chi_math_01_utility.cc

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#include "chi_math.h"
 
//###################################################################
/**Computes the factorial of an integer.*/
double chi_math::Factorial(const int x)
{
  double factorial_value = 1.0;
  for (int i=2; i<=x; ++i)
    factorial_value *= i;
 
  return factorial_value;
}
 
//###################################################################
/**Determines the azimuthal- and polar-angle associated with
 * the given direction vector.
 * Returns a pair = [azimuthal-angle,polar-angle].*/
std::pair<double,double> chi_math::
  OmegaToPhiThetaSafe(const chi_mesh::Vector3 &omega)
{
  // Notes: asin maps [-1,+1] to [-pi/2,+pi/2]
  //        acos maps [-1,+1] to [0,pi]
  // This mapping requires some logic for determining the azimuthal angle.
  //
  const auto omega_hat = omega.Normalized();
 
  double mu = omega_hat.z;
  mu = std::min(mu,  1.0);
  mu = std::max(mu, -1.0);
 
  double theta = acos(mu);
 
  //===== Handling omega aligned to k_hat
  if (std::fabs(omega_hat.z) < 1.0e-16) return {0.0,theta};
 
  double cos_phi = omega_hat.x/sin(theta);
  cos_phi = std::min(cos_phi,  1.0);
  cos_phi = std::max(cos_phi, -1.0);
 
  //===== Computing varphi for NE and NW quadrant
  if (omega_hat.y >= 0.0)
    return {acos(cos_phi), theta};
  //===== Computing varphi for SE and SW quadrant
  else
    return {2.0*M_PI - acos(cos_phi), theta};
 
}