FormFactorHemiEllipsoid.cpp

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// ************************************************************************** //
//
//  BornAgain: simulate and fit scattering at grazing incidence
//
//! @file      Sample/HardParticle/FormFactorHemiEllipsoid.cpp
//! @brief     Implements class FormFactorHemiEllipsoid.
//!
//! @homepage  http://www.bornagainproject.org
//! @license   GNU General Public License v3 or higher (see COPYING)
//! @copyright Forschungszentrum Jülich GmbH 2018
//! @authors   Scientific Computing Group at MLZ (see CITATION, AUTHORS)
//
// ************************************************************************** //
 
#include "Sample/HardParticle/FormFactorHemiEllipsoid.h"
#include "Base/Const/MathConstants.h"
#include "Base/Utils/Integrator.h"
#include "Base/Utils/MathFunctions.h"
#include "Sample/Shapes/TruncatedEllipsoid.h"
#include <limits>
 
FormFactorHemiEllipsoid::FormFactorHemiEllipsoid(const std::vector<double> P)
    : IFormFactorBorn({"HemiEllipsoid",
                       "actually a spheroid, truncated at central xy plane",
                       {{"RadiusX", "nm", "radius in x direction", 0, +INF, 0},
                        {"RadiusY", "nm", "radius in y direction", 0, +INF, 0},
                        {"Height", "nm", "height = radius in z direction", 0, +INF, 0}}},
                      P),
      m_radius_x(m_P[0]), m_radius_y(m_P[1]), m_height(m_P[2])
{
    onChange();
}
 
FormFactorHemiEllipsoid::FormFactorHemiEllipsoid(double radius_x, double radius_y, double height)
    : FormFactorHemiEllipsoid(std::vector<double>{radius_x, radius_y, height})
{
}
 
double FormFactorHemiEllipsoid::radialExtension() const
{
    return (m_radius_x + m_radius_y) / 2.0;
}
 
//! Integrand for complex form factor.
complex_t FormFactorHemiEllipsoid::Integrand(double Z) const
{
    double R = m_radius_x;
    double W = m_radius_y;
    double H = m_height;
 
    double Rz = R * std::sqrt(1.0 - Z * Z / (H * H));
    double Wz = W * std::sqrt(1.0 - Z * Z / (H * H));
 
    complex_t qxRz = m_q.x() * Rz;
    complex_t qyWz = m_q.y() * Wz;
 
    complex_t gamma = std::sqrt(qxRz * qxRz + qyWz * qyWz);
    complex_t J1_gamma_div_gamma = MathFunctions::Bessel_J1c(gamma);
 
    return Rz * Wz * J1_gamma_div_gamma * exp_I(m_q.z() * Z);
}
 
complex_t FormFactorHemiEllipsoid::evaluate_for_q(cvector_t q) const
{
    m_q = q;
    double R = m_radius_x;
    double W = m_radius_y;
    double H = m_height;
 
    if (std::abs(m_q.mag()) <= std::numeric_limits<double>::epsilon())
        return M_TWOPI * R * W * H / 3.;
    return M_TWOPI * ComplexIntegrator().integrate([&](double Z) { return Integrand(Z); }, 0., H);
}
 
void FormFactorHemiEllipsoid::onChange()
{
    mP_shape =
        std::make_unique<TruncatedEllipsoid>(m_radius_x, m_radius_x, m_height, m_height, 0.0);
}