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// ************************************************************************************************
//
// BornAgain: simulate and fit reflection and scattering
//
//! @file Img3D/Build/ParacrystalLatticePositions.cpp
//! @brief Implements function Paracrystal::latticePositions.
//!
//! @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 "Img3D/Build/ParacrystalLatticePositions.h"
#include "Base/Math/Functions.h"
#include "Base/Util/Assert.h"
#include "Sample/Aggregate/Interference2DParacrystal.h"
namespace {
void ResizeLatticePositions(double2d_t& lattice_positions, double l1, double l2, double layer_size)
{
// Estimate the limit n1 and n2 of the integer multiple j and i of the lattice vectors l1 and l2
// required for populating particles correctly within the 3D model's boundaries
int n1 = 0, n2 = 0;
n1 = l1 == 0.0 ? 2 : static_cast<int>(layer_size * 2 / l1);
n2 = l2 == 0.0 ? 2 : static_cast<int>(layer_size * 2 / l2);
n1 = std::max(n1, n2);
lattice_positions.resize((2 * n1 + 1) * (2 * n1 + 1));
for (auto& it : lattice_positions)
it.resize(2);
lattice_positions[0][0] = 0.0; // x coordinate of reference particle - at the origin
lattice_positions[0][1] = 0.0; // y coordinate of reference particle - at the origin
}
void FindLatticePositionsIndex(size_t& index, size_t& index_prev, int i, int j, int size,
double l_alpha)
{
int newindex = i * (2 * size + 1) + j;
ASSERT(newindex > 0);
index = newindex;
if (std::sin(l_alpha) == 0) { // along l1
// particles along +l1 stored every odd iter (e.g. 1,3,5...) index of lattice_positions
// particles along -l1 stored every even iter (e.g. 2,4,6...) index of lattice_positions
index_prev = i * (2 * size + 1);
if (j - 2 > 0)
index_prev = index - 2;
} else { // along l2
// particles along +l2/-l2 stored every (odd/even iter)*(2*n1+1) index of lattice_positions
index_prev = j;
if (i - 2 > 0)
index_prev = index - (2 * (2 * size + 1));
}
}
std::pair<double, double> ComputePositionAlongPositiveLatticeVector(const size_t index_prev,
double2d_t& lattice_positions,
const IProfile2D* pdf, double l,
double l_xi, double l_alpha,
int seed)
{
double gamma_pdf = pdf->gamma();
std::pair<double, double> sampleXYpdf = pdf->createSampler()->randomSample(seed);
double offset_x_pdf = sampleXYpdf.first;
double offset_y_pdf = sampleXYpdf.second;
double x = lattice_positions[index_prev][0] + l * std::cos(l_xi + l_alpha)
+ offset_x_pdf * std::cos(gamma_pdf + l_xi)
+ offset_y_pdf * std::cos((pi / 2) + gamma_pdf + l_xi); // x coordinate
double y = lattice_positions[index_prev][1] + l * std::sin(l_xi + l_alpha)
+ offset_x_pdf * std::sin(gamma_pdf + l_xi)
+ offset_y_pdf * std::sin((pi / 2) + gamma_pdf + l_xi); // y coordinate
return std::make_pair(x, y);
}
std::pair<double, double> ComputePositionAlongNegativeLatticeVector(const size_t index_prev,
double2d_t& lattice_positions,
const IProfile2D* pdf, double l,
double l_xi, double l_alpha,
int seed)
{
double gamma_pdf = pdf->gamma();
std::pair<double, double> sampleXYpdf = pdf->createSampler()->randomSample(seed);
double offset_x_pdf = sampleXYpdf.first;
double offset_y_pdf = sampleXYpdf.second;
double x = lattice_positions[index_prev][0] - l * std::cos(l_xi + l_alpha)
+ offset_x_pdf * std::cos(gamma_pdf + l_xi)
+ offset_y_pdf * std::cos((pi / 2) + gamma_pdf + l_xi); // x coordinate
double y = lattice_positions[index_prev][1] - l * std::sin(l_xi + l_alpha)
+ offset_x_pdf * std::sin(gamma_pdf + l_xi)
+ offset_y_pdf * std::sin((pi / 2) + gamma_pdf + l_xi); // y coordinate
return std::make_pair(x, y);
}
std::pair<double, double> ComputeLatticePosition(const size_t index_prev, int i, int j,
double2d_t& lattice_positions,
const IProfile2D* pdf, double l, double l_xi,
double l_alpha, int seed)
{
if (std::sin(l_alpha) == 0) {
if (!(j % 2 == 0)) // along +l1
return ComputePositionAlongPositiveLatticeVector(index_prev, lattice_positions, pdf, l,
l_xi, 0, seed);
// else along -l1
return ComputePositionAlongNegativeLatticeVector(index_prev, lattice_positions, pdf, l,
l_xi, 0, seed);
}
if (!(i % 2 == 0)) // along +l2
return ComputePositionAlongPositiveLatticeVector(index_prev, lattice_positions, pdf, l,
l_xi, l_alpha, seed);
// else along -l2
return ComputePositionAlongNegativeLatticeVector(index_prev, lattice_positions, pdf, l, l_xi,
l_alpha, seed);
}
void ComputePositionsAlongLatticeVectorAxes(double2d_t& lattice_positions, const IProfile2D* pdf,
double l, double l_xi, double l_alpha, int seed)
{
int n = static_cast<int>((std::sqrt(lattice_positions.size()) - 1) / 2);
size_t index = 0; // lattice_positions index for current particle
size_t index_prev = 0; // lattice_positions index for previous particle
std::pair<double, double> xy;
int upd_seed = Math::GenerateNextSeed(seed);
for (int iter = 1; iter <= 2 * n; ++iter) {
int iterl1, iterl2;
if (std::sin(l_alpha) == 0) {
iterl1 = iter;
iterl2 = 0;
} else {
iterl1 = 0;
iterl2 = iter;
}
// The 2*n+1 particles that are situated ONLY along the l1 axis (both +/- axes)
// are stored in i = 1,2,3,...2*n1 indices of lattice_positions
// The 2*n+1 particles that are situated ONLY along the l2 axis (both +/- axes)
// are stored every i*(2*n1+1) index of lattice_positions
FindLatticePositionsIndex(index, index_prev, iterl2, iterl1, n, l_alpha);
upd_seed = Math::GenerateNextSeed(upd_seed);
xy = ComputeLatticePosition(index_prev, iterl2, iterl1, lattice_positions, pdf, l, l_xi,
l_alpha, upd_seed);
lattice_positions[index][0] = xy.first; // x coordinate
lattice_positions[index][1] = xy.second; // y coordinate
}
}
void ComputePositionsInsideLatticeQuadrants(double2d_t& lattice_positions, const IProfile2D* pdf1,
const IProfile2D* pdf2, double l1, double l2,
double l_xi, double l_alpha, int seed)
{
int n = static_cast<int>((std::sqrt(lattice_positions.size()) - 1) / 2);
size_t index = 0; // lattice_positions index for current particle
size_t index_prev = 0; // lattice_positions index for previous particle
std::pair<double, double> xy_l1, xy_l2;
int upd_seed = Math::GenerateNextSeed(seed);
for (int i = 1; i <= 2 * n; ++i) {
for (int j = 1; j <= 2 * n; ++j) {
FindLatticePositionsIndex(index, index_prev, i, j, n, 0);
upd_seed = Math::GenerateNextSeed(upd_seed);
xy_l1 = ComputeLatticePosition(index_prev, i, j, lattice_positions, pdf1, l1, l_xi, 0,
upd_seed);
FindLatticePositionsIndex(index, index_prev, i, j, n, l_alpha);
upd_seed = Math::GenerateNextSeed(upd_seed);
xy_l2 = ComputeLatticePosition(index_prev, i, j, lattice_positions, pdf2, l2, l_xi,
l_alpha, upd_seed);
lattice_positions[index][0] = (xy_l1.first + xy_l2.first) / 2;
lattice_positions[index][1] = (xy_l1.second + xy_l2.second) / 2;
}
}
}
} // namespace
// ************************************************************************************************
// implement namespace Img3D::Paracrystal2D
// ************************************************************************************************
double2d_t Paracrystal::latticePositions(const Interference2DParacrystal* p_iff, double layer_size,
int seed)
{
const auto& lattice = p_iff->lattice();
double l1 = lattice.length1();
double l2 = lattice.length2();
double alpha = lattice.latticeAngle();
double xi = lattice.rotationAngle();
double2d_t lattice_positions;
ResizeLatticePositions(lattice_positions, l1, l2, layer_size);
int upd_seed = Math::GenerateNextSeed(seed);
ComputePositionsAlongLatticeVectorAxes(lattice_positions, p_iff->pdf1(), l1, xi, 0, upd_seed);
upd_seed = Math::GenerateNextSeed(upd_seed);
ComputePositionsAlongLatticeVectorAxes(lattice_positions, p_iff->pdf2(), l2, xi, alpha,
upd_seed);
upd_seed = Math::GenerateNextSeed(upd_seed);
ComputePositionsInsideLatticeQuadrants(lattice_positions, p_iff->pdf1(), p_iff->pdf2(), l1, l2,
xi, alpha, upd_seed);
return lattice_positions;
}
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