/// <summary>
/// Finds the horizontal tension to set the lowest point on the catenary.
/// </summary>
/// <param name="span"></param>
/// <param name="w"></param>
/// <param name="C">The specified vertical separation between the left
/// support and the lowest point on the curve. Always positive.</param>
/// <param name="tol"></param>
/// <returns></returns>
public static double SetClearance(Vector2 span, double w, double C, double tol)
{
if (tol <= 0)
{
tol = 1e-4;
}
C = Math.Max(C, MinSag);
double H_init = DoubleEx.Sqr(span.X) * w / (8 * C);
Func <double, double> f = (H_) => - CenterPosition(span, w, H_).Y;
if (f.Bisection(C, H_init, tol, out double H))
{
return(H);
}
return(H_init);
}
/// <summary>
/// Calculates the horizontal tension needed to achieve specified maximum sag
/// </summary>
/// <param name="span">The span</param>
/// <param name="w">The unit weight</param>
/// <param name="D">The specified sag</param>
/// <param name="tol">The tension tolerance for numeric solution (default 0.001)</param>
/// <returns>The horizontal tension value</returns>
public static double SetMaximumSag(Vector2 span, double w, double D, double tol)
{
if (tol <= 0)
{
tol = 1e-4;
}
D = Math.Max(D, MinSag);
double H_init = DoubleEx.Sqr(span.X) * w / (8 * D);
Func <double, double> f = (H_) => MaximumSag(span, w, H_);
if (f.Bisection(D, H_init, tol, out double H))
{
return(H);
}
return(H_init);
}
/// <summary>
/// Calculates the horizontal tension needed to achieve specified average tension
/// </summary>
/// <param name="span">The span</param>
/// <param name="w">The unit weight</param>
/// <param name="P">The specified average tension</param>
/// <param name="tol">The tension tolerance for numeric solution (default 0.001)</param>
/// <returns></returns>
public static double SetAverageTension(Vector2 span, double w, double P, double tol)
{
if (tol <= 0)
{
tol = 1e-8;
}
P = Math.Max(P, MinTension);
double σ = span.X * w;
double H_init = P / 2 + Math.Sqrt(DoubleEx.Sqr(P / 2) - DoubleEx.Sqr(σ) / 24);
Func <double, double> f = (H_) => AverageTension(span, w, H_);
if (f.Bisection(P, H_init, tol, out double H))
{
return(H);
}
return(H_init);
}
