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1136 lines (994 loc) · 36.7 KB
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#include "openmc/lattice.h"
#include <cmath>
#include <string>
#include <fmt/core.h>
#include "openmc/cell.h"
#include "openmc/error.h"
#include "openmc/geometry.h"
#include "openmc/geometry_aux.h"
#include "openmc/hdf5_interface.h"
#include "openmc/string_utils.h"
#include "openmc/vector.h"
#include "openmc/xml_interface.h"
namespace openmc {
//==============================================================================
// Global variables
//==============================================================================
namespace model {
std::unordered_map<int32_t, int32_t> lattice_map;
vector<unique_ptr<Lattice>> lattices;
} // namespace model
//==============================================================================
// Lattice implementation
//==============================================================================
Lattice::Lattice(pugi::xml_node lat_node)
{
if (check_for_node(lat_node, "id")) {
id_ = std::stoi(get_node_value(lat_node, "id"));
} else {
fatal_error("Must specify id of lattice in geometry XML file.");
}
if (check_for_node(lat_node, "name")) {
name_ = get_node_value(lat_node, "name");
}
if (check_for_node(lat_node, "outer")) {
outer_ = std::stoi(get_node_value(lat_node, "outer"));
}
}
//==============================================================================
LatticeIter Lattice::begin()
{
return LatticeIter(*this, 0);
}
LatticeIter Lattice::end()
{
return LatticeIter(*this, universes_.size());
}
int32_t& Lattice::back()
{
return universes_.back();
}
ReverseLatticeIter Lattice::rbegin()
{
return ReverseLatticeIter(*this, universes_.size() - 1);
}
ReverseLatticeIter Lattice::rend()
{
return ReverseLatticeIter(*this, -1);
}
//==============================================================================
void Lattice::adjust_indices()
{
// Adjust the indices for the universes array.
for (LatticeIter it = begin(); it != end(); ++it) {
int uid = *it;
auto search = model::universe_map.find(uid);
if (search != model::universe_map.end()) {
*it = search->second;
} else {
fatal_error(fmt::format(
"Invalid universe number {} specified on lattice {}", uid, id_));
}
}
// Adjust the index for the outer universe.
if (outer_ != NO_OUTER_UNIVERSE) {
auto search = model::universe_map.find(outer_);
if (search != model::universe_map.end()) {
outer_ = search->second;
} else {
fatal_error(fmt::format(
"Invalid universe number {} specified on lattice {}", outer_, id_));
}
}
}
//==============================================================================
int32_t Lattice::fill_offset_table(int32_t target_univ_id, int map,
std::unordered_map<int32_t, int32_t>& univ_count_memo)
{
// If the offsets have already been determined for this "map", don't bother
// recalculating all of them and just return the total offset. Note that the
// offsets_ array doesn't actually include the offset accounting for the last
// universe, so we get the before-last offset for the given map and then
// explicitly add the count for the last universe.
if (offsets_[map * universes_.size() + this->begin().indx_] != C_NONE) {
int last_offset =
offsets_[(map + 1) * universes_.size() - this->begin().indx_ - 1];
int last_univ = this->back();
return last_offset +
count_universe_instances(last_univ, target_univ_id, univ_count_memo);
}
int32_t offset = 0;
for (LatticeIter it = begin(); it != end(); ++it) {
offsets_[map * universes_.size() + it.indx_] = offset;
offset += count_universe_instances(*it, target_univ_id, univ_count_memo);
}
return offset;
}
//==============================================================================
void Lattice::to_hdf5(hid_t lattices_group) const
{
// Make a group for the lattice.
std::string group_name {"lattice "};
group_name += std::to_string(id_);
hid_t lat_group = create_group(lattices_group, group_name);
// Write the name and outer universe.
if (!name_.empty()) {
write_string(lat_group, "name", name_, false);
}
if (outer_ != NO_OUTER_UNIVERSE) {
int32_t outer_id = model::universes[outer_]->id_;
write_dataset(lat_group, "outer", outer_id);
} else {
write_dataset(lat_group, "outer", outer_);
}
// Call subclass-overriden function to fill in other details.
to_hdf5_inner(lat_group);
close_group(lat_group);
}
//==============================================================================
// RectLattice implementation
//==============================================================================
RectLattice::RectLattice(pugi::xml_node lat_node) : Lattice {lat_node}
{
type_ = LatticeType::rect;
// Read the number of lattice cells in each dimension.
std::string dimension_str {get_node_value(lat_node, "dimension")};
vector<std::string> dimension_words {split(dimension_str)};
if (dimension_words.size() == 2) {
n_cells_[0] = std::stoi(dimension_words[0]);
n_cells_[1] = std::stoi(dimension_words[1]);
n_cells_[2] = 1;
is_3d_ = false;
} else if (dimension_words.size() == 3) {
n_cells_[0] = std::stoi(dimension_words[0]);
n_cells_[1] = std::stoi(dimension_words[1]);
n_cells_[2] = std::stoi(dimension_words[2]);
is_3d_ = true;
} else {
fatal_error("Rectangular lattice must be two or three dimensions.");
}
// Read the lattice lower-left location.
std::string ll_str {get_node_value(lat_node, "lower_left")};
vector<std::string> ll_words {split(ll_str)};
if (ll_words.size() != dimension_words.size()) {
fatal_error("Number of entries on <lower_left> must be the same as the "
"number of entries on <dimension>.");
}
lower_left_[0] = stod(ll_words[0]);
lower_left_[1] = stod(ll_words[1]);
if (is_3d_) {
lower_left_[2] = stod(ll_words[2]);
}
// Read the lattice pitches.
std::string pitch_str {get_node_value(lat_node, "pitch")};
vector<std::string> pitch_words {split(pitch_str)};
if (pitch_words.size() != dimension_words.size()) {
fatal_error("Number of entries on <pitch> must be the same as the "
"number of entries on <dimension>.");
}
pitch_[0] = stod(pitch_words[0]);
pitch_[1] = stod(pitch_words[1]);
if (is_3d_) {
pitch_[2] = stod(pitch_words[2]);
}
// Read the universes and make sure the correct number was specified.
std::string univ_str {get_node_value(lat_node, "universes")};
vector<std::string> univ_words {split(univ_str)};
if (univ_words.size() != n_cells_[0] * n_cells_[1] * n_cells_[2]) {
fatal_error(fmt::format(
"Expected {} universes for a rectangular lattice of size {}x{}x{} but {} "
"were specified.",
n_cells_[0] * n_cells_[1] * n_cells_[2], n_cells_[0], n_cells_[1],
n_cells_[2], univ_words.size()));
}
// Parse the universes.
universes_.resize(n_cells_[0] * n_cells_[1] * n_cells_[2], C_NONE);
for (int iz = 0; iz < n_cells_[2]; iz++) {
for (int iy = n_cells_[1] - 1; iy > -1; iy--) {
for (int ix = 0; ix < n_cells_[0]; ix++) {
int indx1 = n_cells_[0] * n_cells_[1] * iz +
n_cells_[0] * (n_cells_[1] - iy - 1) + ix;
int indx2 = n_cells_[0] * n_cells_[1] * iz + n_cells_[0] * iy + ix;
universes_[indx1] = std::stoi(univ_words[indx2]);
}
}
}
}
//==============================================================================
const int32_t& RectLattice::operator[](const array<int, 3>& i_xyz)
{
return universes_[get_flat_index(i_xyz)];
}
//==============================================================================
bool RectLattice::are_valid_indices(const array<int, 3>& i_xyz) const
{
return ((i_xyz[0] >= 0) && (i_xyz[0] < n_cells_[0]) && (i_xyz[1] >= 0) &&
(i_xyz[1] < n_cells_[1]) && (i_xyz[2] >= 0) &&
(i_xyz[2] < n_cells_[2]));
}
//==============================================================================
std::pair<double, array<int, 3>> RectLattice::distance(
Position r, Direction u, const array<int, 3>& i_xyz) const
{
// Get short aliases to the coordinates.
double x = r.x;
double y = r.y;
double z = r.z;
// Determine the oncoming edge.
double x0 {copysign(0.5 * pitch_[0], u.x)};
double y0 {copysign(0.5 * pitch_[1], u.y)};
// Left and right sides
double d {INFTY};
array<int, 3> lattice_trans;
if ((std::abs(x - x0) > FP_PRECISION) && u.x != 0) {
d = (x0 - x) / u.x;
if (u.x > 0) {
lattice_trans = {1, 0, 0};
} else {
lattice_trans = {-1, 0, 0};
}
}
// Front and back sides
if ((std::abs(y - y0) > FP_PRECISION) && u.y != 0) {
double this_d = (y0 - y) / u.y;
if (this_d < d) {
d = this_d;
if (u.y > 0) {
lattice_trans = {0, 1, 0};
} else {
lattice_trans = {0, -1, 0};
}
}
}
// Top and bottom sides
if (is_3d_) {
double z0 {copysign(0.5 * pitch_[2], u.z)};
if ((std::abs(z - z0) > FP_PRECISION) && u.z != 0) {
double this_d = (z0 - z) / u.z;
if (this_d < d) {
d = this_d;
if (u.z > 0) {
lattice_trans = {0, 0, 1};
} else {
lattice_trans = {0, 0, -1};
}
}
}
}
return {d, lattice_trans};
}
//==============================================================================
void RectLattice::get_indices(
Position r, Direction u, array<int, 3>& result) const
{
// Determine x index, accounting for coincidence
double ix_ {(r.x - lower_left_.x) / pitch_.x};
long ix_close {std::lround(ix_)};
if (coincident(ix_, ix_close)) {
result[0] = (u.x > 0) ? ix_close : ix_close - 1;
} else {
result[0] = std::floor(ix_);
}
// Determine y index, accounting for coincidence
double iy_ {(r.y - lower_left_.y) / pitch_.y};
long iy_close {std::lround(iy_)};
if (coincident(iy_, iy_close)) {
result[1] = (u.y > 0) ? iy_close : iy_close - 1;
} else {
result[1] = std::floor(iy_);
}
// Determine z index, accounting for coincidence
result[2] = 0;
if (is_3d_) {
double iz_ {(r.z - lower_left_.z) / pitch_.z};
long iz_close {std::lround(iz_)};
if (coincident(iz_, iz_close)) {
result[2] = (u.z > 0) ? iz_close : iz_close - 1;
} else {
result[2] = std::floor(iz_);
}
}
}
int RectLattice::get_flat_index(const array<int, 3>& i_xyz) const
{
return n_cells_[0] * n_cells_[1] * i_xyz[2] + n_cells_[0] * i_xyz[1] +
i_xyz[0];
}
//==============================================================================
Position RectLattice::get_local_position(
Position r, const array<int, 3>& i_xyz) const
{
r.x -= (lower_left_.x + (i_xyz[0] + 0.5) * pitch_.x);
r.y -= (lower_left_.y + (i_xyz[1] + 0.5) * pitch_.y);
if (is_3d_) {
r.z -= (lower_left_.z + (i_xyz[2] + 0.5) * pitch_.z);
}
return r;
}
//==============================================================================
int32_t& RectLattice::offset(int map, const array<int, 3>& i_xyz)
{
return offsets_[n_cells_[0] * n_cells_[1] * n_cells_[2] * map +
n_cells_[0] * n_cells_[1] * i_xyz[2] +
n_cells_[0] * i_xyz[1] + i_xyz[0]];
}
//==============================================================================
int32_t RectLattice::offset(int map, int indx) const
{
return offsets_[n_cells_[0] * n_cells_[1] * n_cells_[2] * map + indx];
}
//==============================================================================
std::string RectLattice::index_to_string(int indx) const
{
int iz {indx / (n_cells_[0] * n_cells_[1])};
int iy {(indx - n_cells_[0] * n_cells_[1] * iz) / n_cells_[0]};
int ix {indx - n_cells_[0] * n_cells_[1] * iz - n_cells_[0] * iy};
std::string out {std::to_string(ix)};
out += ',';
out += std::to_string(iy);
if (is_3d_) {
out += ',';
out += std::to_string(iz);
}
return out;
}
//==============================================================================
void RectLattice::to_hdf5_inner(hid_t lat_group) const
{
// Write basic lattice information.
write_string(lat_group, "type", "rectangular", false);
if (is_3d_) {
write_dataset(lat_group, "pitch", pitch_);
write_dataset(lat_group, "lower_left", lower_left_);
write_dataset(lat_group, "dimension", n_cells_);
} else {
array<double, 2> pitch_short {{pitch_[0], pitch_[1]}};
write_dataset(lat_group, "pitch", pitch_short);
array<double, 2> ll_short {{lower_left_[0], lower_left_[1]}};
write_dataset(lat_group, "lower_left", ll_short);
array<int, 2> nc_short {{n_cells_[0], n_cells_[1]}};
write_dataset(lat_group, "dimension", nc_short);
}
// Write the universe ids. The convention here is to switch the ordering on
// the y-axis to match the way universes are input in a text file.
if (is_3d_) {
hsize_t nx {static_cast<hsize_t>(n_cells_[0])};
hsize_t ny {static_cast<hsize_t>(n_cells_[1])};
hsize_t nz {static_cast<hsize_t>(n_cells_[2])};
vector<int> out(nx * ny * nz);
for (int m = 0; m < nz; m++) {
for (int k = 0; k < ny; k++) {
for (int j = 0; j < nx; j++) {
int indx1 = nx * ny * m + nx * k + j;
int indx2 = nx * ny * m + nx * (ny - k - 1) + j;
out[indx2] = model::universes[universes_[indx1]]->id_;
}
}
}
hsize_t dims[3] {nz, ny, nx};
write_int(lat_group, 3, dims, "universes", out.data(), false);
} else {
hsize_t nx {static_cast<hsize_t>(n_cells_[0])};
hsize_t ny {static_cast<hsize_t>(n_cells_[1])};
vector<int> out(nx * ny);
for (int k = 0; k < ny; k++) {
for (int j = 0; j < nx; j++) {
int indx1 = nx * k + j;
int indx2 = nx * (ny - k - 1) + j;
out[indx2] = model::universes[universes_[indx1]]->id_;
}
}
hsize_t dims[3] {1, ny, nx};
write_int(lat_group, 3, dims, "universes", out.data(), false);
}
}
//==============================================================================
// HexLattice implementation
//==============================================================================
HexLattice::HexLattice(pugi::xml_node lat_node) : Lattice {lat_node}
{
type_ = LatticeType::hex;
// Read the number of lattice cells in each dimension.
n_rings_ = std::stoi(get_node_value(lat_node, "n_rings"));
if (check_for_node(lat_node, "n_axial")) {
n_axial_ = std::stoi(get_node_value(lat_node, "n_axial"));
is_3d_ = true;
} else {
n_axial_ = 1;
is_3d_ = false;
}
// Read the lattice orientation. Default to 'y'.
if (check_for_node(lat_node, "orientation")) {
std::string orientation = get_node_value(lat_node, "orientation");
if (orientation == "y") {
orientation_ = Orientation::y;
} else if (orientation == "x") {
orientation_ = Orientation::x;
} else {
fatal_error("Unrecognized orientation '" + orientation +
"' for lattice " + std::to_string(id_));
}
} else {
orientation_ = Orientation::y;
}
// Read the lattice center.
std::string center_str {get_node_value(lat_node, "center")};
vector<std::string> center_words {split(center_str)};
if (is_3d_ && (center_words.size() != 3)) {
fatal_error("A hexagonal lattice with <n_axial> must have <center> "
"specified by 3 numbers.");
} else if (!is_3d_ && center_words.size() != 2) {
fatal_error("A hexagonal lattice without <n_axial> must have <center> "
"specified by 2 numbers.");
}
center_[0] = stod(center_words[0]);
center_[1] = stod(center_words[1]);
if (is_3d_) {
center_[2] = stod(center_words[2]);
}
// Read the lattice pitches.
std::string pitch_str {get_node_value(lat_node, "pitch")};
vector<std::string> pitch_words {split(pitch_str)};
if (is_3d_ && (pitch_words.size() != 2)) {
fatal_error("A hexagonal lattice with <n_axial> must have <pitch> "
"specified by 2 numbers.");
} else if (!is_3d_ && (pitch_words.size() != 1)) {
fatal_error("A hexagonal lattice without <n_axial> must have <pitch> "
"specified by 1 number.");
}
pitch_[0] = stod(pitch_words[0]);
if (is_3d_) {
pitch_[1] = stod(pitch_words[1]);
}
// Read the universes and make sure the correct number was specified.
int n_univ = (3 * n_rings_ * n_rings_ - 3 * n_rings_ + 1) * n_axial_;
std::string univ_str {get_node_value(lat_node, "universes")};
vector<std::string> univ_words {split(univ_str)};
if (univ_words.size() != n_univ) {
fatal_error(fmt::format(
"Expected {} universes for a hexagonal lattice with {} rings and {} "
"axial levels but {} were specified.",
n_univ, n_rings_, n_axial_, univ_words.size()));
}
// Parse the universes.
// Universes in hexagonal lattices are stored in a manner that represents
// a skewed coordinate system: (x, alpha) in case of 'y' orientation
// and (alpha,y) in 'x' one rather than (x, y). There is
// no obvious, direct relationship between the order of universes in the
// input and the order that they will be stored in the skewed array so
// the following code walks a set of index values across the skewed array
// in a manner that matches the input order. Note that i_x = 0, i_a = 0
// or i_a = 0, i_y = 0 corresponds to the center of the hexagonal lattice.
universes_.resize((2 * n_rings_ - 1) * (2 * n_rings_ - 1) * n_axial_, C_NONE);
if (orientation_ == Orientation::y) {
fill_lattice_y(univ_words);
} else {
fill_lattice_x(univ_words);
}
}
//==============================================================================
void HexLattice::fill_lattice_x(const vector<std::string>& univ_words)
{
int input_index = 0;
for (int m = 0; m < n_axial_; m++) {
// Initialize lattice indecies.
int i_a = -(n_rings_ - 1);
int i_y = n_rings_ - 1;
// Map upper region of hexagonal lattice which is found in the
// first n_rings-1 rows of the input.
for (int k = 0; k < n_rings_ - 1; k++) {
// Iterate over the input columns.
for (int j = 0; j < k + n_rings_; j++) {
int indx = (2 * n_rings_ - 1) * (2 * n_rings_ - 1) * m +
(2 * n_rings_ - 1) * (i_y + n_rings_ - 1) +
(i_a + n_rings_ - 1);
universes_[indx] = std::stoi(univ_words[input_index]);
input_index++;
// Move to the next right neighbour cell
i_a += 1;
}
// Return the lattice index to the start of the current row.
i_a = -(n_rings_ - 1);
i_y -= 1;
}
// Map the lower region from the centerline of cart to down side
for (int k = 0; k < n_rings_; k++) {
// Walk the index to the lower-right neighbor of the last row start.
i_a = -(n_rings_ - 1) + k;
// Iterate over the input columns.
for (int j = 0; j < 2 * n_rings_ - k - 1; j++) {
int indx = (2 * n_rings_ - 1) * (2 * n_rings_ - 1) * m +
(2 * n_rings_ - 1) * (i_y + n_rings_ - 1) +
(i_a + n_rings_ - 1);
universes_[indx] = std::stoi(univ_words[input_index]);
input_index++;
// Move to the next right neighbour cell
i_a += 1;
}
// Return lattice index to start of current row.
i_y -= 1;
}
}
}
//==============================================================================
void HexLattice::fill_lattice_y(const vector<std::string>& univ_words)
{
int input_index = 0;
for (int m = 0; m < n_axial_; m++) {
// Initialize lattice indecies.
int i_x = 1;
int i_a = n_rings_ - 1;
// Map upper triangular region of hexagonal lattice which is found in the
// first n_rings-1 rows of the input.
for (int k = 0; k < n_rings_ - 1; k++) {
// Walk the index to lower-left neighbor of last row start.
i_x -= 1;
// Iterate over the input columns.
for (int j = 0; j < k + 1; j++) {
int indx = (2 * n_rings_ - 1) * (2 * n_rings_ - 1) * m +
(2 * n_rings_ - 1) * (i_a + n_rings_ - 1) +
(i_x + n_rings_ - 1);
universes_[indx] = std::stoi(univ_words[input_index]);
input_index++;
// Walk the index to the right neighbor (which is not adjacent).
i_x += 2;
i_a -= 1;
}
// Return the lattice index to the start of the current row.
i_x -= 2 * (k + 1);
i_a += (k + 1);
}
// Map the middle square region of the hexagonal lattice which is found in
// the next 2*n_rings-1 rows of the input.
for (int k = 0; k < 2 * n_rings_ - 1; k++) {
if ((k % 2) == 0) {
// Walk the index to the lower-left neighbor of the last row start.
i_x -= 1;
} else {
// Walk the index to the lower-right neighbor of the last row start.
i_x += 1;
i_a -= 1;
}
// Iterate over the input columns.
for (int j = 0; j < n_rings_ - (k % 2); j++) {
int indx = (2 * n_rings_ - 1) * (2 * n_rings_ - 1) * m +
(2 * n_rings_ - 1) * (i_a + n_rings_ - 1) +
(i_x + n_rings_ - 1);
universes_[indx] = std::stoi(univ_words[input_index]);
input_index++;
// Walk the index to the right neighbor (which is not adjacent).
i_x += 2;
i_a -= 1;
}
// Return the lattice index to the start of the current row.
i_x -= 2 * (n_rings_ - (k % 2));
i_a += n_rings_ - (k % 2);
}
// Map the lower triangular region of the hexagonal lattice.
for (int k = 0; k < n_rings_ - 1; k++) {
// Walk the index to the lower-right neighbor of the last row start.
i_x += 1;
i_a -= 1;
// Iterate over the input columns.
for (int j = 0; j < n_rings_ - k - 1; j++) {
int indx = (2 * n_rings_ - 1) * (2 * n_rings_ - 1) * m +
(2 * n_rings_ - 1) * (i_a + n_rings_ - 1) +
(i_x + n_rings_ - 1);
universes_[indx] = std::stoi(univ_words[input_index]);
input_index++;
// Walk the index to the right neighbor (which is not adjacent).
i_x += 2;
i_a -= 1;
}
// Return lattice index to start of current row.
i_x -= 2 * (n_rings_ - k - 1);
i_a += n_rings_ - k - 1;
}
}
}
//==============================================================================
const int32_t& HexLattice::operator[](const array<int, 3>& i_xyz)
{
return universes_[get_flat_index(i_xyz)];
}
//==============================================================================
// The HexLattice iterators need their own versions b/c the universes array is
// "square", meaning that it is allocated with entries that are intentionally
// left empty. As such, the iterator indices need to skip the empty entries to
// get cell instances and geometry paths correct. See the image in the Theory
// and Methodology section on "Hexagonal Lattice Indexing" for a visual of where
// the empty positions are.
LatticeIter HexLattice::begin()
{
return LatticeIter(*this, n_rings_ - 1);
}
ReverseLatticeIter HexLattice::rbegin()
{
return ReverseLatticeIter(*this, universes_.size() - n_rings_);
}
int32_t& HexLattice::back()
{
return universes_[universes_.size() - n_rings_];
}
LatticeIter HexLattice::end()
{
return LatticeIter(*this, universes_.size() - n_rings_ + 1);
}
ReverseLatticeIter HexLattice::rend()
{
return ReverseLatticeIter(*this, n_rings_ - 2);
}
//==============================================================================
bool HexLattice::are_valid_indices(const array<int, 3>& i_xyz) const
{
// Check if (x, alpha, z) indices are valid, accounting for number of rings
return ((i_xyz[0] >= 0) && (i_xyz[1] >= 0) && (i_xyz[2] >= 0) &&
(i_xyz[0] < 2 * n_rings_ - 1) && (i_xyz[1] < 2 * n_rings_ - 1) &&
(i_xyz[0] + i_xyz[1] > n_rings_ - 2) &&
(i_xyz[0] + i_xyz[1] < 3 * n_rings_ - 2) && (i_xyz[2] < n_axial_));
}
//==============================================================================
std::pair<double, array<int, 3>> HexLattice::distance(
Position r, Direction u, const array<int, 3>& i_xyz) const
{
// Short description of the direction vectors used here. The beta, gamma, and
// delta vectors point towards the flat sides of each hexagonal tile.
// Y - orientation:
// basis0 = (1, 0)
// basis1 = (-1/sqrt(3), 1) = +120 degrees from basis0
// beta = (sqrt(3)/2, 1/2) = +30 degrees from basis0
// gamma = (sqrt(3)/2, -1/2) = -60 degrees from beta
// delta = (0, 1) = +60 degrees from beta
// X - orientation:
// basis0 = (1/sqrt(3), -1)
// basis1 = (0, 1) = +120 degrees from basis0
// beta = (1, 0) = +30 degrees from basis0
// gamma = (1/2, -sqrt(3)/2) = -60 degrees from beta
// delta = (1/2, sqrt(3)/2) = +60 degrees from beta
// The z-axis is considered separately.
double beta_dir;
double gamma_dir;
double delta_dir;
if (orientation_ == Orientation::y) {
beta_dir = u.x * std::sqrt(3.0) / 2.0 + u.y / 2.0;
gamma_dir = u.x * std::sqrt(3.0) / 2.0 - u.y / 2.0;
delta_dir = u.y;
} else {
beta_dir = u.x;
gamma_dir = u.x / 2.0 - u.y * std::sqrt(3.0) / 2.0;
delta_dir = u.x / 2.0 + u.y * std::sqrt(3.0) / 2.0;
}
// Note that hexagonal lattice distance calculations are performed
// using the particle's coordinates relative to the neighbor lattice
// cells, not relative to the particle's current cell. This is done
// because there is significant disagreement between neighboring cells
// on where the lattice boundary is due to finite precision issues.
// beta direction
double d {INFTY};
array<int, 3> lattice_trans;
double edge = -copysign(0.5 * pitch_[0], beta_dir); // Oncoming edge
Position r_t;
if (beta_dir > 0) {
const array<int, 3> i_xyz_t {i_xyz[0] + 1, i_xyz[1], i_xyz[2]};
r_t = get_local_position(r, i_xyz_t);
} else {
const array<int, 3> i_xyz_t {i_xyz[0] - 1, i_xyz[1], i_xyz[2]};
r_t = get_local_position(r, i_xyz_t);
}
double beta;
if (orientation_ == Orientation::y) {
beta = r_t.x * std::sqrt(3.0) / 2.0 + r_t.y / 2.0;
} else {
beta = r_t.x;
}
if ((std::abs(beta - edge) > FP_PRECISION) && beta_dir != 0) {
d = (edge - beta) / beta_dir;
if (beta_dir > 0) {
lattice_trans = {1, 0, 0};
} else {
lattice_trans = {-1, 0, 0};
}
}
// gamma direction
edge = -copysign(0.5 * pitch_[0], gamma_dir);
if (gamma_dir > 0) {
const array<int, 3> i_xyz_t {i_xyz[0] + 1, i_xyz[1] - 1, i_xyz[2]};
r_t = get_local_position(r, i_xyz_t);
} else {
const array<int, 3> i_xyz_t {i_xyz[0] - 1, i_xyz[1] + 1, i_xyz[2]};
r_t = get_local_position(r, i_xyz_t);
}
double gamma;
if (orientation_ == Orientation::y) {
gamma = r_t.x * std::sqrt(3.0) / 2.0 - r_t.y / 2.0;
} else {
gamma = r_t.x / 2.0 - r_t.y * std::sqrt(3.0) / 2.0;
}
if ((std::abs(gamma - edge) > FP_PRECISION) && gamma_dir != 0) {
double this_d = (edge - gamma) / gamma_dir;
if (this_d < d) {
if (gamma_dir > 0) {
lattice_trans = {1, -1, 0};
} else {
lattice_trans = {-1, 1, 0};
}
d = this_d;
}
}
// delta direction
edge = -copysign(0.5 * pitch_[0], delta_dir);
if (delta_dir > 0) {
const array<int, 3> i_xyz_t {i_xyz[0], i_xyz[1] + 1, i_xyz[2]};
r_t = get_local_position(r, i_xyz_t);
} else {
const array<int, 3> i_xyz_t {i_xyz[0], i_xyz[1] - 1, i_xyz[2]};
r_t = get_local_position(r, i_xyz_t);
}
double delta;
if (orientation_ == Orientation::y) {
delta = r_t.y;
} else {
delta = r_t.x / 2.0 + r_t.y * std::sqrt(3.0) / 2.0;
}
if ((std::abs(delta - edge) > FP_PRECISION) && delta_dir != 0) {
double this_d = (edge - delta) / delta_dir;
if (this_d < d) {
if (delta_dir > 0) {
lattice_trans = {0, 1, 0};
} else {
lattice_trans = {0, -1, 0};
}
d = this_d;
}
}
// Top and bottom sides
if (is_3d_) {
double z = r.z;
double z0 {copysign(0.5 * pitch_[1], u.z)};
if ((std::abs(z - z0) > FP_PRECISION) && u.z != 0) {
double this_d = (z0 - z) / u.z;
if (this_d < d) {
d = this_d;
if (u.z > 0) {
lattice_trans = {0, 0, 1};
} else {
lattice_trans = {0, 0, -1};
}
d = this_d;
}
}
}
return {d, lattice_trans};
}
//==============================================================================
void HexLattice::get_indices(
Position r, Direction u, array<int, 3>& result) const
{
// Offset the xyz by the lattice center.
Position r_o {r.x - center_.x, r.y - center_.y, r.z};
if (is_3d_) {
r_o.z -= center_.z;
}
// Index the z direction, accounting for coincidence
result[2] = 0;
if (is_3d_) {
double iz_ {r_o.z / pitch_[1] + 0.5 * n_axial_};
long iz_close {std::lround(iz_)};
if (coincident(iz_, iz_close)) {
result[2] = (u.z > 0) ? iz_close : iz_close - 1;
} else {
result[2] = std::floor(iz_);
}
}
if (orientation_ == Orientation::y) {
// Convert coordinates into skewed bases. The (x, alpha) basis is used to
// find the index of the global coordinates to within 4 cells.
double alpha = r_o.y - r_o.x / std::sqrt(3.0);
result[0] = std::floor(r_o.x / (0.5 * std::sqrt(3.0) * pitch_[0]));
result[1] = std::floor(alpha / pitch_[0]);
} else {
// Convert coordinates into skewed bases. The (alpha, y) basis is used to
// find the index of the global coordinates to within 4 cells.
double alpha = r_o.y - r_o.x * std::sqrt(3.0);
result[0] = std::floor(-alpha / (std::sqrt(3.0) * pitch_[0]));
result[1] = std::floor(r_o.y / (0.5 * std::sqrt(3.0) * pitch_[0]));
}
// Add offset to indices (the center cell is (i1, i2) = (0, 0) but
// the array is offset so that the indices never go below 0).
result[0] += n_rings_ - 1;
result[1] += n_rings_ - 1;
// Calculate the (squared) distance between the particle and the centers of
// the four possible cells. Regular hexagonal tiles form a Voronoi
// tessellation so the xyz should be in the hexagonal cell that it is closest
// to the center of. This method is used over a method that uses the
// remainders of the floor divisions above because it provides better finite
// precision performance. Squared distances are used because they are more
// computationally efficient than normal distances.
// COINCIDENCE CHECK
// if a distance to center, d, is within the coincidence tolerance of the
// current minimum distance, d_min, the particle is on an edge or vertex.
// In this case, the dot product of the position vector and direction vector
// for the current indices, dp, and the dot product for the currently selected
// indices, dp_min, are compared. The cell which the particle is moving into
// is kept (i.e. the cell with the lowest dot product as the vectors will be
// completely opposed if the particle is moving directly toward the center of
// the cell).
int i1_chg;
int i2_chg;
double d_min {INFTY};
double dp_min {INFTY};
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
// get local coordinates
const array<int, 3> i_xyz {result[0] + j, result[1] + i, 0};
Position r_t = get_local_position(r, i_xyz);
// calculate distance
double d = r_t.x * r_t.x + r_t.y * r_t.y;
// check for coincidence. Because the numerical error incurred
// in hex geometry is higher than other geometries, the relative
// coincidence is checked here so that coincidence is successfully
// detected on large hex lattice with particles far from the origin
// which have rounding errors larger than the FP_COINCIDENT thresdhold.
bool on_boundary = coincident(1.0, d_min / d);
if (d < d_min || on_boundary) {
// normalize r_t and find dot product
r_t /= std::sqrt(d);
double dp = u.x * r_t.x + u.y * r_t.y;
// do not update values if particle is on a
// boundary and not moving into this cell
if (on_boundary && dp > dp_min)
continue;
// update values
d_min = d;
i1_chg = j;
i2_chg = i;
dp_min = dp;
}
}
}
// update outgoing indices
result[0] += i1_chg;
result[1] += i2_chg;
}
int HexLattice::get_flat_index(const array<int, 3>& i_xyz) const
{
return (2 * n_rings_ - 1) * (2 * n_rings_ - 1) * i_xyz[2] +
(2 * n_rings_ - 1) * i_xyz[1] + i_xyz[0];
}
//==============================================================================
Position HexLattice::get_local_position(
Position r, const array<int, 3>& i_xyz) const
{
if (orientation_ == Orientation::y) {
// x_l = x_g - (center + pitch_x*cos(30)*index_x)
r.x -=
center_.x + std::sqrt(3.0) / 2.0 * (i_xyz[0] - n_rings_ + 1) * pitch_[0];
// y_l = y_g - (center + pitch_x*index_x + pitch_y*sin(30)*index_y)
r.y -= (center_.y + (i_xyz[1] - n_rings_ + 1) * pitch_[0] +
(i_xyz[0] - n_rings_ + 1) * pitch_[0] / 2.0);
} else {
// x_l = x_g - (center + pitch_x*index_a + pitch_y*sin(30)*index_y)
r.x -= (center_.x + (i_xyz[0] - n_rings_ + 1) * pitch_[0] +
(i_xyz[1] - n_rings_ + 1) * pitch_[0] / 2.0);
// y_l = y_g - (center + pitch_y*cos(30)*index_y)
r.y -=
center_.y + std::sqrt(3.0) / 2.0 * (i_xyz[1] - n_rings_ + 1) * pitch_[0];
}