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// ************************************************************************************************
//
// BornAgain: simulate and fit reflection and scattering
//
//! @file Sample/HardParticle/SphericalSegment.cpp
//! @brief Implements class SphericalSegment.
//!
//! @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/SphericalSegment.h"
#include "Base/Math/Bessel.h"
#include "Base/Math/IntegratorGK.h"
#include "Base/Util/Assert.h"
#include "Sample/Shape/TruncatedEllipsoidNet.h"
#include <limits>
#include <numbers>
using std::numbers::pi;
SphericalSegment::SphericalSegment(const std::vector<double> P)
: IFormfactor(P)
, m_radius(m_P[0])
, m_rm_top(m_P[1])
, m_rm_bottom(m_P[2])
{
validateOrThrow();
}
SphericalSegment::SphericalSegment(double radius, double top_cut, double bottom_cut)
: SphericalSegment(std::vector<double>{radius, top_cut, bottom_cut})
{
}
//! Complex form factor.
complex_t SphericalSegment::formfactor(C3 q) const
{
ASSERT(m_validated);
double untruncated_height = 2 * m_radius - m_rm_bottom;
if (std::abs(q.mag()) < std::numeric_limits<double>::epsilon())
return pi / 3.
* (untruncated_height * untruncated_height * (3. * m_radius - untruncated_height)
- m_rm_top * m_rm_top * (3. * m_radius - m_rm_top));
const complex_t Q2 = std::sqrt(q.x() * q.x() + q.y() * q.y()); // NOT the modulus!
const double R2 = m_radius * m_radius;
complex_t integral = ComplexIntegrator().integrate(
[=](double Z) {
const double R2Z2 = R2 - Z * Z;
return R2Z2 * Math::Bessel::J1c(Q2 * sqrt(R2Z2)) * exp_I(q.z() * Z);
},
m_radius - untruncated_height, m_radius - m_rm_top);
return (2 * pi) * integral * exp_I(q.z() * (untruncated_height - m_radius));
}
std::string SphericalSegment::validate() const
{
std::vector<std::string> errs;
requestGt0(errs, m_radius, "radius");
requestGe0(errs, m_rm_top, "removed_top");
requestGe0(errs, m_rm_bottom, "removed_bottom");
if (m_rm_top > (2 * m_radius - m_rm_bottom))
errs.emplace_back("parameters violate condition rm_top<=H");
if (m_rm_bottom > (2 * m_radius - m_rm_top))
errs.emplace_back("parameters violate condition rm_bottom<=H");
if (!errs.empty())
return jointError(errs);
double untruncated_height = 2 * m_radius - m_rm_bottom;
m_shape3D = std::make_unique<TruncatedEllipsoidNet>(m_radius, m_radius, m_radius,
untruncated_height, m_rm_top);
m_validated = true;
return "";
}
bool SphericalSegment::contains(const R3& position) const
{
double R = radius();
double H = 2 * R - cutFromBottom();
double deltaH = cutFromTop();
if (std::abs(position.x()) > R || std::abs(position.y()) > R || position.z() < 0
|| position.z() > (H - deltaH))
return false;
if (std::pow(position.x() / R, 2) + std::pow(position.y() / R, 2)
+ std::pow((position.z() - (H - R)) / R, 2)
<= 1)
return true;
return false;
}
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