/// <summary>
/// Gets the calculated length.
/// https://github.com/HTD/FastBezier
/// </summary>
/// <remarks>
/// Integral calculation by Dave Eberly, slightly modified for the edge case with colinear control point.
/// See: http://www.gamedev.net/topic/551455-length-of-a-generalized-quadratic-bezier-curve-in-3d/
/// </remarks>
public static double Length(GPoint P0, GPoint P1, GPoint P2)
{
if (P0 == P2)
{
if (P0 == P1)
{
return(0.0);
}
return(P0.Distance(P1));
}
if (P1 == P0 || P1 == P2)
{
return(P0.Distance(P2));
}
GPoint A0 = P1 - P0;
GPoint A1 = P0 - 2.0 * P1 + P2;
if (!A1.Zero)
{
double c = 4.0 * A1.DotProduct(A1);
double b = 8.0 * A0.DotProduct(A1);
double a = 4.0 * A0.DotProduct(A0);
double q = 4.0 * a * c - b * b;
double twoCpB = 2.0 * c + b;
double sumCBA = c + b + a;
var l0 = (0.25 / c) * (twoCpB * Math.Sqrt(sumCBA) - b * Math.Sqrt(a));
double k1 = 2.0 * Math.Sqrt(c * sumCBA) + twoCpB;
double k2 = 2.0 * Math.Sqrt(c * a) + b;
if ((k1 <= 0.0) || (k2 <= 0.0))
{
return(l0);
}
var l1 = (q / (8.0 * Math.Pow(c, 1.5))) * (Math.Log(k1) - Math.Log(k2));
return(l0 + l1);
}
else
{
return(2.0 * A0.Length());
}
}