tree_node.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2026 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
 
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
 
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 
 
 
// C++ includes
#include <set>
#include <array>
 
// Local includes
#include "libmesh/libmesh_config.h"
#include "libmesh/tree_node.h"
#include "libmesh/mesh_base.h"
#include "libmesh/elem.h"
 
namespace libMesh
{
 
// ------------------------------------------------------------
// TreeNode class methods
template <unsigned int N>
bool TreeNode<N>::insert (const Node * nd)
{
  libmesh_assert(nd);
  libmesh_assert_less (nd->id(), mesh.n_nodes());
 
  // Return if we don't bound the node
  if (!this->bounds_node(nd))
    return false;
 
  // Add the node to ourself if we are active
  if (this->active())
    {
      nodes.push_back (nd);
 
      // Refine ourself if we reach the target bin size for a TreeNode.
      if (nodes.size() == tgt_bin_size)
        this->refine();
 
      return true;
    }
 
  // If we are not active simply pass the node along to
  // our children
  libmesh_assert_equal_to (children.size(), N);
 
  bool was_inserted = false;
  for (unsigned int c=0; c<N; c++)
    if (children[c]->insert (nd))
      was_inserted = true;
  return was_inserted;
}
 
 
 
template <unsigned int N>
bool TreeNode<N>::insert (const Elem * elem)
{
  libmesh_assert(elem);
 
  // We first want to find the corners of the cuboid surrounding the cell.
  const BoundingBox bbox = elem->loose_bounding_box();
 
  // If we are using a QuadTree, it's either because LIBMESH_DIM==2 or
  // we have a planar xy mesh.  Either way, the bounding box
  // comparison in this case needs to do something slightly different
  // for the z-coordinate.
  bool bboxes_intersect = false;
 
  if (N == 8) // OctTree
    bboxes_intersect = this->bounding_box.intersects(bbox);
  else if (N == 4) // QuadTree
    {
      // Perform a specialized BoundingBox intersection check that
      // ignores z-coords.  Copied from geom/bounding_box.C Check for
      // "real" intersection in the x and y directions, then check
      // that the z-coordinate is "close".
 
      // Helper macro
#define IS_BETWEEN(min, check, max)             \
      ((min) <= (check) && (check) <= (max))
 
      // Make local variables first to make things more clear in a moment
      const Real & elem_min_x = bbox.first(0);
      const Real & elem_max_x = bbox.second(0);
      const Real & tree_min_x = this->bounding_box.first(0);
      const Real & tree_max_x = this->bounding_box.second(0);
 
      const Real & elem_min_y = bbox.first(1);
      const Real & elem_max_y = bbox.second(1);
      const Real & tree_min_y = this->bounding_box.first(1);
      const Real & tree_max_y = this->bounding_box.second(1);
 
      bool x_int =
        IS_BETWEEN(elem_min_x, tree_min_x, elem_max_x) ||
        IS_BETWEEN(elem_min_x, tree_max_x, elem_max_x) ||
        IS_BETWEEN(tree_min_x, elem_min_x, tree_max_x) ||
        IS_BETWEEN(tree_min_x, elem_max_x, tree_max_x);
 
      bool y_int =
        IS_BETWEEN(elem_min_y, tree_min_y, elem_max_y) ||
        IS_BETWEEN(elem_min_y, tree_max_y, elem_max_y) ||
        IS_BETWEEN(tree_min_y, elem_min_y, tree_max_y) ||
        IS_BETWEEN(tree_min_y, elem_max_y, tree_max_y);
 
      // When LIBMESH_DIM==3, check that the z-coordinates of the elem
      // bbox and the tree bbox are "close" since the QuadTree is
      // meant to work in the case when the mesh is planar_xy but not
      // necessarily lying in the z=0 plane.
      bool z_match = true;
      if (LIBMESH_DIM == 3)
        {
          const Real & elem_min_z = bbox.first(2);
          const Real & elem_max_z = bbox.second(2);
          const Real & tree_min_z = this->bounding_box.first(2);
          const Real & tree_max_z = this->bounding_box.second(2);
 
          z_match =
            (std::abs(elem_min_z - elem_max_z) < TOLERANCE) &&
            (std::abs(tree_min_z - tree_max_z) < TOLERANCE) &&
            (std::abs(elem_min_z - tree_max_z) < TOLERANCE);
        }
 
      bboxes_intersect = z_match && x_int && y_int;
    }
  else // binary tree
    {
      // TODO: implement 1D bounding box intersection check
      libmesh_not_implemented();
    }
 
  // Next, find out whether this cuboid has got non-empty intersection
  // with the bounding box of the current tree node.
  //
  // If not, we should not care about this element.
  if (!bboxes_intersect)
    return false;
 
  // Only add the element if we are active
  if (this->active())
    {
      elements.push_back (elem);
 
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
 
      // flag indicating this node contains
      // infinite elements
      if (elem->infinite())
        this->contains_ifems = true;
 
#endif
 
      unsigned int element_count = cast_int<unsigned int>(elements.size());
      if (!mesh.get_count_lower_dim_elems_in_point_locator())
        {
          const std::set<unsigned char> & elem_dimensions = mesh.elem_dimensions();
          if (elem_dimensions.size() > 1)
            {
              element_count = 0;
              unsigned char highest_dim_elem = *elem_dimensions.rbegin();
              for (const Elem * other_elem : elements)
                if (other_elem->dim() == highest_dim_elem)
                  element_count++;
            }
        }
 
      // Refine ourself if we reach the target bin size for a TreeNode.
      if (element_count == tgt_bin_size)
        this->refine();
 
      return true;
    }
 
  // If we are not active simply pass the element along to
  // our children
  libmesh_assert_equal_to (children.size(), N);
 
  bool was_inserted = false;
  for (unsigned int c=0; c<N; c++)
    if (children[c]->insert (elem))
      was_inserted = true;
  return was_inserted;
}
 
 
 
template <unsigned int N>
void TreeNode<N>::refine ()
{
  // Huh?  better be active...
  libmesh_assert (this->active());
  libmesh_assert (children.empty());
 
  // A TreeNode<N> has by definition N children
  children.resize(N);
 
  // Scale up the target bin size in child TreeNodes if we have reached
  // the maximum number of refinement levels.
  unsigned int new_target_bin_size = tgt_bin_size;
  if (level() >= target_bin_size_increase_level)
    {
      new_target_bin_size *= 2;
    }
 
  for (unsigned int c=0; c<N; c++)
    {
      // Create the child and set its bounding box.
      children[c] = std::make_unique<TreeNode<N>>(mesh, new_target_bin_size, this);
      children[c]->set_bounding_box(this->create_bounding_box(c));
 
      // Pass off our nodes to our children
      for (const Node * node : nodes)
        children[c]->insert(node);
 
      // Pass off our elements to our children
      for (const Elem * elem : elements)
        children[c]->insert(elem);
    }
 
  // We don't need to store nodes or elements any more, they have been
  // added to the children.  Use the "swap trick" to actually reduce
  // the capacity of these vectors.
  std::vector<const Node *>().swap(nodes);
  std::vector<const Elem *>().swap(elements);
 
  libmesh_assert_equal_to (nodes.capacity(), 0);
  libmesh_assert_equal_to (elements.capacity(), 0);
}
 
 
 
template <unsigned int N>
void TreeNode<N>::set_bounding_box (const std::pair<Point, Point> & bbox)
{
  bounding_box = bbox;
}
 
 
 
template <unsigned int N>
bool TreeNode<N>::bounds_node (const Node * nd,
                               Real relative_tol) const
{
  libmesh_assert(nd);
  return bounds_point(*nd, relative_tol);
}
 
 
 
template <unsigned int N>
bool TreeNode<N>::bounds_point (const Point & p,
                                Real relative_tol) const
{
  const Point & min = bounding_box.first;
  const Point & max = bounding_box.second;
 
  const Real tol = (max - min).norm() * relative_tol;
 
  if ((p(0) >= min(0) - tol)
      && (p(0) <= max(0) + tol)
#if LIBMESH_DIM > 1
      && (p(1) >= min(1) - tol)
      && (p(1) <= max(1) + tol)
#endif
#if LIBMESH_DIM > 2
      && (p(2) >= min(2) - tol)
      && (p(2) <= max(2) + tol)
#endif
      )
    return true;
 
  return false;
}
 
 
 
template <unsigned int N>
BoundingBox
TreeNode<N>::create_bounding_box (unsigned int c) const
{
  switch (N)
    {
      // How to refine an OctTree Node
    case 8:
      {
        const Real xmin = bounding_box.first(0);
        const Real ymin = bounding_box.first(1);
        const Real zmin = bounding_box.first(2);
 
        const Real xmax = bounding_box.second(0);
        const Real ymax = bounding_box.second(1);
        const Real zmax = bounding_box.second(2);
 
        const Real xc = .5*(xmin + xmax);
        const Real yc = .5*(ymin + ymax);
        const Real zc = .5*(zmin + zmax);
 
        switch (c)
          {
          case 0:
            return BoundingBox (Point(xmin, ymin, zmin),
                                Point(xc,   yc,   zc));
          case 1:
            return BoundingBox (Point(xc,   ymin, zmin),
                                Point(xmax, yc,   zc));
          case 2:
            return BoundingBox (Point(xmin, yc,   zmin),
                                Point(xc,   ymax, zc));
          case 3:
            return BoundingBox (Point(xc,   yc,   zmin),
                                Point(xmax, ymax, zc));
          case 4:
            return BoundingBox (Point(xmin, ymin, zc),
                                Point(xc,   yc,   zmax));
          case 5:
            return BoundingBox (Point(xc,   ymin, zc),
                                Point(xmax, yc,   zmax));
          case 6:
            return BoundingBox (Point(xmin, yc,   zc),
                                Point(xc,   ymax, zmax));
          case 7:
            return BoundingBox (Point(xc,   yc,   zc),
                                Point(xmax, ymax, zmax));
          default:
            libmesh_error_msg("c >= N! : " << c);
          }
 
        break;
      } // case 8
 
      // How to refine an QuadTree Node
    case 4:
      {
        const Real xmin = bounding_box.first(0);
        const Real ymin = bounding_box.first(1);
 
        const Real xmax = bounding_box.second(0);
        const Real ymax = bounding_box.second(1);
 
        const Real xc = .5*(xmin + xmax);
        const Real yc = .5*(ymin + ymax);
 
        switch (c)
          {
          case 0:
            return BoundingBox (Point(xmin, ymin),
                                Point(xc,   yc));
          case 1:
            return BoundingBox (Point(xc,   ymin),
                                Point(xmax, yc));
          case 2:
            return BoundingBox (Point(xmin, yc),
                                Point(xc,   ymax));
          case 3:
            return BoundingBox (Point(xc,   yc),
                                Point(xmax, ymax));
          default:
            libmesh_error_msg("c >= N!");
          }
 
        break;
      } // case 4
 
      // How to refine a BinaryTree Node
    case 2:
      {
        const Real xmin = bounding_box.first(0);
 
        const Real xmax = bounding_box.second(0);
 
        const Real xc = .5*(xmin + xmax);
 
        switch (c)
          {
          case 0:
            return BoundingBox (Point(xmin),
                                Point(xc));
          case 1:
            return BoundingBox (Point(xc),
                                Point(xmax));
          default:
            libmesh_error_msg("c >= N!");
          }
 
        break;
      } // case 2
 
    default:
      libmesh_error_msg("Only implemented for Octrees, QuadTrees, and Binary Trees!");
    }
}
 
 
 
template <unsigned int N>
void TreeNode<N>::print_nodes(std::ostream & out_stream) const
{
  if (this->active())
    {
      out_stream << "TreeNode Level: " << this->level() << std::endl;
 
      for (const Node * node : nodes)
        out_stream << " " << node->id();
 
      out_stream << std::endl << std::endl;
    }
  else
    for (const auto & child : children)
      child->print_nodes();
}
 
 
 
template <unsigned int N>
void TreeNode<N>::print_elements(std::ostream & out_stream) const
{
  if (this->active())
    {
      out_stream << "TreeNode Level: " << this->level() << std::endl;
 
      for (const auto & elem : elements)
        out_stream << " " << elem;
 
      out_stream << std::endl << std::endl;
    }
  else
    for (const auto & child : children)
      child->print_elements();
}
 
 
 
template <unsigned int N>
void TreeNode<N>::transform_nodes_to_elements (std::vector<std::vector<const Elem *>> & nodes_to_elem)
{
  if (this->active())
    {
      elements.clear();
 
      // Temporarily use a set. Since multiple nodes
      // will likely map to the same element we use a
      // set to eliminate the duplication.
      std::set<const Elem *> elements_set;
 
      for (const Node * node : nodes)
        {
          // the actual global node number we are replacing
          // with the connected elements
          const dof_id_type node_number = node->id();
 
          libmesh_assert_less (node_number, mesh.n_nodes());
          libmesh_assert_less (node_number, nodes_to_elem.size());
 
          for (const Elem * elem : nodes_to_elem[node_number])
            elements_set.insert(elem);
        }
 
      // Done with the nodes.
      std::vector<const Node *>().swap(nodes);
 
      // Now the set is built.  We can copy this to the
      // vector.  Note that the resulting vector will
      // already be sorted, and will require less memory
      // than the set.
      elements.reserve(elements_set.size());
 
      for (const auto & elem : elements_set)
        {
          elements.push_back(elem);
 
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
 
          // flag indicating this node contains
          // infinite elements
          if (elem->infinite())
            this->contains_ifems = true;
 
#endif
        }
    }
  else
    for (auto & child : children)
      child->transform_nodes_to_elements (nodes_to_elem);
}
 
 
 
template <unsigned int N>
void TreeNode<N>::transform_nodes_to_elements (std::unordered_map<dof_id_type, std::vector<const Elem *>> & nodes_to_elem)
{
  if (this->active())
    {
      elements.clear();
 
      // Temporarily use a set. Since multiple nodes
      // will likely map to the same element we use a
      // set to eliminate the duplication.
      std::set<const Elem *> elements_set;
 
      for (const Node * node : nodes)
        {
          // the actual global node number we are replacing
          // with the connected elements
          const dof_id_type node_number = node->id();
 
          libmesh_assert_less (node_number, mesh.n_nodes());
 
          auto & my_elems = nodes_to_elem[node_number];
          elements_set.insert(my_elems.begin(), my_elems.end());
        }
 
      // Done with the nodes.
      std::vector<const Node *>().swap(nodes);
 
      // Now the set is built.  We can copy this to the
      // vector.  Note that the resulting vector will
      // already be sorted, and will require less memory
      // than the set.
      elements.reserve(elements_set.size());
 
      for (const auto & elem : elements_set)
        {
          elements.push_back(elem);
 
#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
 
          // flag indicating this node contains
          // infinite elements
          if (elem->infinite())
            this->contains_ifems = true;
 
#endif
        }
    }
  else
    for (auto & child : children)
      child->transform_nodes_to_elements (nodes_to_elem);
}
 
 
 
template <unsigned int N>
unsigned int TreeNode<N>::n_active_bins() const
{
  if (this->active())
    return 1;
 
  else
    {
      unsigned int sum=0;
 
      for (const auto & child : children)
        sum += child->n_active_bins();
 
      return sum;
    }
}
 
 
 
template <unsigned int N>
const Elem *
TreeNode<N>::find_element (const Point & p,
                           const std::set<subdomain_id_type> * allowed_subdomains,
                           Real relative_tol) const
{
  if (this->active())
    {
      // Only check our children if the point is in our bounding box
      // or if the node contains infinite elements
      if (this->bounds_point(p, relative_tol) || this->contains_ifems)
        // Search the active elements in the active TreeNode.
        for (const auto & elem : elements)
          if (!allowed_subdomains || allowed_subdomains->count(elem->subdomain_id()))
            if (elem->active())
              {
                bool found = relative_tol > TOLERANCE
                  ? elem->close_to_point(p, relative_tol)
                  : elem->contains_point(p);
 
                if (found)
                  return elem;
              }
 
      // The point was not found in any element
      return nullptr;
    }
  else
    return this->find_element_in_children(p,allowed_subdomains,
                                          relative_tol);
}
 
 
 
template <unsigned int N>
void
TreeNode<N>::find_elements (const Point & p,
                            std::set<const Elem *> & candidate_elements,
                            const std::set<subdomain_id_type> * allowed_subdomains,
                            Real relative_tol) const
{
  if (this->active())
    {
      // Only check our children if the point is in our bounding box
      // or if the node contains infinite elements
      if (this->bounds_point(p, relative_tol) || this->contains_ifems)
        // Search the active elements in the active TreeNode.
        for (const auto & elem : elements)
          if (!allowed_subdomains || allowed_subdomains->count(elem->subdomain_id()))
            if (elem->active())
              {
                bool found = relative_tol > TOLERANCE
                  ? elem->close_to_point(p, relative_tol)
                  : elem->contains_point(p);
 
                if (found)
                  candidate_elements.insert(elem);
              }
    }
  else
    this->find_elements_in_children(p, candidate_elements,
                                    allowed_subdomains, relative_tol);
}
 
 
 
template <unsigned int N>
const Elem * TreeNode<N>::find_element_in_children (const Point & p,
                                                    const std::set<subdomain_id_type> * allowed_subdomains,
                                                    Real relative_tol) const
{
  libmesh_assert (!this->active());
 
  // value-initialization sets all array members to false
  auto searched_child = std::array<bool, N>();
 
  // First only look in the children whose bounding box
  // contain the point p.
  for (auto c : index_range(children))
    if (children[c]->bounds_point(p, relative_tol))
      {
        const Elem * e =
          children[c]->find_element(p,allowed_subdomains,
                                    relative_tol);
 
        if (e != nullptr)
          return e;
 
        // If we get here then a child that bounds the
        // point does not have any elements that contain
        // the point.  So, we will search all our children.
        // However, we have already searched child c so there
        // is no use searching her again.
        searched_child[c] = true;
      }
 
 
  // If we get here then our child whose bounding box
  // was searched and did not find any elements containing
  // the point p.  So, let's look at the other children
  // but exclude the one we have already searched.
  for (auto c : index_range(children))
    if (!searched_child[c])
      {
        const Elem * e =
          children[c]->find_element(p,allowed_subdomains,
                                    relative_tol);
 
        if (e != nullptr)
          return e;
      }
 
  // If we get here we have searched all our children.
  // Since this process was started at the root node then
  // we have searched all the elements in the tree without
  // success.  So, we should return nullptr since at this point
  // _no_ elements in the tree claim to contain point p.
  return nullptr;
}
 
 
 
template <unsigned int N>
void TreeNode<N>::find_elements_in_children (const Point & p,
                                             std::set<const Elem *> & candidate_elements,
                                             const std::set<subdomain_id_type> * allowed_subdomains,
                                             Real relative_tol) const
{
  libmesh_assert (!this->active());
 
  // First only look in the children whose bounding box
  // contain the point p.
  for (std::size_t c=0; c<children.size(); c++)
    if (children[c]->bounds_point(p, relative_tol))
      children[c]->find_elements(p, candidate_elements,
                                 allowed_subdomains, relative_tol);
}
 
 
 
// ------------------------------------------------------------
// Explicit Instantiations
template class LIBMESH_EXPORT TreeNode<2>;
template class LIBMESH_EXPORT TreeNode<4>;
template class LIBMESH_EXPORT TreeNode<8>;
 
} // namespace libMesh