HemiEllipsoid.cpp

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//  ************************************************************************************************
//
//  BornAgain: simulate and fit reflection and scattering
//
//! @file      Sample/HardParticle/HemiEllipsoid.cpp
//! @brief     Implements class HemiEllipsoid.
//!
//! @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/HemiEllipsoid.h"
#include "Base/Math/Bessel.h"
#include "Base/Math/Constants.h"
#include "Base/Math/IntegratorGK.h"
#include "Sample/Shapes/TruncatedEllipsoidNet.h"
#include <limits>
 
HemiEllipsoid::HemiEllipsoid(const std::vector<double> P)
    : IFormFactor(P)
    , m_radius_x(m_P[0])
    , m_radius_y(m_P[1])
    , m_height(m_P[2])
{
    checkNodeArgs();
    m_shape3D =
        std::make_unique<TruncatedEllipsoidNet>(m_radius_x, m_radius_x, m_height, m_height, 0.0);
}
 
HemiEllipsoid::HemiEllipsoid(double radius_x, double radius_y, double height)
    : HemiEllipsoid(std::vector<double>{radius_x, radius_y, height})
{
}
 
double HemiEllipsoid::radialExtension() const
{
    return (m_radius_x + m_radius_y) / 2.0;
}
 
complex_t HemiEllipsoid::formfactor_at_bottom(C3 q) const
{
    double R = m_radius_x;
    double W = m_radius_y;
    double H = m_height;
 
    if (std::abs(q.mag()) <= std::numeric_limits<double>::epsilon())
        return M_TWOPI * R * W * H / 3.;
 
    return M_TWOPI
           * ComplexIntegrator().integrate(
               [=](double Z) {
                   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 = q.x() * Rz;
                   complex_t qyWz = q.y() * Wz;
 
                   complex_t gamma = std::sqrt(qxRz * qxRz + qyWz * qyWz);
                   complex_t J1_gamma_div_gamma = Math::Bessel::J1c(gamma);
 
                   return Rz * Wz * J1_gamma_div_gamma * exp_I(q.z() * Z);
               },
               0., H);
}