| private GetX ( System.Windows.Vector v ) : System.Double | ||
| v | System.Windows.Vector | |
| return | System.Double | |
/// <summary>
/// Attempts to find a slightly better parameterization for u on the given curve.
/// </summary>
protected void Reparameterize(int first, int last, CubicBezier curve)
{
List <VECTOR> pts = _pts;
List <FLOAT> u = _u;
int nPts = last - first;
for (int i = 1; i < nPts; i++)
{
VECTOR p = pts[first + i];
FLOAT t = u[i];
FLOAT ti = 1 - t;
// Control vertices for Q'
VECTOR qp0 = (curve.p1 - curve.p0) * 3;
VECTOR qp1 = (curve.p2 - curve.p1) * 3;
VECTOR qp2 = (curve.p3 - curve.p2) * 3;
// Control vertices for Q''
VECTOR qpp0 = (qp1 - qp0) * 2;
VECTOR qpp1 = (qp2 - qp1) * 2;
// Evaluate Q(t), Q'(t), and Q''(t)
VECTOR p0 = curve.Sample(t);
VECTOR p1 = ((ti * ti) * qp0) + ((2 * ti * t) * qp1) + ((t * t) * qp2);
VECTOR p2 = (ti * qpp0) + (t * qpp1);
// these are the actual fitting calculations using http://en.wikipedia.org/wiki/Newton%27s_method
// We can't just use .X and .Y because Unity uses lower-case "x" and "y".
FLOAT num = ((VectorHelper.GetX(p0) - VectorHelper.GetX(p)) * VectorHelper.GetX(p1)) + ((VectorHelper.GetY(p0) - VectorHelper.GetY(p)) * VectorHelper.GetY(p1));
FLOAT den = (VectorHelper.GetX(p1) * VectorHelper.GetX(p1)) + (VectorHelper.GetY(p1) * VectorHelper.GetY(p1)) + ((VectorHelper.GetX(p0) - VectorHelper.GetX(p)) * VectorHelper.GetX(p2)) + ((VectorHelper.GetY(p0) - VectorHelper.GetY(p)) * VectorHelper.GetY(p2));
FLOAT newU = t - num / den;
if (Math.Abs(den) > EPSILON && newU >= 0 && newU <= 1)
{
u[i] = newU;
}
}
}
