/// <summary>
/// Developed by: Mehrdad Negahban
/// Date: 11/12/2012
///
/// Purpose: Multi-dimensional root element for boundary
/// Comments: Uses parametric interpolation
/// Uses quadrature integration
///
/// Date modified:
/// Modified by:
/// Comments:
/// </summary>
public double Calculate_NDLine_DsDXi(Vector Xi, Node_ND[] ElementNoes, out Vector N)
{
//Get line length ratio between real line and parametric line
Matrix_Jagged DXDXi;
Interpolator.Calculate_N_DXDXi(Xi, ElementNodes, out N, out DXDXi);
double DsDXi = Math.Sqrt((DXDXi.Transpose() * DXDXi).Trace());//Calculate change of variable
return(DsDXi);
}
public double Calculate_NDArea_DADAo(Vector Xi, Node_ND[] ElementNoes, out Vector N)
{
//Get area ratio between real area and parametric area
Matrix_Jagged DXDXi;
Interpolator.Calculate_N_DXDXi(Xi, ElementNodes, out N, out DXDXi);
Vector DX_1 = DXDXi.GetColumn(0);
Vector DX_2 = DXDXi.GetColumn(1);
double DAXDAo = Vector.CrossProduct(DX_1, DX_2).Magnitude();
return(DAXDAo);
}