public Series CalculateShape()
{
double dl = this[_dl] ;
double dx = this[_dx] ;
double dy = this[_dy] ;
double ell = this[_ell] ;
x1 = this[_x1] ;
x2 = this[_x2] ;
y2 = this[_y2] ;
if (dl <= dx)
return null;
double C = Math.Sqrt(24 * (dl - dx) / (dx* dx * dx));
var A = new SingleVariableEq(i => 2 * Math.Sinh(dx * i * .5) - i *dl);
var B = new SingleVariableEq(i => dx * Math.Cosh(dx * i * .5) - dl);
var D = A.NewtonRaphson(B, C, 0, C * 1.1, 1.0e-12, 100);
double x, y = 0;
double x0 = ((x1 + x2) - Math.Log((ell + dy) / (ell - dy)) / C) * 0.5;
double y0 = y2 - Math.Cosh((x2 - x0) * C) / C;
x = x1;
Series ser = new Series("rope");
dx = .01;
while (x < x2) {
y = Math.Cosh((x - x0) * C) / C + y0;
ser.Points.Add(new DataPoint(x, y));
x += dx;
}
x = x2;
ser.Points.Add(new DataPoint(x, y));
ser.ChartType = SeriesChartType.Point;
return ser;
}
public double GetTension()
{
double dl = this[_dl];
double dx = this[_dx];
double dy = this[_dy];
double ell = this[_ell];
x1 = this[_x1];
x2 = this[_x2];
y2 = this[_y2];
double y1 = this[_y1];
if (dl <= dx)
return double.MinValue;
//f(T) =
var A = new SingleVariableEq(t => 2 * t * Math.Sinh((x2- x1) / (2*t)) - Math.Sqrt(ell.Sqrd() - (y2 - y1).Sqrd()));
//f'(T) =
var B = new SingleVariableEq(t => (2 * Math.Sinh((x2 - x1) / 2 * t) * t - (x2 - x1) * Math.Cosh((x2 - x1) / 2 * t)) / t);
var lowerBoundOnT = Math.Sqrt((x2 - x1).Sqrd() / ((Math.Sqrt(ell.Sqrd() - (y2 - y1).Sqrd()) - (x2 - x1))* 24));
var tension = A.NewtonRaphson(lowerBoundOnT + .1, lowerBoundOnT, 10, 1.0e-12, 100);
//Todo: test the value of the tension and don't return a bad value
return tension;
}
//A bug popped up in this method, not sure why.
private double SolveWithNewtonRaphson(double x, double y)
{
var t2 = new SingleVariableEq(i => y / x - A * (Math.Log(1 - B * Math.Sqrt(1 + i.Sqrd())) + B * Math.Sqrt(1 + i.Sqrd())) - i);
double C = Math.Exp(-(-y / x + 1 + Math.Sqrt(1 / B.Sqrd() - 1) / A));
double initApprox1 = -Math.Sqrt((1 - C).Sqrd() / B.Sqrd() - 1);
double initApprox2 = Math.Sqrt((1 - C).Sqrd() / B.Sqrd() - 1);
var deriv = new SingleVariableEq(i => (A * B.Sqrd() * i) / (1 - B * Math.Sqrt(1 + i.Sqrd())) - 1);
var theta = Math.Atan(t2.NewtonRaphson(deriv, 0, initApprox1, initApprox2, 1.0e-10, 500));
return theta;
}