void PrintQuadRule(const QuadratureRule<2>& q)
{
cout << "QuadRule\n";
cout << "--------\n";
cout << "Order: " << q.order() << "\n";
cout << "Size: " << q.size() << "\n";
for(size_t i = 0; i < q.size(); ++i)
cout << "Weight "<<i<<": "<<q.weight(i) <<"\n";
for(size_t i = 0; i < q.size(); ++i)
cout << "Point "<<i<<": "<<q.point(i) <<"\n";
}
double integrateD(const KernelD & F, const Element & e)
{
double result = 0.0;
// Get the quadrature rules for azimuthal and polar integrations
namespace mpl = boost::mpl;
typedef typename mpl::at<rules_map, mpl::int_<PhiPoints> >::type PhiPolicy;
typedef typename mpl::at<rules_map, mpl::int_<ThetaPoints> >::type ThetaPolicy;
QuadratureRule<PhiPolicy> phiRule;
QuadratureRule<ThetaPolicy> thetaRule;
int upper_phi = PhiPoints / 2; // Upper limit for loop on phi points
int upper_theta = ThetaPoints / 2; // Upper limit for loop on theta points
// Extract relevant data from Element
int nVertices = e.nVertices();
Eigen::Vector3d normal = e.normal();
Sphere sph = e.sphere();
Eigen::Matrix3Xd vertices = e.vertices();
Eigen::Matrix3Xd arcs = e.arcs();
// Calculation of the tangent and the bitangent (binormal) vectors
// Tangent, Bitangent and Normal form a local reference frame:
// T <-> x; B <-> y; N <-> z
Eigen::Vector3d tangent, bitangent;
tangent_and_bitangent(normal, tangent, bitangent);
std::vector<double> theta(nVertices), phi(nVertices), phinumb(nVertices+1);
std::vector<int> numb(nVertices+1);
// Clean-up heap crap
std::fill_n(theta.begin(), nVertices, 0.0);
std::fill_n(phi.begin(), nVertices, 0.0);
std::fill_n(numb.begin(), nVertices+1, 0);
std::fill_n(phinumb.begin(), nVertices+1, 0.0);
// Populate arrays and redefine tangent and bitangent
e.spherical_polygon(tangent, bitangent, theta, phi, phinumb, numb);
// Actual integration occurs here
for (int i = 0; i < nVertices; ++i) { // Loop on edges
double phiLower = phinumb[i]; // Lower vertex of edge
double phiUpper = phinumb[i+1]; // Upper vertex of edge
double phiA = (phiUpper - phiLower) / 2.0;
double phiB = (phiUpper + phiLower) / 2.0;
double thetaLower = theta[numb[i]];
double thetaUpper = theta[numb[i+1]];
double thetaMax = 0.0;
Eigen::Vector3d oc = (arcs.col(i) - sph.center) / sph.radius;
double oc_norm = oc.norm();
double oc_norm2 = std::pow(oc_norm, 2);
for (int j = 0; j < upper_phi; ++j) { // Loop on Gaussian points: phi integration
for (int k = 0; k <= 1; ++k) {
double ph = (2*k - 1) * phiA * phiRule.abscissa(j) + phiB;
double cos_phi = std::cos(ph);
double sin_phi = std::sin(ph);
if (oc_norm2 < 1.0e-07) { // This should check if oc_norm2 is zero
double cotg_thmax = (std::sin(ph-phiLower) / std::tan(thetaUpper) + std::sin(phiUpper-ph) / std::tan(
thetaLower)) / std::sin(phiUpper - phiLower);
thetaMax = std::atan(1.0 / cotg_thmax);
} else {
Eigen::Vector3d scratch;
scratch << tangent.dot(oc), bitangent.dot(oc), normal.dot(oc);
double aa = std::pow(tangent.dot(oc)*cos_phi + bitangent.dot(oc)*sin_phi,
2) + std::pow(normal.dot(oc), 2);
double bb = -normal.dot(oc) * oc_norm2;
double cc = std::pow(oc_norm2,
2) - std::pow(tangent.dot(oc)*cos_phi + bitangent.dot(oc)*sin_phi, 2);
double ds = std::pow(bb, 2) - aa*cc;
if (ds < 0.0) ds = 0.0;
double cs = (-bb + std::sqrt(ds)) / aa;
if (cs > 1.0) cs = 1.0;
if (cs < -1.0) cs = 1.0;
thetaMax = std::acos(cs);
}
double thetaA = thetaMax / 2.0;
double scratch = 0.0;
if (!(thetaMax < 1.0e-08)) {
for (int l = 0; l < upper_theta; ++l) { // Loop on Gaussian points: theta integration
for (int m = 0; m <= 1; ++m) {
double th = (2*m - 1) * thetaA * thetaRule.abscissa(l) + thetaA;
double cos_theta = std::cos(th);
double sin_theta = std::sin(th);
Eigen::Vector3d point;
point(0) = tangent(0) * sin_theta * cos_phi
+ bitangent(0) * sin_theta * sin_phi
+ normal(0) * (cos_theta - 1.0);
point(1) = tangent(1) * sin_theta * cos_phi
+ bitangent(1) * sin_theta * sin_phi
+ normal(1) * (cos_theta - 1.0);
point(2) = tangent(2) * sin_theta * cos_phi
+ bitangent(2) * sin_theta * sin_phi
+ normal(2) * (cos_theta - 1.0);
double value = F(e.normal(),
Eigen::Vector3d::Zero(),
point); // Evaluate integrand at Gaussian point
scratch += std::pow(sph.radius, 2) * value * sin_theta * thetaA * thetaRule.weight(l);
}
}
result += scratch * phiA * phiRule.weight(j);
}
}
}
}
return result;
}