Revision 15416fe1369901f4f9e6f127c6ef80f093c0dfc8 authored by Tobias Meisel on 18 December 2020, 15:22:46 UTC, committed by Tobias Meisel on 18 December 2020, 15:56:19 UTC
1 parent e88c85d
Grid.h
/**
* \file
* \author Thomas Fischer
* \date 2012-02-02
* \brief Definition of the Grid class.
*
* \copyright
* Copyright (c) 2012-2020, OpenGeoSys Community (http://www.opengeosys.org)
* Distributed under a Modified BSD License.
* See accompanying file LICENSE.txt or
* http://www.opengeosys.org/project/license
*
*/
#pragma once
#include <bitset>
#include <vector>
#include "BaseLib/Logging.h"
// GeoLib
#include "AABB.h"
#include "GEOObjects.h"
// MathLib
#include "MathLib/Point3d.h"
#include "MathLib/MathTools.h"
namespace GeoLib
{
template <typename POINT>
class Grid : public GeoLib::AABB
{
public:
/**
* @brief The constructor of the grid object takes a vector of points or
* nodes. Furthermore the user can specify the *average* maximum number of
* points per grid cell.
*
* The number of grid cells are computed with the following formula
* \f$\frac{n_{points}}{n_{cells}} \le n_{max\_per\_cell}\f$
*
* In order to limit the memory wasting the maximum number of points per
* grid cell (in the average) should be a power of two (since std::vector
* objects resize itself with this step size).
*
* @param first, last the range of elements to examine
* @param max_num_per_grid_cell (input) max number per grid cell in the
* average
*/
template <typename InputIterator>
Grid(InputIterator first, InputIterator last,
std::size_t max_num_per_grid_cell = 512);
/**
* This is the destructor of the class. It deletes the internal data structures *not*
* including the pointers to the points.
*/
virtual ~Grid()
{
delete [] _grid_cell_nodes_map;
}
/**
* The method calculates the grid cell the given point is belonging to, i.e.,
* the (internal) coordinates of the grid cell are computed. The method searches the actual
* grid cell and all its neighbors for the POINT object which has the smallest
* distance. A pointer to this object is returned.
*
* If there is not such a point, i.e., all the searched grid cells do not contain any
* POINT object a nullptr is returned.
*
* @param pnt search point
* @return a pointer to the point with the smallest distance within the grid cells that are
* outlined above or nullptr
*/
template <typename P> POINT* getNearestPoint(P const& pnt) const;
template <typename P> std::vector<std::size_t> getPointsInEpsilonEnvironment(
P const& pnt, double eps) const;
/**
* Method fetches the vectors of all grid cells intersecting the axis aligned cuboid
* defined by two points. The first point with minimal coordinates in all directions.
* The second point with maximal coordinates in all directions.
*
* @param center (input) the center point of the axis aligned cube
* @param half_len (input) half of the edge length of the axis aligned cube
* @return vector of vectors of points within grid cells that intersects
* the axis aligned cube
*/
template <typename P>
std::vector<std::vector<POINT*> const*>
getPntVecsOfGridCellsIntersectingCube(P const& center, double half_len) const;
void getPntVecsOfGridCellsIntersectingCuboid(
MathLib::Point3d const& min_pnt,
MathLib::Point3d const& max_pnt,
std::vector<std::vector<POINT*> const*>& pnts) const;
#ifndef NDEBUG
/**
* Method creates a geometry for every mesh grid box. Additionally it
* creates one geometry containing all the box geometries.
* @param geo_obj
*/
void createGridGeometry(GeoLib::GEOObjects* geo_obj) const;
#endif
private:
/// Computes the number of grid cells per spatial dimension the objects
/// (points or mesh nodes) will be sorted in.
/// On the one hand the number of grid cells should be small to reduce the
/// management overhead. On the other hand the number should be large such
/// that each grid cell contains only a small number of objects.
/// Under the assumption that the points are distributed equidistant in
/// space the grid cells should be as cubical as possible.
/// At first it is necessary to determine the spatial dimension the grid
/// should have. The dimensions are computed from the spatial extensions
/// Let \f$\max\f$ be the largest spatial extension. The grid will have a
/// spatial dimension if the ratio of the corresponding spatial extension
/// and the maximal extension is \f$\ge 10^{-4}\f$.
/// The second step consists of computing the number of cells per dimension.
void initNumberOfSteps(std::size_t n_per_cell,
std::size_t n_pnts, std::array<double,3> const& extensions);
/**
* Method calculates the grid cell coordinates for the given point pnt. If
* the point is located outside of the bounding box the coordinates of the
* grid cell on the border that is nearest to given point will be returned.
* @param pnt (input) the coordinates of the point
* @return the coordinates of the grid cell
*/
template <typename T>
std::array<std::size_t,3> getGridCoords(T const& pnt) const;
/**
*
* point numbering of the grid cell is as follow
* @code
* 7 -------- 6
* /: /|
* / : / |
* / : / |
* / : / |
* 4 -------- 5 |
* | 3 ....|... 2
* | . | /
* | . | /
* | . | /
* |. |/
* 0 -------- 1
* @endcode
* the face numbering is as follow:
* face nodes
* 0 0,3,2,1 bottom
* 1 0,1,5,4 front
* 2 1,2,6,5 right
* 3 2,3,7,6 back
* 4 3,0,4,7 left
* 5 4,5,6,7 top
* @param pnt (input) coordinates of the point
* @param coords of the grid cell
* @return squared distances of the point to the faces of the grid cell
* ordered in the same sequence as above described
*/
template <typename P>
std::array<double, 6> getPointCellBorderDistances(
P const& pnt, std::array<std::size_t, 3> const& coords) const;
template <typename P>
bool calcNearestPointInGridCell(P const& pnt,
std::array<std::size_t,3> const& coords,
double &sqr_min_dist,
POINT* &nearest_pnt) const;
static POINT* copyOrAddress(POINT& p) { return &p; }
static POINT const* copyOrAddress(POINT const& p) { return &p; }
static POINT* copyOrAddress(POINT* p) { return p; }
std::array<std::size_t,3> _n_steps = {{1, 1, 1}};
std::array<double, 3> _step_sizes = {{0.0, 0.0, 0.0}};
/**
* This is an array that stores pointers to POINT objects.
*/
std::vector<POINT*>* _grid_cell_nodes_map = nullptr;
};
template <typename POINT>
template <typename InputIterator>
Grid<POINT>::Grid(InputIterator first, InputIterator last,
std::size_t max_num_per_grid_cell)
: GeoLib::AABB(first, last)
{
auto const n_pnts(std::distance(first,last));
std::array<double, 3> delta = {{_max_pnt[0] - _min_pnt[0],
_max_pnt[1] - _min_pnt[1],
_max_pnt[2] - _min_pnt[2]}};
// enlarge delta
for (auto& d : delta)
{
d = std::nextafter(d, std::numeric_limits<double>::max());
}
assert(n_pnts > 0);
initNumberOfSteps(max_num_per_grid_cell, static_cast<std::size_t>(n_pnts), delta);
const std::size_t n_plane(_n_steps[0] * _n_steps[1]);
_grid_cell_nodes_map = new std::vector<POINT*>[n_plane * _n_steps[2]];
// some frequently used expressions to fill the grid vectors
for (std::size_t k(0); k < 3; k++) {
if (std::abs(delta[k]) < std::numeric_limits<double>::epsilon()) {
delta[k] = std::numeric_limits<double>::epsilon();
}
_step_sizes[k] = delta[k] / _n_steps[k];
}
// fill the grid vectors
InputIterator it(first);
while (it != last) {
std::array<std::size_t,3> coords(getGridCoords(*copyOrAddress(*it)));
if (coords < _n_steps) {
std::size_t const pos(coords[0]+coords[1]*_n_steps[0]+coords[2]*n_plane);
_grid_cell_nodes_map[pos].push_back(const_cast<POINT*>(copyOrAddress(*it)));
} else {
ERR("Grid constructor: error computing indices [{:d}, {:d}, {:d}], "
"max indices [{:d}, {:d}, {:d}].",
coords[0], coords[1], coords[2], _n_steps[0], _n_steps[1],
_n_steps[2]);
}
it++;
}
}
template<typename POINT>
template <typename P>
std::vector<std::vector<POINT*> const*>
Grid<POINT>::getPntVecsOfGridCellsIntersectingCube(P const& center,
double half_len) const
{
std::vector<std::vector<POINT*> const*> pnts;
MathLib::Point3d tmp_pnt{
{{center[0]-half_len, center[1]-half_len, center[2]-half_len}}}; // min
std::array<std::size_t,3> min_coords(getGridCoords(tmp_pnt));
tmp_pnt[0] = center[0] + half_len;
tmp_pnt[1] = center[1] + half_len;
tmp_pnt[2] = center[2] + half_len;
std::array<std::size_t,3> max_coords(getGridCoords(tmp_pnt));
std::size_t coords[3], steps0_x_steps1(_n_steps[0] * _n_steps[1]);
for (coords[0] = min_coords[0]; coords[0] < max_coords[0] + 1; coords[0]++) {
for (coords[1] = min_coords[1]; coords[1] < max_coords[1] + 1; coords[1]++) {
const std::size_t coords0_p_coords1_x_steps0(coords[0] + coords[1] * _n_steps[0]);
for (coords[2] = min_coords[2]; coords[2] < max_coords[2] + 1; coords[2]++) {
pnts.push_back(&(_grid_cell_nodes_map[coords0_p_coords1_x_steps0 + coords[2]
* steps0_x_steps1]));
}
}
}
return pnts;
}
template<typename POINT>
void Grid<POINT>::getPntVecsOfGridCellsIntersectingCuboid(
MathLib::Point3d const& min_pnt,
MathLib::Point3d const& max_pnt,
std::vector<std::vector<POINT*> const*>& pnts) const
{
std::array<std::size_t,3> min_coords(getGridCoords(min_pnt));
std::array<std::size_t,3> max_coords(getGridCoords(max_pnt));
std::size_t coords[3], steps0_x_steps1(_n_steps[0] * _n_steps[1]);
for (coords[0] = min_coords[0]; coords[0] < max_coords[0] + 1; coords[0]++) {
for (coords[1] = min_coords[1]; coords[1] < max_coords[1] + 1; coords[1]++) {
const std::size_t coords0_p_coords1_x_steps0(coords[0] + coords[1] * _n_steps[0]);
for (coords[2] = min_coords[2]; coords[2] < max_coords[2] + 1; coords[2]++) {
pnts.push_back(&(_grid_cell_nodes_map[coords0_p_coords1_x_steps0 + coords[2]
* steps0_x_steps1]));
}
}
}
}
#ifndef NDEBUG
template <typename POINT>
void Grid<POINT>::createGridGeometry(GeoLib::GEOObjects* geo_obj) const
{
std::vector<std::string> grid_names;
GeoLib::Point const& llf (getMinPoint());
GeoLib::Point const& urb (getMaxPoint());
const double dx ((urb[0] - llf[0]) / _n_steps[0]);
const double dy ((urb[1] - llf[1]) / _n_steps[1]);
const double dz ((urb[2] - llf[2]) / _n_steps[2]);
// create grid names and grid boxes as geometry
for (std::size_t i(0); i<_n_steps[0]; i++) {
for (std::size_t j(0); j<_n_steps[1]; j++) {
for (std::size_t k(0); k<_n_steps[2]; k++) {
std::string name("Grid-");
name += std::to_string(i);
name += "-";
name += std::to_string(j);
name += "-";
name += std::to_string (k);
grid_names.push_back(name);
{
auto points =
std::make_unique<std::vector<GeoLib::Point*>>();
points->push_back(new GeoLib::Point(llf[0]+i*dx, llf[1]+j*dy, llf[2]+k*dz));
points->push_back(new GeoLib::Point(llf[0]+i*dx, llf[1]+(j+1)*dy, llf[2]+k*dz));
points->push_back(new GeoLib::Point(llf[0]+(i+1)*dx, llf[1]+(j+1)*dy, llf[2]+k*dz));
points->push_back(new GeoLib::Point(llf[0]+(i+1)*dx, llf[1]+j*dy, llf[2]+k*dz));
points->push_back(new GeoLib::Point(llf[0]+i*dx, llf[1]+j*dy, llf[2]+(k+1)*dz));
points->push_back(new GeoLib::Point(llf[0]+i*dx, llf[1]+(j+1)*dy, llf[2]+(k+1)*dz));
points->push_back(new GeoLib::Point(llf[0]+(i+1)*dx, llf[1]+(j+1)*dy, llf[2]+(k+1)*dz));
points->push_back(new GeoLib::Point(llf[0]+(i+1)*dx, llf[1]+j*dy, llf[2]+(k+1)*dz));
geo_obj->addPointVec(std::move(points), grid_names.back(),
nullptr);
}
auto plys = std::make_unique<std::vector<GeoLib::Polyline*>>();
auto const& points = *geo_obj->getPointVec(grid_names.back());
auto* ply0(new GeoLib::Polyline(points));
for (std::size_t l(0); l < 4; l++)
ply0->addPoint(l);
ply0->addPoint(0);
plys->push_back(ply0);
auto* ply1(new GeoLib::Polyline(points));
for (std::size_t l(4); l < 8; l++)
ply1->addPoint(l);
ply1->addPoint(4);
plys->push_back(ply1);
auto* ply2(new GeoLib::Polyline(points));
ply2->addPoint(0);
ply2->addPoint(4);
plys->push_back(ply2);
auto* ply3(new GeoLib::Polyline(points));
ply3->addPoint(1);
ply3->addPoint(5);
plys->push_back(ply3);
auto* ply4(new GeoLib::Polyline(points));
ply4->addPoint(2);
ply4->addPoint(6);
plys->push_back(ply4);
auto* ply5(new GeoLib::Polyline(points));
ply5->addPoint(3);
ply5->addPoint(7);
plys->push_back(ply5);
geo_obj->addPolylineVec(std::move(plys), grid_names.back(),
nullptr);
}
}
}
std::string merged_geo_name("Grid");
geo_obj->mergeGeometries(grid_names, merged_geo_name);
}
#endif
template <typename POINT>
template <typename T>
std::array<std::size_t,3> Grid<POINT>::getGridCoords(T const& pnt) const
{
std::array<std::size_t,3> coords{};
for (std::size_t k(0); k < 3; k++)
{
if (pnt[k] < _min_pnt[k])
{
coords[k] = 0;
}
else
{
if (pnt[k] >= _max_pnt[k])
{
coords[k] = _n_steps[k] - 1;
}
else
{
coords[k] = static_cast<std::size_t>(
std::floor((pnt[k] - _min_pnt[k])) /
std::nextafter(_step_sizes[k],
std::numeric_limits<double>::max()));
}
}
}
return coords;
}
template <typename POINT>
template <typename P>
std::array<double,6> Grid<POINT>::getPointCellBorderDistances(P const& p,
std::array<std::size_t,3> const& coords) const
{
std::array<double,6> dists{};
dists[0] = std::abs(p[2]-_min_pnt[2] + coords[2]*_step_sizes[2]); // bottom
dists[5] = std::abs(p[2]-_min_pnt[2] + (coords[2]+1)*_step_sizes[2]); // top
dists[1] = std::abs(p[1]-_min_pnt[1] + coords[1]*_step_sizes[1]); // front
dists[3] = std::abs(p[1]-_min_pnt[1] + (coords[1]+1)*_step_sizes[1]); // back
dists[4] = std::abs(p[0]-_min_pnt[0] + coords[0]*_step_sizes[0]); // left
dists[2] = std::abs(p[0]-_min_pnt[0] + (coords[0]+1)*_step_sizes[0]); // right
return dists;
}
template <typename POINT>
template <typename P>
POINT* Grid<POINT>::getNearestPoint(P const& pnt) const
{
std::array<std::size_t,3> coords(getGridCoords(pnt));
double sqr_min_dist(MathLib::sqrDist(_min_pnt, _max_pnt));
POINT* nearest_pnt(nullptr);
std::array<double,6> dists(getPointCellBorderDistances(pnt, coords));
if (calcNearestPointInGridCell(pnt, coords, sqr_min_dist, nearest_pnt)) {
double min_dist(sqrt(sqr_min_dist));
if (dists[0] >= min_dist && dists[1] >= min_dist
&& dists[2] >= min_dist && dists[3] >= min_dist
&& dists[4] >= min_dist && dists[5] >= min_dist) {
return nearest_pnt;
}
} else {
// search in all border cells for at least one neighbor
double sqr_min_dist_tmp;
POINT * nearest_pnt_tmp(nullptr);
std::size_t offset(1);
while (nearest_pnt == nullptr) {
std::array<std::size_t,3> ijk{{
coords[0]<offset ? 0 : coords[0]-offset,
coords[1]<offset ? 0 : coords[1]-offset,
coords[2]<offset ? 0 : coords[2]-offset}};
for (; ijk[0]<coords[0]+offset; ijk[0]++) {
for (; ijk[1] < coords[1] + offset; ijk[1]++) {
for (; ijk[2] < coords[2] + offset; ijk[2]++) {
// do not check the origin grid cell twice
if (ijk[0] == coords[0]
&& ijk[1] == coords[1]
&& ijk[2] == coords[2]) {
continue;
}
// check if temporary grid cell coordinates are valid
if (ijk[0] >= _n_steps[0]
|| ijk[1] >= _n_steps[1]
|| ijk[2] >= _n_steps[2]) {
continue;
}
if (calcNearestPointInGridCell(pnt, ijk,
sqr_min_dist_tmp, nearest_pnt_tmp)) {
if (sqr_min_dist_tmp < sqr_min_dist) {
sqr_min_dist = sqr_min_dist_tmp;
nearest_pnt = nearest_pnt_tmp;
}
}
} // end k
} // end j
} // end i
offset++;
} // end while
} // end else
double len(sqrt(MathLib::sqrDist(pnt, *nearest_pnt)));
// search all other grid cells within the cube with the edge nodes
std::vector<std::vector<POINT*> const*> vecs_of_pnts(
getPntVecsOfGridCellsIntersectingCube(pnt, len));
const std::size_t n_vecs(vecs_of_pnts.size());
for (std::size_t j(0); j<n_vecs; j++) {
std::vector<POINT*> const& pnts(*(vecs_of_pnts[j]));
const std::size_t n_pnts(pnts.size());
for (std::size_t k(0); k<n_pnts; k++) {
const double sqr_dist(MathLib::sqrDist(pnt, *pnts[k]));
if (sqr_dist < sqr_min_dist) {
sqr_min_dist = sqr_dist;
nearest_pnt = pnts[k];
}
}
}
return nearest_pnt;
}
template <typename POINT>
void Grid<POINT>::initNumberOfSteps(std::size_t n_per_cell,
std::size_t n_pnts, std::array<double,3> const& extensions)
{
double const max_extension(
*std::max_element(extensions.cbegin(), extensions.cend()));
std::bitset<3> dim; // all bits set to zero
for (std::size_t k(0); k<3; ++k) {
// set dimension if the ratio kth-extension/max_extension >= 1e-4
if (extensions[k] >= 1e-4 * max_extension) {
dim[k] = true;
}
}
// structured grid: n_cells = _n_steps[0] * _n_steps[1] * _n_steps[2]
// *** condition: n_pnts / n_cells < n_per_cell
// => n_pnts / n_per_cell < n_cells
// _n_steps[1] = _n_steps[0] * extensions[1]/extensions[0],
// _n_steps[2] = _n_steps[0] * extensions[2]/extensions[0],
// => n_cells = _n_steps[0]^3 * extensions[1]/extensions[0] *
// extensions[2]/extensions[0],
// => _n_steps[0] = cbrt(n_cells * extensions[0]^2 /
// (extensions[1]*extensions[2]))
auto sc_ceil = [](double v) {
return static_cast<std::size_t>(ceil(v));
};
switch (dim.count()) {
case 3: // 3d case
_n_steps[0] =
sc_ceil(std::cbrt(n_pnts * (extensions[0] / extensions[1]) *
(extensions[0] / extensions[2]) / n_per_cell));
_n_steps[1] = sc_ceil(_n_steps[0] *
std::min(extensions[1] / extensions[0], 100.0));
_n_steps[2] = sc_ceil(_n_steps[0] *
std::min(extensions[2] / extensions[0], 100.0));
break;
case 2: // 2d cases
if (dim[0] && dim[1]) { // xy
_n_steps[0] = sc_ceil(std::sqrt(n_pnts * extensions[0] /
(n_per_cell * extensions[1])));
_n_steps[1] = sc_ceil(
_n_steps[0] * std::min(extensions[1] / extensions[0], 100.0));
} else if (dim[0] && dim[2]) { // xz
_n_steps[0] = sc_ceil(std::sqrt(n_pnts * extensions[0] /
(n_per_cell * extensions[2])));
_n_steps[2] = sc_ceil(
_n_steps[0] * std::min(extensions[2] / extensions[0], 100.0));
} else if (dim[1] && dim[2]) { // yz
_n_steps[1] = sc_ceil(std::sqrt(n_pnts * extensions[1] /
(n_per_cell * extensions[2])));
_n_steps[2] = sc_ceil(std::min(extensions[2]/extensions[1],100.0));
}
break;
case 1: // 1d cases
for (std::size_t k(0); k<3; ++k) {
if (dim[k]) {
_n_steps[k] = sc_ceil(static_cast<double>(n_pnts)/n_per_cell);
}
}
}
}
template <typename POINT>
template <typename P>
bool Grid<POINT>::calcNearestPointInGridCell(P const& pnt,
std::array<std::size_t,3> const& coords,
double &sqr_min_dist,
POINT* &nearest_pnt) const
{
const std::size_t grid_idx (coords[0]+coords[1]*_n_steps[0]+coords[2]*_n_steps[0]*_n_steps[1]);
std::vector<typename std::add_pointer<typename std::remove_pointer<POINT>::type>::type> const& pnts(_grid_cell_nodes_map[grid_idx]);
if (pnts.empty()) return false;
const std::size_t n_pnts(pnts.size());
sqr_min_dist = MathLib::sqrDist(*pnts[0], pnt);
nearest_pnt = pnts[0];
for (std::size_t i(1); i < n_pnts; i++) {
const double sqr_dist(MathLib::sqrDist(*pnts[i], pnt));
if (sqr_dist < sqr_min_dist) {
sqr_min_dist = sqr_dist;
nearest_pnt = pnts[i];
}
}
return true;
}
template <typename POINT>
template <typename P>
std::vector<std::size_t>
Grid<POINT>::getPointsInEpsilonEnvironment(P const& pnt, double eps) const
{
std::vector<std::vector<POINT*> const*> vec_pnts(
getPntVecsOfGridCellsIntersectingCube(pnt, eps));
double const sqr_eps(eps*eps);
std::vector<std::size_t> pnts;
for (auto vec : vec_pnts) {
for (auto const p : *vec) {
if (MathLib::sqrDist(*p, pnt) < sqr_eps) {
pnts.push_back(p->getID());
}
}
}
return pnts;
}
} // end namespace GeoLib
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