public ShapeNURBS2D(NURBSElement2D element, IGAModel model, IVector <double> parametricCoordinateKsi, IVector <double> parametricCoordinateHeta, IList <ControlPoint> controlPoints)
{
int numberOfCPHeta = model.KnotValueVectorHeta.Length - model.DegreeHeta - 1;
BSPLines1D bsplinesKsi = new BSPLines1D(model.DegreeKsi, model.KnotValueVectorKsi, parametricCoordinateKsi);
BSPLines1D bsplinesHeta = new BSPLines1D(model.DegreeHeta, model.KnotValueVectorHeta, parametricCoordinateHeta);
nurbsValues = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1), element.gaussPoints.Count);
nurbsDerivativeValuesKsi = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1), element.gaussPoints.Count);
nurbsDerivativeValuesHeta = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1), element.gaussPoints.Count);
int supportKsi = model.DegreeKsi + 1;
int supportHeta = model.DegreeHeta + 1;
int numberOfElementGaussPoints = (model.DegreeKsi + 1) * (model.DegreeHeta + 1);
for (int i = 0; i < supportKsi; i++)
{
for (int j = 0; j < supportHeta; j++)
{
double sumKsiHeta = 0;
double sumdKsiHeta = 0;
double sumKsidHeta = 0;
for (int k = 0; k < numberOfElementGaussPoints; k++)
{
sumKsiHeta += bsplinesKsi.BSPLValues[element.connectivity[k] / numberOfCPHeta, i] *
bsplinesHeta.BSPLValues[element.connectivity[k] % numberOfCPHeta, j] *
controlPoints[k].Weight;
sumdKsiHeta = +bsplinesKsi.BSPLDerivativeValues[element.connectivity[k] / numberOfCPHeta, i] *
bsplinesHeta.BSPLDerivativeValues[element.connectivity[k] % numberOfCPHeta, j] *
controlPoints[k].Weight;
sumKsidHeta = +bsplinesKsi.BSPLValues[element.connectivity[k] / numberOfCPHeta, i] *
bsplinesHeta.BSPLDerivativeValues[element.connectivity[k] % numberOfCPHeta, j] *
controlPoints[k].Weight;
}
for (int k = 0; k < numberOfElementGaussPoints; k++)
{
nurbsValues[k, i *supportHeta + j] = bsplinesKsi.BSPLValues[element.connectivity[k] / numberOfCPHeta, i] *
bsplinesHeta.BSPLValues[element.connectivity[k] % numberOfCPHeta, j] *
controlPoints[k].Weight / sumKsiHeta;
nurbsDerivativeValuesKsi[k, i *supportHeta + j] = bsplinesHeta.BSPLValues[element.connectivity[k] % numberOfCPHeta, j] * controlPoints[k].Weight *
(bsplinesKsi.BSPLDerivativeValues[element.connectivity[k] / numberOfCPHeta, i] * sumKsiHeta -
bsplinesKsi.BSPLValues[element.connectivity[k] / numberOfCPHeta, i] * sumdKsiHeta) / Math.Pow(sumKsiHeta, 2);
nurbsDerivativeValuesHeta[k, i *supportHeta + j] = bsplinesKsi.BSPLValues[element.connectivity[k] / numberOfCPHeta, i] *
controlPoints[k].Weight *
(bsplinesHeta.BSPLDerivativeValues[element.connectivity[k] % numberOfCPHeta, j] * sumKsiHeta -
bsplinesHeta.BSPLValues[element.connectivity[k] % numberOfCPHeta, j] * sumKsidHeta) / Math.Pow(sumKsiHeta, 2);
}
}
}
}
public ShapeNURBS3D(NURBSElement3D element, IGAModel model, IVector <double> parametricCoordinateKsi, IVector <double> parametricCoordinateHeta, IVector <double> parametricCoordinateZeta, IList <ControlPoint> controlPoints)
{
int numberOfCPHeta = model.KnotValueVectorHeta.Length - model.DegreeHeta - 1;
int numberOfCPZeta = model.KnotValueVectorZeta.Length - model.DegreeZeta - 1;
BSPLines1D bsplinesKsi = new BSPLines1D(model.DegreeKsi, model.KnotValueVectorKsi, parametricCoordinateKsi);
BSPLines1D bsplinesHeta = new BSPLines1D(model.DegreeHeta, model.KnotValueVectorHeta, parametricCoordinateHeta);
BSPLines1D bsplinesZeta = new BSPLines1D(model.DegreeZeta, model.KnotValueVectorZeta, parametricCoordinateZeta);
nurbsValues = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1) * (model.DegreeZeta + 1), element.gaussPoints.Count);
nurbsDerivativeValuesKsi = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1) * (model.DegreeZeta + 1), element.gaussPoints.Count);
nurbsDerivativeValuesHeta = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1) * (model.DegreeZeta + 1), element.gaussPoints.Count);
nurbsDerivativeValuesZeta = new Matrix2D <double>((model.DegreeKsi + 1) * (model.DegreeHeta + 1) * (model.DegreeZeta + 1), element.gaussPoints.Count);
int supportKsi = model.DegreeKsi + 1;
int supportHeta = model.DegreeHeta + 1;
int supportZeta = model.DegreeZeta + 1;
int numberOfElementGaussPoints = (model.DegreeKsi + 1) * (model.DegreeHeta + 1) * (model.DegreeZeta + 1);
for (int i = 0; i < supportKsi; i++)
{
for (int j = 0; j < supportHeta; j++)
{
for (int k = 0; k < supportZeta; k++)
{
double sumKsiHetaZeta = 0;
double sumdKsiHetaZeta = 0;
double sumKsidHetaZeta = 0;
double sumKsiHetadZeta = 0;
for (int m = 0; m < numberOfElementGaussPoints; m++)
{
int indexKsi = element.connectivity[m] / (numberOfCPHeta * numberOfCPZeta);
int indexHeta = element.connectivity[m] % (numberOfCPHeta * numberOfCPZeta) / numberOfCPZeta;
int indexZeta = element.connectivity[m] % (numberOfCPHeta * numberOfCPZeta) % numberOfCPZeta;
sumKsiHetaZeta += bsplinesKsi.BSPLValues[indexKsi, i] *
bsplinesHeta.BSPLValues[indexHeta, j] *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight;
sumdKsiHetaZeta += bsplinesKsi.BSPLDerivativeValues[indexKsi, i] *
bsplinesHeta.BSPLValues[indexHeta, j] *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight;
sumKsidHetaZeta += bsplinesKsi.BSPLValues[indexKsi, i] *
bsplinesHeta.BSPLDerivativeValues[indexHeta, j] *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight;
sumKsiHetadZeta += bsplinesKsi.BSPLValues[indexKsi, i] *
bsplinesHeta.BSPLValues[indexHeta, j] *
bsplinesZeta.BSPLDerivativeValues[indexZeta, k] *
controlPoints[m].Weight;
}
for (int m = 0; m < numberOfElementGaussPoints; m++)
{
int indexKsi = element.connectivity[m] / (numberOfCPHeta * numberOfCPZeta);
int indexHeta = element.connectivity[m] % (numberOfCPHeta * numberOfCPZeta) / numberOfCPZeta;
int indexZeta = element.connectivity[m] % (numberOfCPHeta * numberOfCPZeta) % numberOfCPZeta;
nurbsValues[m, i *supportHeta *supportZeta + j * supportZeta + k] =
bsplinesKsi.BSPLValues[indexKsi, i] *
bsplinesHeta.BSPLValues[indexHeta, j] *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight / sumKsiHetaZeta;
nurbsDerivativeValuesKsi[m, i *supportHeta *supportZeta + j * supportZeta + k] =
(bsplinesKsi.BSPLDerivativeValues[indexKsi, i] * sumKsiHetaZeta -
bsplinesKsi.BSPLValues[indexKsi, i] * sumdKsiHetaZeta) *
bsplinesHeta.BSPLValues[indexHeta, j] *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight / Math.Pow(sumKsiHetaZeta, 2);
nurbsDerivativeValuesHeta[m, i *supportHeta *supportZeta + j * supportZeta + k] =
bsplinesKsi.BSPLValues[indexKsi, i] *
(bsplinesHeta.BSPLDerivativeValues[indexHeta, j] * sumKsiHetaZeta -
bsplinesHeta.BSPLValues[indexHeta, j] * sumKsidHetaZeta) *
bsplinesZeta.BSPLValues[indexZeta, k] *
controlPoints[m].Weight / Math.Pow(sumKsiHetaZeta, 2);
nurbsDerivativeValuesZeta[m, i *supportHeta *supportZeta + j * supportZeta + k] =
bsplinesKsi.BSPLValues[indexKsi, i] *
bsplinesHeta.BSPLValues[indexHeta, j] *
(bsplinesZeta.BSPLDerivativeValues[indexZeta, k] * sumKsiHetaZeta -
bsplinesZeta.BSPLValues[indexZeta, k] * sumKsiHetadZeta) *
controlPoints[m].Weight / Math.Pow(sumKsiHetaZeta, 2);
}
}
}
}
}