points for a bezier curve. You need 4 total points to accurately determine the curve, maybe there is a similar curve that apple is solving for?

http://www.antigrain.com/research/bezier_interpolation/

// Assume we need to calculate the control

// points between (x1,y1) and (x2,y2).

// Then x0,y0 - the previous vertex,

// x3,y3 - the next one.