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cgal/Octree/include/CGAL/Octree.h

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// Copyright (c) 2007-2020 INRIA (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL$
// $Id$
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s) : Jackson Campolattaro, Cédric Portaneri, Tong Zhao
#ifndef CGAL_OCTREE_3_H
#define CGAL_OCTREE_3_H
#include <CGAL/Octree/Node.h>
#include <CGAL/Octree/Split_criterion.h>
#include <CGAL/Octree/Walker_criterion.h>
#include <CGAL/Octree/Walker_iterator.h>
#include <CGAL/bounding_box.h>
#include <CGAL/Aff_transformation_3.h>
#include <CGAL/aff_transformation_tags.h>
#include <CGAL/Orthogonal_k_neighbor_search.h>
#include <CGAL/Search_traits_3.h>
#include <CGAL/Search_traits_adapter.h>
#include <CGAL/intersections.h>
#include <CGAL/squared_distance_3.h>
#include <boost/function.hpp>
#include <boost/iterator/iterator_facade.hpp>
#include <boost/range/iterator_range.hpp>
#include <iostream>
#include <fstream>
#include <ostream>
#include <functional>
#include <stack>
#include <queue>
#include <vector>
#include <math.h>
namespace CGAL {
namespace Octree {
/*!
* \ingroup PkgOctreeClasses
*
* \brief Class Octree is a data structure for efficient computations in 3D space.
*
* \details It builds a heirarchy of nodes which subdivide the space based on a collection of points.
* Each node represents an axis aligned cubic region of space.
* A node contains the range of points that are present in the region it defines,
* and it may contain eight other nodes which further subdivide the region.
*
* \tparam PointRange is a range type that provides random access iterators over the indices of a set of points.
* \tparam PointMap is a type that maps items in the PointRange to Point data
*/
template<class PointRange, class PointMap>
class Octree {
public:
/// \name Public Types
/// @{
/*!
* \brief The point type is deduced from the type of the property map used
*/
typedef typename boost::property_traits<PointMap>::value_type Point;
/*!
* \brief The Kernel used is deduced from the point type
*/
typedef typename CGAL::Kernel_traits<Point>::Kernel Kernel;
/*!
* \brief The floating point type is decided by the Kernel
*/
typedef typename Kernel::FT FT;
/*!
* \brief
*/
typedef boost::iterator_range<typename PointRange::iterator> Points_iterator_range;
/*!
* \brief The Sub-tree / Octant type
*/
typedef Node::Node<typename PointRange::iterator> Node;
/*!
* \brief A function that determines whether a node needs to be split when refining a tree
*/
typedef std::function<bool(const Node &)> Split_criterion_function;
/*!
* \brief A range that provides input-iterator access to the nodes of a tree
*/
typedef boost::iterator_range<Walker_iterator<const Node>> Node_range;
/*!
* \brief A function that determines the next node in a traversal given the current one
*/
typedef std::function<const Node *(const Node *)> Node_walker;
/// @}
private: // Private types
typedef typename Kernel::Vector_3 Vector;
typedef typename Kernel::Iso_cuboid_3 Iso_cuboid;
typedef typename Kernel::Sphere_3 Sphere;
typedef typename CGAL::Bbox_3 Bbox;
typedef typename PointRange::iterator Range_iterator;
typedef typename std::iterator_traits<Range_iterator>::value_type Range_type;
private: // data members :
Node m_root; /* root node of the octree */
uint8_t m_max_depth_reached = 0; /* octree actual highest depth reached */
PointRange &m_ranges; /* input point range */
PointMap m_points_map; /* property map: `value_type of InputIterator` -> `Point` (Position) */
Point m_bbox_min; /* input bounding box min value */
FT m_bbox_side; /* input bounding box side length (cube) */
std::vector<FT> m_side_per_depth; /* side length per node's depth */
std::vector<size_t> m_unit_per_depth; /* number of unit node (smallest) inside one node for each depth for one axis */
public:
/// \name Construction, Destruction
/// @{
/*!
* \brief Create an octree from a collection of points
*
* The resulting octree will have a root node with no children that contains the points passed.
* That root node will have a bounding box that encloses all of the points passed,
* with padding according to the enlarge_ratio
*
* \param point_range random access iterator over the indices of the points
* \param point_map maps the point indices to their coordinate locations
* \param enlarge_ratio the degree to which the bounding box should be enlarged
*/
Octree(
PointRange &point_range,
PointMap &point_map,
const FT enlarge_ratio = 1.2) :
m_ranges(point_range),
m_points_map(point_map) {
// compute bounding box that encloses all points
Iso_cuboid bbox = CGAL::bounding_box(boost::make_transform_iterator
(m_ranges.begin(),
CGAL::Property_map_to_unary_function<PointMap>(
m_points_map)),
boost::make_transform_iterator
(m_ranges.end(),
CGAL::Property_map_to_unary_function<PointMap>(
m_points_map)));
// Find the center point of the box
Point bbox_centroid = midpoint(bbox.min(), bbox.max());
// scale bounding box to add padding
bbox = bbox.transform(Aff_transformation_3<Kernel>(SCALING, enlarge_ratio));
// Convert the bounding box into a cube
FT x_len = bbox.xmax() - bbox.xmin();
FT y_len = bbox.ymax() - bbox.ymin();
FT z_len = bbox.zmax() - bbox.zmin();
FT max_len = std::max({x_len, y_len, z_len});
bbox = Iso_cuboid(bbox.min(), bbox.min() + max_len * Vector(1.0, 1.0, 1.0));
// Shift the squared box to make sure it's centered in the original place
Point bbox_transformed_centroid = midpoint(bbox.min(), bbox.max());
Vector diff_centroid = bbox_centroid - bbox_transformed_centroid;
bbox = bbox.transform(Aff_transformation_3<Kernel>(TRANSLATION, diff_centroid));
// save octree attributes
m_bbox_min = bbox.min();
m_bbox_side = bbox.max()[0] - m_bbox_min[0];
m_root.points() = {point_range.begin(), point_range.end()};
}
/// @}
/// \name Tree Building
/// @{
/*!
* \brief Subdivide an octree's nodes and sub-nodes until it meets the given criteria
*
* \todo
*
* \param split_criterion rule to use when determining whether or not a node needs to be subdivided
*/
void refine(const Split_criterion_function &split_criterion) {
// create a side length map
for (int i = 0; i <= (int) 32; i++)
m_side_per_depth.push_back(m_bbox_side / (FT) (1 << i));
// Initialize a queue of nodes that need to be refined
std::queue<Node *> todo;
todo.push(&m_root);
// Process items in the queue until it's consumed fully
while (!todo.empty()) {
// Get the next element
auto current = todo.front();
todo.pop();
int depth = current->depth();
// Check if this node needs to be processed
if (split_criterion(*current)) {
// Split this node
current->split();
// Redistribute its points
reassign_points((*current));
// Process each of its children
for (int i = 0; i < 8; ++i)
todo.push(&(*current)[i]);
}
}
}
/*!
* \brief Refine an octree using a max depth and max number of points in a node as split criterion
*
* \todo
*
* \param max_depth deepest a tree is allowed to be (nodes at this depth will not be split)
* \param bucket_size maximum points a node is allowed to contain
*/
void refine(size_t max_depth, size_t bucket_size) {
refine(Split_criterion::Max_depth_or_bucket_size(max_depth, bucket_size));
}
/// @}
/// \name Accessors
/// @{
/*!
* \brief Provides read and write access to the root node, and by extension the rest of the tree
*
* \todo
*
* \return a reference to the root node of the tree
*/
Node &root() { return m_root; }
/*!
* \brief Provides read-only access to the root node, and by extension the rest of the tree
*
* \todo
*
* \return a const reference to the root node of the tree
*/
const Node &root() const { return m_root; }
/*!
* \brief Constructs an input range of nodes using a tree walker function
*
* \todo
*
* \tparam Walker type of the walker rule
* \param walker the rule to use when determining the order of the sequence of points produced
* \return a forward input iterator over the nodes of the tree
*/
template<class Walker>
Node_range walk(const Walker &walker = Walker()) const {
const Node *first = walker.first(&m_root);
Node_walker next = std::bind(&Walker::template next<Points_iterator_range>,
walker, std::placeholders::_1);
return boost::make_iterator_range(Walker_iterator<const Node>(first, next),
Walker_iterator<const Node>());
}
/*!
* \brief Find the leaf node which would contain a point
*
* Traverses the octree and finds the deepest cell that has a domain enclosing the point passed.
*
* \param p The point to find a node for
* \return A reference to the node which would contain the point
*/
const Node &locate(const Point &p) const {
// Start at the root node
auto *node_for_point = &m_root;
// Descend the tree until reaching a leaf node
while (!node_for_point->is_leaf()) {
// Find the point to split around
Point center = compute_barycenter_position(*node_for_point);
// Find the index of the correct sub-node
typename Node::Index index;
for (int dimension = 0; dimension < 3; ++dimension) {
index[dimension] = center[dimension] < p[dimension];
}
// Find the correct sub-node of the current node
node_for_point = &(*node_for_point)[index.to_ulong()];
}
// Return the result
return *node_for_point;
}
/*!
* \brief Find the bounding box of a node
*
* \todo
*
* \param node the node to determine the bounding box of
* \return the bounding box defined by that node's relationship to the tree
*/
Bbox bbox(const Node &node) const {
// Determine the side length of this node
FT size = m_side_per_depth[node.depth()];
// Determine the location this node should be split
FT min_corner[3];
FT max_corner[3];
for (int i = 0; i < 3; i++) {
min_corner[i] = m_bbox_min[i] + (node.location()[i] * size);
max_corner[i] = min_corner[i] + size;
}
// Create the cube
return {min_corner[0], min_corner[1], min_corner[2],
max_corner[0], max_corner[1], max_corner[2]};
}
/*!
* \brief Find the K points in a tree that are nearest to the search point and within a specific radius
*
* \todo
*
* \tparam Point_output_iterator an output iterator type that will accept points
* \param search_point the location to find points near
* \param search_radius_squared the size of the region to search within
* \param k the number of points to find
* \param output the output iterator to add the found points to
*/
template<typename Point_output_iterator>
void nearest_k_neighbours_in_radius(const Point &search_point, FT search_radius_squared, std::size_t k,
Point_output_iterator output) const {
// Create an empty list of points
std::vector<Point_with_distance> points_list;
points_list.reserve(k);
// Invoking the recursive function adds those points to the vector (passed by reference)
auto search_bounds = Sphere(search_point, search_radius_squared);
nearest_k_neighbours_recursive(search_bounds, m_root, points_list);
// Add all the points found to the output
for (auto &item : points_list)
*output++ = item.point;
}
/*!
* \brief Find the K points in a tree that are nearest to the search point
*
* \todo
*
* \tparam Point_output_iterator an output iterator type that will accept points
* \param search_point the location to find points near
* \param k the number of points to find
* \param output the output iterator to add the found points to
*/
template<typename Point_output_iterator>
void nearest_k_neighbours(const Point &search_point, std::size_t k, Point_output_iterator output) const {
return nearest_k_neighbours_in_radius(search_point, std::numeric_limits<FT>::max(), k, output);
}
/// @}
/// \name Operators
/// @{
/*!
* \brief Compares the topology of a pair of Octrees
*
* \todo
*
* \param rhs tree to compare with
* \return whether the trees have the same topology
*/
bool operator==(const Octree<PointRange, PointMap> &rhs) const {
// Identical trees should have the same bounding box
if (rhs.m_bbox_min != m_bbox_min || rhs.m_bbox_side != m_bbox_side)
return false;
// Identical trees should have the same depth
if (rhs.m_max_depth_reached != m_max_depth_reached)
return false;
// If all else is equal, recursively compare the trees themselves
return rhs.m_root == m_root;
}
bool operator!=(const Octree<PointRange, PointMap> &rhs) const {
return !operator==(rhs);
}
/// @}
private: // functions :
Point compute_barycenter_position(const Node &node) const {
// Determine the side length of this node
FT size = m_side_per_depth[node.depth()];
// Determine the location this node should be split
FT bary[3];
for (int i = 0; i < 3; i++)
bary[i] = node.location()[i] * size + (size / 2.0) + m_bbox_min[i];
// Convert that location into a point
return {bary[0], bary[1], bary[2]};
}
void reassign_points(Node &node, Range_iterator begin, Range_iterator end, const Point &center,
std::bitset<3> coord = {},
std::size_t dimension = 0) {
// Root case: reached the last dimension
if (dimension == 3) {
node[coord.to_ulong()].points() = {begin, end};
return;
}
// Split the point collection around the center point on this dimension
Range_iterator split_point = std::partition(begin, end,
[&](const Range_type &a) -> bool {
return (get(m_points_map, a)[dimension] < center[dimension]);
});
// Further subdivide the first side of the split
std::bitset<3> coord_left = coord;
coord_left[dimension] = false;
reassign_points(node, begin, split_point, center, coord_left, dimension + 1);
// Further subdivide the second side of the split
std::bitset<3> coord_right = coord;
coord_right[dimension] = true;
reassign_points(node, split_point, end, center, coord_right, dimension + 1);
}
void reassign_points(Node &node) {
Point center = compute_barycenter_position(node);
reassign_points(node, node.points().begin(), node.points().end(), center);
}
bool do_intersect(const Node &node, const Sphere &sphere) const {
// Create a cubic bounding box from the node
Bbox node_cube = bbox(node);
// Check for overlap between the node's box and the sphere as a box, to quickly catch some cases
// FIXME: Activating this causes slower times!
// if (!do_overlap(node_cube, sphere.bbox()))
// return false;
// Check for intersection between the node and the sphere
return CGAL::do_intersect(node_cube, sphere);
}
// TODO: There has to be a better way than using structs like these!
struct Point_with_distance {
Point point;
FT distance;
};
struct Node_index_with_distance {
typename Node::Index index;
FT distance;
};
void nearest_k_neighbours_recursive(Sphere &search_bounds, const Node &node,
std::vector<Point_with_distance> &results, FT epsilon = 0) const {
// Check whether the node has children
if (node.is_leaf()) {
// Base case: the node has no children
// Loop through each of the points contained by the node
// Note: there might be none, and that should be fine!
for (auto point_index : node.points()) {
// Retrieve each point from the octree's point map
auto point = get(m_points_map, point_index);
// Pair that point with its distance from the search point
Point_with_distance current_point_with_distance =
{point, squared_distance(point, search_bounds.center())};
// Check if the new point is within the bounds
if (current_point_with_distance.distance < search_bounds.squared_radius()) {
// Check if the results list is full
if (results.size() == results.capacity()) {
// Delete a point if we need to make room
results.pop_back();
}
// Add the new point
results.push_back(current_point_with_distance);
// Sort the list
std::sort(results.begin(), results.end(), [=](auto &left, auto &right) {
return left.distance < right.distance;
});
// Check if the results list is full
if (results.size() == results.capacity()) {
// Set the search radius
search_bounds = Sphere(search_bounds.center(), results.back().distance + epsilon);
}
}
}
} else {
// Recursive case: the node has children
// Create a list to map children to their distances
std::vector<Node_index_with_distance> children_with_distances;
children_with_distances.reserve(8);
// Fill the list with child nodes
for (int index = 0; index < 8; ++index) {
auto &child_node = node[index];
// Add a child to the list, with its distance
children_with_distances.push_back(
{typename Node::Index(index),
CGAL::squared_distance(search_bounds.center(), compute_barycenter_position(child_node))}
);
}
// Sort the children by their distance from the search point
std::sort(children_with_distances.begin(), children_with_distances.end(), [=](auto &left, auto &right) {
return left.distance < right.distance;
});
// Loop over the children
for (auto child_with_distance : children_with_distances) {
auto &child_node = node[child_with_distance.index.to_ulong()];
// Check whether the bounding box of the child intersects with the search bounds
if (do_intersect(child_node, search_bounds)) {
// Recursively invoke this function
nearest_k_neighbours_recursive(search_bounds, child_node, results);
}
}
}
}
}; // end class Octree
} // namespace Octree
} // namespace CGAL
#endif // CGAL_OCTREE_3_H
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