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#ifndef COMPUTEMEASURES_H
#define COMPUTEMEASURES_H
#include "MeshFunctionsDefine.h"
#include "MeshApply.h"
#include "../MeshDataContainer/MeshDataContainer.h"
#include <array>
template <unsigned int dim, unsigned int Dimension, ComputationMethod Method = DEFAULT>
struct _ComputeMeasures{
template <typename IndexType, typename Real, unsigned int ...Reserve>
static void compute(MakeMeshDataContainer_t<Real, make_custom_integer_sequence_t<unsigned int, 1, Dimension>>&,MeshElements<Dimension, IndexType, Real, Reserve...>&){
static_assert (Dimension <= 3,"The measure computation of mesh of dimension higher than 3 is not implemented yet.");
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throw std::runtime_error("The measure computation of mesh of dimension higher than 3 is not implemented yet.");
}
};
template <unsigned int Dimension, ComputationMethod Method>
struct _ComputeMeasures<1, Dimension, Method>{
template <typename IndexType, typename Real, unsigned int ...Reserve>
static void compute(MakeMeshDataContainer_t<Real, make_custom_integer_sequence_t<unsigned int, 1, Dimension>>& measures,MeshElements<Dimension, IndexType, Real, Reserve...>& mesh){
auto& edgeLengths = measures.template getDataByDim<1>();
for (auto& edge : mesh.getEdges()) {
edgeLengths.at(edge.getIndex()) = (mesh.getVertices().at(edge.getVertexAIndex()) -
mesh.getVertices().at(edge.getVertexBIndex())).normEukleid();
}
_ComputeMeasures<2, Dimension>::compute(measures, mesh);
}
};
template <ComputationMethod Method>
struct _ComputeMeasures<3, 3, Method>{
template <typename IndexType, typename Real, unsigned int ...Reserve>
static void compute(MakeMeshDataContainer_t<Real, make_custom_integer_sequence_t<unsigned int, 1, 3>>& measures,MeshElements<3, IndexType, Real, Reserve...>& mesh){
auto& cellMeasures = measures.template getDataByDim<3>();
for (typename MeshElements<3, IndexType, Real, Reserve...>::template ElementType<3>& cell : mesh.getCells()) {
IndexType tmpFace = cell.getBoundaryElementIndex();
Real measure = Real();
Vertex<3,Real>& cellCenter = cell.getCenter();
do {
// select 3 different vertices
IndexType vAIndex = mesh.getEdges().at(mesh.getFaces().at(tmpFace).getSubelements()[0].index).getVertexAIndex();
IndexType vBIndex = mesh.getEdges().at(mesh.getFaces().at(tmpFace).getSubelements()[0].index).getVertexBIndex();
IndexType vCIndex = mesh.getEdges().at(mesh.getFaces().at(tmpFace).getSubelements()[1].index).getVertexAIndex();
if(vCIndex == vAIndex || vCIndex == vBIndex) {
vCIndex = mesh.getEdges().at(mesh.getFaces().at(tmpFace).getSubelements()[1].index).getVertexBIndex();
}
Vertex<3,Real>& a = mesh.getVertices().at(vAIndex);
Vertex<3,Real>& b = mesh.getVertices().at(vBIndex);
Vertex<3,Real>& c = mesh.getVertices().at(vCIndex);
// preparing quiantities
Vertex<3,Real> vAmcC = (a-cellCenter);
Vertex<3,Real> vBmA = (b-a);
Vertex<3,Real> vCmA = (c-a);
Real inv_sqrBmA = 1.0 / vBmA.sumOfSquares();
Real inv_sqrCmA = 1.0 / vCmA.sumOfSquares();
Real denominator = 1.0 / (1.0 - (pow(vCmA*vBmA,2) * inv_sqrBmA * inv_sqrCmA));
Real param_t = -denominator * (((vAmcC*vBmA) * inv_sqrBmA) - (inv_sqrBmA*inv_sqrCmA*(vAmcC * vCmA)*(vCmA*vBmA)));
//param_t *= inv_sqrBmA;
Real param_s = -denominator * (((vAmcC*vCmA) * inv_sqrCmA) - (inv_sqrBmA*inv_sqrCmA*(vAmcC * vBmA)*(vCmA*vBmA)));
Real distance = (vAmcC + (vBmA * param_t) + (vCmA * param_s)).normEukleid();
Real tmp = distance * measures.template getDataByDim<2>().at(tmpFace);
measure += tmp / 3.0;
tmpFace = mesh.getFaces().at(tmpFace).getNextBElem(cell.getIndex());
} while (tmpFace != cell.getBoundaryElementIndex());
cellMeasures.at(cell.getIndex()) = measure;
}
}
};
template <ComputationMethod Method>
struct _ComputeMeasures<2, 2, Method>{
template <typename IndexType, typename Real, unsigned int ...Reserve>
static void compute(MakeMeshDataContainer_t<Real, make_custom_integer_sequence_t<unsigned int, 1, 2>>& measures,MeshElements<2, IndexType, Real, Reserve...>& mesh){
auto& surfaceMeasures = measures.template getDataByDim<2>();
for (typename MeshElements<2, IndexType, Real, Reserve...>::template ElementType<2>& cell : mesh.getCells()) {
IndexType tmpEdge = cell.getBoundaryElementIndex();
Real measure = Real();
Vertex<2,Real>& cellCenter = cell.getCenter();
do {
Vertex<2,Real>& a = mesh.getVertices().at(mesh.getEdges().at(tmpEdge).getVertexAIndex());
Vertex<2,Real>& b = mesh.getVertices().at(mesh.getEdges().at(tmpEdge).getVertexBIndex());
double tmp = (cellCenter[0] - a[0]) * (b[1] - a[1]);
tmp -= (cellCenter[1] - a[1]) * (b[0] - a[0]);
measure += 0.5 * fabs(tmp);
tmpEdge = mesh.getEdges().at(tmpEdge).getNextBElem(cell.getIndex());
} while (tmpEdge != cell.getBoundaryElementIndex());
surfaceMeasures.at(cell.getIndex()) = measure;
}
}
};
template <ComputationMethod Method>
struct _ComputeMeasures<2, 3, Method>{
template <typename IndexType, typename Real, unsigned int ...Reserve>
static void compute(MakeMeshDataContainer_t<Real, make_custom_integer_sequence_t<unsigned int, 1, 3>>& measures,MeshElements<3, IndexType, Real, Reserve...>& mesh){
auto& surfaceMeasures = measures.template getDataByDim<2>();
for (typename MeshElements<3, IndexType, Real, Reserve...>::template ElementType<2>& face : mesh.template getElements<2>()) {
Real measure = Real();
Vertex<3,Real>& faceCenter = face.getCenter();
for(auto sube : face.getSubelements()){
Vertex<3,Real>& a = mesh.getVertices().at(mesh.getEdges().at(sube.index).getVertexAIndex());
Vertex<3,Real>& b = mesh.getVertices().at(mesh.getEdges().at(sube.index).getVertexBIndex());
Real distance = Real();
Real param = -1.0*(((a-faceCenter)*(b-a))/((b-a).sumOfSquares()));
distance = (a-faceCenter+(b-a)*param).normEukleid();
Real tmp = distance * measures.template getDataByDim<1>().at(sube.index);
measure += tmp * 0.5;
}
surfaceMeasures.at(face.getIndex()) = measure;
}
_ComputeMeasures<3, 3>::compute(measures, mesh);
}
};
template <>
struct _ComputeMeasures<3, 3, TESSELLATED>{
template <typename IndexType, typename Real, unsigned int ...Reserve>
static void compute(MakeMeshDataContainer_t<Real, make_custom_integer_sequence_t<unsigned int, 1, 3>>& measures,MeshElements<3, IndexType, Real, Reserve...>& mesh){
auto& cellMeasures = measures.template getDataByDim<3>();
for (typename MeshElements<3, IndexType, Real, Reserve...>::template ElementType<3>& cell : mesh.getCells()) {
Vertex<3,Real>& cellCenter = cell.getCenter();
Real measure = Real();
MeshApply<3,2,3>::apply(
cell.getIndex(),
mesh,
[&cellCenter, &cellMeasures, &mesh, &measure](IndexType , IndexType faceIndex){
Vertex<3,Real>& faceCenter = mesh.getFaces().at(faceIndex).getCenter();
MeshApply<2,1,3>::apply(faceIndex, mesh, [&](IndexType , IndexType edgeIndex){
Vertex<3,Real>& vertA = mesh.getVertices().at(mesh.getEdges().at(edgeIndex).getVertexAIndex());
Vertex<3,Real>& vertB = mesh.getVertices().at(mesh.getEdges().at(edgeIndex).getVertexBIndex());
std::array<Vertex<3,Real>, 3> pyramidVec = {vertA - faceCenter, vertB - faceCenter, cellCenter - faceCenter};
std::array<Real, 3> norms;
grammSchmidt<3, 3, IndexType, Real>(pyramidVec, norms);
measure += norms.at(0) * norms.at(1) * norms.at(2) * (1.0/6.0);
});
}
);
cellMeasures.at(cell.getIndex()) = measure;
}
}
};
template <ComputationMethod Method, unsigned int Dimension,typename IndexType, typename Real, unsigned int ...Reserve>
MakeMeshDataContainer_t<Real, make_custom_integer_sequence_t<unsigned int, 1, Dimension>> ComputeMeasures(MeshElements<Dimension, IndexType, Real, Reserve...>& mesh){
MakeMeshDataContainer_t<Real, make_custom_integer_sequence_t<unsigned int, 1, Dimension>> measures(mesh);
Detail::_ComputeMeasures<1, Dimension, Method>::compute(measures, mesh);
return measures;
}
#endif // COMPUTEMEASURES_H