Quadratic Bezier Control Point Calculation

ctrlpt.m

// http://en.wikipedia.org/wiki/Bézier_curve#Quadratic_B.C3.A9zier_curves
// `t` is the percentage of curve where `third` resides, and should be in [0, 1]
CGPoint GetControlPointForQuadBezier(CGPoint start, CGPoint end, CGPoint third, CGFloat t) {
    CGPoint ctrl = CGPointZero;
    CGFloat t2 = pow(t, 2);
    ctrl.x = -(((pow((1 - t), 2) * start.x) + (t2 * end.x) - third.x) / (2 * t * (1 - t)));
    ctrl.y = -(((pow((1 - t), 2) * start.y) + (t2 * end.y) - third.y) / (2 * t * (1 - t)));
    return ctrl;
}