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/*=========================================================================
Program: Visualization Toolkit
Module: vtkLagrangeTriangle.cxx
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
This software is distributed WITHOUT ANY WARRANTY; without even
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE. See the above copyright notice for more information.
=========================================================================*/
#include "vtkLagrangeTriangle.h"
#include "vtkCellArray.h"
#include "vtkCellData.h"
#include "vtkDoubleArray.h"
#include "vtkIncrementalPointLocator.h"
#include "vtkLagrangeCurve.h"
#include "vtkLine.h"
#include "vtkMath.h"
#include "vtkObjectFactory.h"
#include "vtkPointData.h"
#include "vtkPoints.h"
#include "vtkTriangle.h"
#define ENABLE_CACHING
#define SEVEN_POINT_TRIANGLE
vtkStandardNewMacro(vtkLagrangeTriangle);
//----------------------------------------------------------------------------
vtkLagrangeTriangle::vtkLagrangeTriangle()
: vtkHigherOrderTriangle()
{
}
//----------------------------------------------------------------------------
vtkLagrangeTriangle::~vtkLagrangeTriangle() = default;
void vtkLagrangeTriangle::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os, indent);
}
vtkCell* vtkLagrangeTriangle::GetEdge(int edgeId)
{
vtkLagrangeCurve* result = EdgeCell;
const auto set_number_of_ids_and_points = [&](const vtkIdType& npts) -> void {
result->Points->SetNumberOfPoints(npts);
result->PointIds->SetNumberOfIds(npts);
};
const auto set_ids_and_points = [&](const vtkIdType& edge_id, const vtkIdType& face_id) -> void {
result->Points->SetPoint(edge_id, this->Points->GetPoint(face_id));
result->PointIds->SetId(edge_id, this->PointIds->GetId(face_id));
};
this->SetEdgeIdsAndPoints(edgeId, set_number_of_ids_and_points, set_ids_and_points);
return result;
}
//----------------------------------------------------------------------------
void vtkLagrangeTriangle::InterpolateFunctions(const double pcoords[3], double* weights)
{
// Adapted from P. Silvester, "High-Order Polynomial Triangular Finite
// Elements for Potential Problems". Int. J. Engng Sci. Vol. 7, pp. 849-861.
// Pergamon Press, 1969. The generic method is valid for all orders, but we
// unroll the first two orders to reduce computational cost.
double tau[3] = { pcoords[0], pcoords[1], 1. - pcoords[0] - pcoords[1] };
vtkIdType n = this->GetOrder();
if (n == 1)
{
// for the linear case, we simply return the parametric coordinates, rotated
// into the parametric frame (e.g. barycentric tau_2 = parametric x).
weights[0] = tau[2];
weights[1] = tau[0];
weights[2] = tau[1];
}
else if (n == 2)
{
#ifdef SEVEN_POINT_TRIANGLE
if (this->GetPoints()->GetNumberOfPoints() == 7)
{
double rs = tau[0] * tau[1];
double rt = tau[0] * tau[2];
double st = tau[1] * tau[2];
double rst = rs * tau[2];
weights[0] = tau[2] + 3.0 * rst - 2.0 * rt - 2.0 * st;
weights[1] = tau[0] + 3.0 * rst - 2.0 * rt - 2.0 * rs;
weights[2] = tau[1] + 3.0 * rst - 2.0 * rs - 2.0 * st;
weights[3] = 4.0 * rt - 12.0 * rst;
weights[4] = 4.0 * rs - 12.0 * rst;
weights[5] = 4.0 * st - 12.0 * rst;
weights[6] = 27.0 * rst;
return;
}
#endif
weights[0] = tau[2] * (2.0 * tau[2] - 1.0);
weights[1] = tau[0] * (2.0 * tau[0] - 1.0);
weights[2] = tau[1] * (2.0 * tau[1] - 1.0);
weights[3] = 4.0 * tau[0] * tau[2];
weights[4] = 4.0 * tau[0] * tau[1];
weights[5] = 4.0 * tau[1] * tau[2];
}
else
{
vtkIdType nPoints = this->GetPoints()->GetNumberOfPoints();
for (vtkIdType idx = 0; idx < nPoints; idx++)
{
weights[idx] = 1.;
vtkIdType lambda[3];
this->ToBarycentricIndex(idx, lambda);
for (vtkIdType dim = 0; dim < 3; dim++)
{
weights[idx] *= eta(n, lambda[dim], tau[dim]);
}
}
}
}
//----------------------------------------------------------------------------
void vtkLagrangeTriangle::InterpolateDerivs(const double pcoords[3], double* derivs)
{
// Analytic differentiation of the triangle shape functions, as defined in
// P. Silvester, "High-Order Polynomial Triangular Finite Elements for
// Potential Problems". Int. J. Engng Sci. Vol. 7, pp. 849-861. Pergamon
// Press, 1969. The generic method is valid for all orders, but we unroll the
// first two orders to reduce computational cost.
double tau[3] = { pcoords[0], pcoords[1], 1. - pcoords[0] - pcoords[1] };
vtkIdType n = this->GetOrder();
if (n == 1)
{
derivs[0] = -1;
derivs[1] = 1;
derivs[2] = 0;
derivs[3] = -1;
derivs[4] = 0;
derivs[5] = 1;
}
else if (n == 2)
{
#ifdef SEVEN_POINT_TRIANGLE
if (this->GetPoints()->GetNumberOfPoints() == 7)
{
double tmr = tau[2] - tau[0];
double tms = tau[2] - tau[1];
derivs[0] = -1.0 + 3.0 * tau[1] * tmr - 2.0 * tmr + 2.0 * tau[1];
derivs[1] = 1.0 + 3.0 * tau[1] * tmr - 2.0 * tmr - 2.0 * tau[1];
derivs[2] = 3.0 * tau[1] * tmr;
derivs[3] = 4.0 * tmr - 12.0 * tau[1] * tmr;
derivs[4] = 4.0 * tau[1] - 12.0 * tau[1] * tmr;
derivs[5] = -4.0 * tau[1] - 12.0 * tau[1] * tmr;
derivs[6] = 27.0 * tau[1] * tmr;
derivs[7] = -1.0 + 3.0 * tau[0] * tms - 2.0 * tms + 2.0 * tau[0];
derivs[8] = 3.0 * tau[0] * tms;
derivs[9] = 1.0 + 3.0 * tau[0] * tms - 2.0 * tms - 2.0 * tau[0];
derivs[10] = -4.0 * tau[0] - 12.0 * tau[0] * tms;
derivs[11] = 4.0 * tau[0] - 12.0 * tau[0] * tms;
derivs[12] = 4.0 * tms - 12.0 * tau[0] * tms;
derivs[13] = 27.0 * tau[0] * tms;
return;
}
#endif
derivs[0] = 1.0 - 4.0 * tau[2];
derivs[1] = 4.0 * tau[0] - 1.0;
derivs[2] = 0.0;
derivs[3] = 4.0 * (tau[2] - tau[0]);
derivs[4] = 4.0 * tau[1];
derivs[5] = -4.0 * tau[1];
derivs[6] = 1.0 - 4.0 * tau[2];
derivs[7] = 0.0;
derivs[8] = 4.0 * tau[1] - 1.0;
derivs[9] = -4.0 * tau[0];
derivs[10] = 4.0 * tau[0];
derivs[11] = 4.0 * (tau[2] - tau[1]);
}
else
{
vtkIdType nPoints = this->GetPoints()->GetNumberOfPoints();
for (vtkIdType idx = 0; idx < nPoints; idx++)
{
vtkIdType lambda[3];
this->ToBarycentricIndex(idx, lambda);
double eta_alpha = eta(n, lambda[0], tau[0]);
double eta_beta = eta(n, lambda[1], tau[1]);
double eta_gamma = eta(n, lambda[2], tau[2]);
double d_eta_alpha = d_eta(n, lambda[0], tau[0]);
double d_eta_beta = d_eta(n, lambda[1], tau[1]);
double d_eta_gamma = d_eta(n, lambda[2], tau[2]);
double d_f_d_tau1 = (d_eta_alpha * eta_beta * eta_gamma - eta_alpha * eta_beta * d_eta_gamma);
double d_f_d_tau2 = (eta_alpha * d_eta_beta * eta_gamma - eta_alpha * eta_beta * d_eta_gamma);
derivs[idx] = d_f_d_tau1;
derivs[nPoints + idx] = d_f_d_tau2;
}
}
}
vtkHigherOrderCurve* vtkLagrangeTriangle::getEdgeCell()
{
return EdgeCell;
}
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