/// <summary>
/// Calculates the cartesian coordinate of a parametric point.
/// </summary>
/// <param name="numberOfCPKsi">Number of <see cref="ControlPoint"/> in the parametric axis Ksi.</param>
/// <param name="degreeKsi">Degree of splines for the parametric axis Ksi.</param>
/// <param name="knotValueVectorKsi"> Knot Value Vector for the parametric axis Ksi.</param>
/// <param name="numberOfCPHeta">Number of <see cref="ControlPoint"/> in the parametric axis Heta.</param>
/// <param name="degreeHeta">Degree of splines for the parametric axis Heta.</param>
/// <param name="knotValueVectorHeta"> Knot Value Vector for the parametric axis Heta.</param>
/// <param name="numberOfCPZeta">Number of <see cref="ControlPoint"/> in the parametric axis Zeta.</param>
/// <param name="degreeZeta">Degree of splines for the parametric axis Zeta.</param>
/// <param name="knotValueVectorZeta"> Knot Value Vector for the parametric axis Zeta.</param>
/// <param name="projectiveControlPointCoordinates">A <see cref="double"/> two dimensional array containing the projective coordinates of the control points.</param>
/// <param name="ksiCoordinate">Parametric coordinate Ksi of the physical point to be evaluated.</param>
/// <param name="hetaCoordinate">Parametric coordinate Heta of the physical point to be evaluated.</param>
/// <param name="zetaCoordinate">Parametric coordinate Zeta of the physical point to be evaluated.</param>
/// <returns>A <see cref="Vector"/> containing the physical coordinates of the solid point calculated.</returns>
public static Vector SolidPoint3D(int numberOfCPKsi, int degreeKsi, Vector knotValueVectorKsi,
int numberOfCPHeta, int degreeHeta, Vector knotValueVectorHeta, int numberOfCPZeta, int degreeZeta,
Vector knotValueVectorZeta, double[,] projectiveControlPointCoordinates, double ksiCoordinate, double hetaCoordinate,
double zetaCoordinate)
{
var spanKsi = ParaviewNurbs2D.FindSpan(numberOfCPKsi, degreeKsi, ksiCoordinate, knotValueVectorKsi);
var spanHeta = ParaviewNurbs2D.FindSpan(numberOfCPHeta, degreeHeta, hetaCoordinate, knotValueVectorHeta);
var spanZeta = ParaviewNurbs2D.FindSpan(numberOfCPZeta, degreeZeta, zetaCoordinate, knotValueVectorZeta);
var pointFunctionsKsi = ParaviewNurbs2D.BasisFunctions(spanKsi, ksiCoordinate, degreeKsi, knotValueVectorKsi);
var pointFunctionsHeta = ParaviewNurbs2D.BasisFunctions(spanHeta, hetaCoordinate, degreeHeta, knotValueVectorHeta);
var pointFunctionsZeta = ParaviewNurbs2D.BasisFunctions(spanZeta, zetaCoordinate, degreeZeta, knotValueVectorZeta);
var cartesianPoint = Vector.CreateZero(4);
var indexKsi = spanKsi - degreeKsi;
for (int k = 0; k <= degreeZeta; k++)
{
var indexZeta = spanZeta - degreeZeta + k;
for (int j = 0; j <= degreeHeta; j++)
{
var indexHeta = spanHeta - degreeHeta + j;
for (int i = 0; i <= degreeKsi; i++)
{
var cpIndex = (indexKsi + i) * (numberOfCPHeta + 1) * (numberOfCPZeta + 1) +
indexHeta * (numberOfCPZeta + 1) + indexZeta;
var cpCoordinates = Vector.CreateFromArray(new double[]
{
projectiveControlPointCoordinates[cpIndex, 0],
projectiveControlPointCoordinates[cpIndex, 1],
projectiveControlPointCoordinates[cpIndex, 2],
projectiveControlPointCoordinates[cpIndex, 3]
});
cpCoordinates.Scale(pointFunctionsKsi[i]);
cpCoordinates.Scale(pointFunctionsHeta[j]);
cpCoordinates.Scale(pointFunctionsZeta[k]);
cartesianPoint = cartesianPoint + cpCoordinates;
}
}
}
return(cartesianPoint);
}
/// <summary>
/// Creates Paraview File of the NURBS Shells geometry.
/// </summary>
public void CreateParaview2DFile()
{
var uniqueKnotsKsi = _model.PatchesDictionary[0].KnotValueVectorKsi.RemoveDuplicatesFindMultiplicity();
var uniqueKnotsHeta = _model.PatchesDictionary[0].KnotValueVectorHeta.RemoveDuplicatesFindMultiplicity();
var numberOfKnotsKsi = uniqueKnotsKsi[0].Length;
var numberOfKnotsHeta = uniqueKnotsHeta[0].Length;
var knots = new double[numberOfKnotsKsi * numberOfKnotsHeta, 3];
var count = 0;
var patch = _model.PatchesDictionary[0];
var projectiveControlPoints = CalculateProjectiveControlPoints();
for (var knotKsiIndex = 0; knotKsiIndex < numberOfKnotsKsi; knotKsiIndex++)
{
for (var knotHetaIndex = 0; knotHetaIndex < numberOfKnotsHeta; knotHetaIndex++)
{
var hetaCoordinate = uniqueKnotsHeta[0][knotHetaIndex];
var ksiCoordinate = uniqueKnotsKsi[0][knotKsiIndex];
var point3D = ParaviewNurbs2D.SurfacePoint2D(patch.NumberOfControlPointsKsi - 1, patch.DegreeKsi,
patch.KnotValueVectorKsi, patch.NumberOfControlPointsHeta - 1, patch.DegreeHeta,
patch.KnotValueVectorHeta, projectiveControlPoints, ksiCoordinate, hetaCoordinate);
knots[count, 0] = point3D[0] / point3D[3];
knots[count, 1] = point3D[1] / point3D[3];
knots[count++, 2] = point3D[2] / point3D[3];
}
}
var incrementKsi = numberOfKnotsHeta;
var incrementHeta = 1;
var nodePattern = new int[] { 0, incrementKsi, incrementKsi + 1, 1 };
var elementConnectivity = CreateElement2DConnectivity(nodePattern, uniqueKnotsKsi[0].Length - 1,
uniqueKnotsHeta[0].Length - 1, incrementKsi, incrementHeta);
var knotDisplacements = new double[knots.GetLength(0), 3];
foreach (var element in _model.Elements)
{
var localDisplacements = Matrix.CreateZero(element.ControlPointsDictionary.Count, 3);
var counterCP = 0;
foreach (var controlPoint in element.ControlPoints)
{
localDisplacements[counterCP, 0] =
(!_model.GlobalDofOrdering.GlobalFreeDofs.Contains(controlPoint, StructuralDof.TranslationX))
? 0.0
: _solution[_model.GlobalDofOrdering.GlobalFreeDofs[controlPoint, StructuralDof.TranslationX]];
localDisplacements[counterCP, 1] =
(!_model.GlobalDofOrdering.GlobalFreeDofs.Contains(controlPoint, StructuralDof.TranslationY))
? 0.0
: _solution[_model.GlobalDofOrdering.GlobalFreeDofs[controlPoint, StructuralDof.TranslationY]];
localDisplacements[counterCP++, 2] =
(!_model.GlobalDofOrdering.GlobalFreeDofs.Contains(controlPoint, StructuralDof.TranslationZ))
? 0.0
: _solution[_model.GlobalDofOrdering.GlobalFreeDofs[controlPoint, StructuralDof.TranslationZ]];
}
var elementKnotDisplacements = element.ElementType.CalculateDisplacementsForPostProcessing(element, localDisplacements);
for (int i = 0; i < elementConnectivity.GetLength(1); i++)
{
var knotConnectivity = elementConnectivity[element.ID, i];
knotDisplacements[knotConnectivity, 0] = elementKnotDisplacements[i, 0];
knotDisplacements[knotConnectivity, 1] = elementKnotDisplacements[i, 1];
knotDisplacements[knotConnectivity, 2] = elementKnotDisplacements[i, 2];
}
}
Write2DNurbsFile(knots, elementConnectivity, "Quad4", knotDisplacements);
}
