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/*=========================================================================
Program: Visualization Toolkit
Module: vtkLagrangeInterpolation.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 "vtkLagrangeInterpolation.h"
#include "vtkDoubleArray.h"
#include "vtkLagrangeTriangle.h"
#include "vtkLagrangeWedge.h"
#include "vtkMath.h"
#include "vtkNew.h"
#include "vtkObjectFactory.h"
#include "vtkPoints.h"
#include "vtkVector.h"
#include "vtkVectorOperators.h"
#include <array>
#include <vector>
VTK_ABI_NAMESPACE_BEGIN
vtkStandardNewMacro(vtkLagrangeInterpolation);
vtkLagrangeInterpolation::vtkLagrangeInterpolation() = default;
vtkLagrangeInterpolation::~vtkLagrangeInterpolation() = default;
void vtkLagrangeInterpolation::PrintSelf(ostream& os, vtkIndent indent)
{
this->Superclass::PrintSelf(os, indent);
}
/// Evaluate 1-D shape functions for the given \a order at the given \a pcoord (in [0,1]).
void vtkLagrangeInterpolation::EvaluateShapeFunctions(
const int order, const double pcoord, double* shape)
{
int j, k;
double v = order * pcoord;
for (j = 0; j <= order; ++j)
{
shape[j] = 1.;
for (k = 0; k <= order; ++k)
{
if (j != k)
{ // FIXME: (j - k) could be a register decremented inside the k loop:
// and even better: normalization 1./(j - k) could be pre-computed and stored
// somehow for each order that is actually used, removing division operations.
shape[j] *= (v - k) / (j - k);
}
}
}
}
/// Evaluate 1-D shape functions and their derivatives for the given \a order at the given \a pcoord
/// (in [0,1]).
void vtkLagrangeInterpolation::EvaluateShapeAndGradient(
int order, double pcoord, double* shape, double* derivs)
{
int j, k, q;
double dtmp;
double v = order * pcoord;
for (j = 0; j <= order; ++j)
{
// std::cout << "ShapeDeriv j = " << j << " v = " << v << "\n";
shape[j] = 1.;
derivs[j] = 0.;
for (k = 0; k <= order; ++k)
{
if (j != k)
{ // FIXME: (j - k) could be a register decremented inside the k loop:
// and even better: normalization could be pre-computed and stored
// somehow for each order that is actually used.
shape[j] *= (v - k) / (j - k);
// Now compute the derivative of shape[j]; we use the differentiation
// rule d/dx(a * b) = a * d/dx(b) + b * d/dx(a) instead of faster
// methods because it keeps the truncation error low(er):
dtmp = 1.;
// std::cout << " k = " << k;
for (q = 0; q <= order; ++q)
{
if (q == j)
{
continue;
}
dtmp *= (q == k ? 1. : (v - q)) / (j - q);
// std::cout << " q " << q << " dtmp *= " << ((q == k ? 1. : (v - q)) / (j - q));
}
derivs[j] += order * dtmp;
}
}
}
}
int vtkLagrangeInterpolation::Tensor1ShapeFunctions(
const int order[1], const double* pcoords, double* shape)
{
return vtkHigherOrderInterpolation::Tensor1ShapeFunctions(
order, pcoords, shape, vtkLagrangeInterpolation::EvaluateShapeFunctions);
}
int vtkLagrangeInterpolation::Tensor1ShapeDerivatives(
const int order[1], const double* pcoords, double* derivs)
{
return vtkHigherOrderInterpolation::Tensor1ShapeDerivatives(
order, pcoords, derivs, vtkLagrangeInterpolation::EvaluateShapeAndGradient);
}
/// Quadrilateral shape function computation
int vtkLagrangeInterpolation::Tensor2ShapeFunctions(
const int order[2], const double pcoords[3], double* shape)
{
return vtkHigherOrderInterpolation::Tensor2ShapeFunctions(
order, pcoords, shape, vtkLagrangeInterpolation::EvaluateShapeFunctions);
}
// Quadrilateral shape-function derivatives
int vtkLagrangeInterpolation::Tensor2ShapeDerivatives(
const int order[2], const double pcoords[3], double* derivs)
{
return vtkHigherOrderInterpolation::Tensor2ShapeDerivatives(
order, pcoords, derivs, vtkLagrangeInterpolation::EvaluateShapeAndGradient);
}
/// Hexahedral shape function computation
int vtkLagrangeInterpolation::Tensor3ShapeFunctions(
const int order[3], const double pcoords[3], double* shape)
{
return vtkHigherOrderInterpolation::Tensor3ShapeFunctions(
order, pcoords, shape, vtkLagrangeInterpolation::EvaluateShapeFunctions);
}
int vtkLagrangeInterpolation::Tensor3ShapeDerivatives(
const int order[3], const double pcoords[3], double* derivs)
{
return vtkHigherOrderInterpolation::Tensor3ShapeDerivatives(
order, pcoords, derivs, vtkLagrangeInterpolation::EvaluateShapeAndGradient);
}
void vtkLagrangeInterpolation::Tensor3EvaluateDerivative(const int order[3], const double* pcoords,
vtkPoints* points, const double* fieldVals, int fieldDim, double* fieldDerivs)
{
this->vtkHigherOrderInterpolation::Tensor3EvaluateDerivative(order, pcoords, points, fieldVals,
fieldDim, fieldDerivs, vtkLagrangeInterpolation::EvaluateShapeAndGradient);
}
/// Wedge shape function computation
void vtkLagrangeInterpolation::WedgeShapeFunctions(
const int order[3], const vtkIdType numberOfPoints, const double pcoords[3], double* shape)
{
vtkNew<vtkLagrangeTriangle> tri;
vtkHigherOrderInterpolation::WedgeShapeFunctions(
order, numberOfPoints, pcoords, shape, *tri, vtkLagrangeInterpolation::EvaluateShapeFunctions);
}
/// Wedge shape-function derivative evaluation
void vtkLagrangeInterpolation::WedgeShapeDerivatives(
const int order[3], const vtkIdType numberOfPoints, const double pcoords[3], double* derivs)
{
vtkNew<vtkLagrangeTriangle> tri;
vtkHigherOrderInterpolation::WedgeShapeDerivatives(order, numberOfPoints, pcoords, derivs, *tri,
vtkLagrangeInterpolation::EvaluateShapeAndGradient);
}
void vtkLagrangeInterpolation::WedgeEvaluate(const int order[3], const vtkIdType numberOfPoints,
const double* pcoords, double* fieldVals, int fieldDim, double* fieldAtPCoords)
{
vtkNew<vtkLagrangeTriangle> tri;
this->vtkHigherOrderInterpolation::WedgeEvaluate(order, numberOfPoints, pcoords, fieldVals,
fieldDim, fieldAtPCoords, *tri, vtkLagrangeInterpolation::EvaluateShapeFunctions);
}
void vtkLagrangeInterpolation::WedgeEvaluateDerivative(const int order[3], const double* pcoords,
vtkPoints* points, const double* fieldVals, int fieldDim, double* fieldDerivs)
{
vtkNew<vtkLagrangeTriangle> tri;
this->vtkHigherOrderInterpolation::WedgeEvaluateDerivative(order, pcoords, points, fieldVals,
fieldDim, fieldDerivs, *tri, vtkLagrangeInterpolation::EvaluateShapeAndGradient);
}
VTK_ABI_NAMESPACE_END
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