/// <summary>
/// determines is the defined converter a valid one for converting iso coord to local coords
/// </summary>
/// <param name="converter"></param>
/// <returns></returns>
private bool IsValidIsoToLocalConverter(Mathh.SingleVariablePolynomial converter)
{
return(true);
var bar = this;
var n = NodeCount;
var xs = new double[n];
var xi_s = new double[n];
{
//var conds = new List<Tuple<double, double>>();//x[i] , ξ[i]
for (var i = 0; i < n; i++)
{
var deltaXi = 2.0 / (n - 1);
var xi = (bar.Nodes[i].Location - bar.Nodes[0].Location).Length;
var xi_i = -1 + deltaXi * i;
xs[i] = xi;
xi_s[i] = xi_i;
}
var poly = converter;
{//test
for (var i = 0; i < n; i++)
{
var epsilon = poly.Evaluate(xi_s[i]) - xs[i];
if (Math.Abs(epsilon) > 1e-10)
{
return(false);
}
}
}
}
return(true);
}
/// <summary>
/// get the polynomial that takes iso coord as input and return local coord as output
/// </summary>
/// <returns>X(ξ) (ξ input, X output)</returns>
public virtual Mathh.SingleVariablePolynomial GetIsoToLocalConverter()
{
var cachekey = "{54CEC6B2-F882-4505-9FC0-E7844C99F249}";
Mathh.SingleVariablePolynomial chd;
if (this.TryGetCache(cachekey, out chd)) //prevent double calculation
{
if (IsValidIsoToLocalConverter(chd)) //Validation of chached polynomial to see if is outdated due to change in node locations
{
return(chd);
}
}
chd = null;
var targetElement = this;
var bar = this;
Mathh.SingleVariablePolynomial x_xi = null;//x(ξ)
var n = targetElement.Nodes.Length;
var xs = new double[n];
var xi_s = new double[n];
{
//var conds = new List<Tuple<double, double>>();//x[i] , ξ[i]
for (var i = 0; i < n; i++)
{
var deltaXi = 2.0 / (n - 1);
var xi = (bar.Nodes[i].Location - bar.Nodes[0].Location).Length;
var xi_i = -1 + deltaXi * i;
xs[i] = xi;
xi_s[i] = xi_i;
//conds.Add(Tuple.Create(xi, xi_i));
}
//polinomial degree of shape function is n-1
var mtx =
//new Matrix(n, n);
MatrixPool.Allocate(n, n);
var right =
//new Matrix(n, 1);
MatrixPool.Allocate(n, 1);
//var o = n - 1;
for (var i = 0; i < n; i++)
{
//fill row i'th of mtx
//x[i] = { ξ[i]^o, ξ[i]^o-1 ... ξ[i]^1 ξ[i]^0} * {a[o] a[o-1] ... a[1] a[0]}'
var kesi_i = xi_s[i];
for (var j = 0; j < n; j++)
{
mtx[i, j] = Math.Pow(kesi_i, n - j - 1);
right[i, 0] = xs[i];
}
}
//var as_ = mtx.Inverse() * right;
var as_ = mtx.Solve(right.CoreArray);
x_xi = new Mathh.SingleVariablePolynomial(as_);
right.ReturnToPool();
mtx.ReturnToPool();
}
SetCache(cachekey, x_xi);
return(x_xi);
}
