hierarchy_tree_array-inl.h

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#ifndef COAL_HIERARCHY_TREE_ARRAY_INL_H
#define COAL_HIERARCHY_TREE_ARRAY_INL_H
 
#include "coal/broadphase/detail/hierarchy_tree_array.h"
 
#include <algorithm>
#include <iostream>
 
namespace coal {
 
namespace detail {
 
namespace implementation_array {
 
//==============================================================================
template <typename BV>
HierarchyTree<BV>::HierarchyTree(int bu_threshold_, int topdown_level_) {
  root_node = NULL_NODE;
  n_nodes = 0;
  n_nodes_alloc = 16;
  nodes = new Node[n_nodes_alloc];
  for (size_t i = 0; i < n_nodes_alloc - 1; ++i) nodes[i].next = i + 1;
  nodes[n_nodes_alloc - 1].next = NULL_NODE;
  n_leaves = 0;
  freelist = 0;
  opath = 0;
  max_lookahead_level = -1;
  bu_threshold = bu_threshold_;
  topdown_level = topdown_level_;
}
 
//==============================================================================
template <typename BV>
HierarchyTree<BV>::~HierarchyTree() {
  delete[] nodes;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::init(Node* leaves, int n_leaves_, int level) {
  switch (level) {
    case 0:
      init_0(leaves, n_leaves_);
      break;
    case 1:
      init_1(leaves, n_leaves_);
      break;
    case 2:
      init_2(leaves, n_leaves_);
      break;
    case 3:
      init_3(leaves, n_leaves_);
      break;
    default:
      init_0(leaves, n_leaves_);
  }
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::init_0(Node* leaves, int n_leaves_) {
  clear();
 
  n_leaves = (size_t)n_leaves_;
  root_node = NULL_NODE;
  nodes = new Node[n_leaves * 2];
  std::copy(leaves, leaves + n_leaves, nodes);
  freelist = n_leaves;
  n_nodes = n_leaves;
  n_nodes_alloc = 2 * n_leaves;
  for (size_t i = n_leaves; i < n_nodes_alloc; ++i) nodes[i].next = i + 1;
  nodes[n_nodes_alloc - 1].next = NULL_NODE;
 
  size_t* ids = new size_t[n_leaves];
  for (size_t i = 0; i < n_leaves; ++i) ids[i] = i;
 
  root_node = topdown(ids, ids + n_leaves);
  delete[] ids;
 
  opath = 0;
  max_lookahead_level = -1;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::init_1(Node* leaves, int n_leaves_) {
  clear();
 
  n_leaves = (size_t)n_leaves_;
  root_node = NULL_NODE;
  nodes = new Node[n_leaves * 2];
  std::copy(leaves, leaves + n_leaves, nodes);
  freelist = n_leaves;
  n_nodes = n_leaves;
  n_nodes_alloc = 2 * n_leaves;
  for (size_t i = n_leaves; i < n_nodes_alloc; ++i) nodes[i].next = i + 1;
  nodes[n_nodes_alloc - 1].next = NULL_NODE;
 
  BV bound_bv;
  if (n_leaves > 0) bound_bv = nodes[0].bv;
  for (size_t i = 1; i < n_leaves; ++i) bound_bv += nodes[i].bv;
 
  morton_functor<Scalar, uint32_t> coder(bound_bv);
  for (size_t i = 0; i < n_leaves; ++i)
    nodes[i].code = coder(nodes[i].bv.center());
 
  size_t* ids = new size_t[n_leaves];
  for (size_t i = 0; i < n_leaves; ++i) ids[i] = i;
 
  const SortByMorton comp{nodes};
  std::sort(ids, ids + n_leaves, comp);
  root_node = mortonRecurse_0(ids, ids + n_leaves, (1 << (coder.bits() - 1)),
                              coder.bits() - 1);
  delete[] ids;
 
  refit();
 
  opath = 0;
  max_lookahead_level = -1;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::init_2(Node* leaves, int n_leaves_) {
  clear();
 
  n_leaves = (size_t)n_leaves_;
  root_node = NULL_NODE;
  nodes = new Node[n_leaves * 2];
  std::copy(leaves, leaves + n_leaves, nodes);
  freelist = n_leaves;
  n_nodes = n_leaves;
  n_nodes_alloc = 2 * n_leaves;
  for (size_t i = n_leaves; i < n_nodes_alloc; ++i) nodes[i].next = i + 1;
  nodes[n_nodes_alloc - 1].next = NULL_NODE;
 
  BV bound_bv;
  if (n_leaves > 0) bound_bv = nodes[0].bv;
  for (size_t i = 1; i < n_leaves; ++i) bound_bv += nodes[i].bv;
 
  morton_functor<Scalar, uint32_t> coder(bound_bv);
  for (size_t i = 0; i < n_leaves; ++i)
    nodes[i].code = coder(nodes[i].bv.center());
 
  size_t* ids = new size_t[n_leaves];
  for (size_t i = 0; i < n_leaves; ++i) ids[i] = i;
 
  const SortByMorton comp{nodes};
  std::sort(ids, ids + n_leaves, comp);
  root_node = mortonRecurse_1(ids, ids + n_leaves, (1 << (coder.bits() - 1)),
                              coder.bits() - 1);
  delete[] ids;
 
  refit();
 
  opath = 0;
  max_lookahead_level = -1;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::init_3(Node* leaves, int n_leaves_) {
  clear();
 
  n_leaves = (size_t)n_leaves_;
  root_node = NULL_NODE;
  nodes = new Node[n_leaves * 2];
  std::copy(leaves, leaves + n_leaves, nodes);
  freelist = n_leaves;
  n_nodes = n_leaves;
  n_nodes_alloc = 2 * n_leaves;
  for (size_t i = n_leaves; i < n_nodes_alloc; ++i) nodes[i].next = i + 1;
  nodes[n_nodes_alloc - 1].next = NULL_NODE;
 
  BV bound_bv;
  if (n_leaves > 0) bound_bv = nodes[0].bv;
  for (size_t i = 1; i < n_leaves; ++i) bound_bv += nodes[i].bv;
 
  morton_functor<Scalar, uint32_t> coder(bound_bv);
  for (size_t i = 0; i < n_leaves; ++i)
    nodes[i].code = coder(nodes[i].bv.center());
 
  size_t* ids = new size_t[n_leaves];
  for (size_t i = 0; i < n_leaves; ++i) ids[i] = i;
 
  const SortByMorton comp{nodes};
  std::sort(ids, ids + n_leaves, comp);
  root_node = mortonRecurse_2(ids, ids + n_leaves);
  delete[] ids;
 
  refit();
 
  opath = 0;
  max_lookahead_level = -1;
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::insert(const BV& bv, void* data) {
  size_t node = createNode(NULL_NODE, bv, data);
  insertLeaf(root_node, node);
  ++n_leaves;
  return node;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::remove(size_t leaf) {
  removeLeaf(leaf);
  deleteNode(leaf);
  --n_leaves;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::clear() {
  delete[] nodes;
  root_node = NULL_NODE;
  n_nodes = 0;
  n_nodes_alloc = 16;
  nodes = new Node[n_nodes_alloc];
  for (size_t i = 0; i < n_nodes_alloc; ++i) nodes[i].next = i + 1;
  nodes[n_nodes_alloc - 1].next = NULL_NODE;
  n_leaves = 0;
  freelist = 0;
  opath = 0;
  max_lookahead_level = -1;
}
 
//==============================================================================
template <typename BV>
bool HierarchyTree<BV>::empty() const {
  return (n_nodes == 0);
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::update(size_t leaf, int lookahead_level) {
  size_t root = removeLeaf(leaf);
  if (root != NULL_NODE) {
    if (lookahead_level > 0) {
      for (int i = 0;
           (i < lookahead_level) && (nodes[root].parent != NULL_NODE); ++i)
        root = nodes[root].parent;
    } else
      root = root_node;
  }
  insertLeaf(root, leaf);
}
 
//==============================================================================
template <typename BV>
bool HierarchyTree<BV>::update(size_t leaf, const BV& bv) {
  if (nodes[leaf].bv.contain(bv)) return false;
  update_(leaf, bv);
  return true;
}
 
//==============================================================================
template <typename BV>
bool HierarchyTree<BV>::update(size_t leaf, const BV& bv, const Vec3s& vel,
                               Scalar margin) {
  COAL_UNUSED_VARIABLE(bv);
  COAL_UNUSED_VARIABLE(vel);
  COAL_UNUSED_VARIABLE(margin);
 
  if (nodes[leaf].bv.contain(bv)) return false;
  update_(leaf, bv);
  return true;
}
 
//==============================================================================
template <typename BV>
bool HierarchyTree<BV>::update(size_t leaf, const BV& bv, const Vec3s& vel) {
  COAL_UNUSED_VARIABLE(vel);
 
  if (nodes[leaf].bv.contain(bv)) return false;
  update_(leaf, bv);
  return true;
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::getMaxHeight() const {
  if (root_node == NULL_NODE) return 0;
 
  return getMaxHeight(root_node);
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::getMaxDepth() const {
  if (root_node == NULL_NODE) return 0;
 
  size_t max_depth;
  getMaxDepth(root_node, 0, max_depth);
  return max_depth;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::balanceBottomup() {
  if (root_node != NULL_NODE) {
    Node* leaves = new Node[n_leaves];
    Node* leaves_ = leaves;
    extractLeaves(root_node, leaves_);
    root_node = NULL_NODE;
    std::copy(leaves, leaves + n_leaves, nodes);
    freelist = n_leaves;
    n_nodes = n_leaves;
    for (size_t i = n_leaves; i < n_nodes_alloc; ++i) nodes[i].next = i + 1;
    nodes[n_nodes_alloc - 1].next = NULL_NODE;
 
    size_t* ids = new size_t[n_leaves];
    for (size_t i = 0; i < n_leaves; ++i) ids[i] = i;
 
    bottomup(ids, ids + n_leaves);
    root_node = *ids;
 
    delete[] ids;
  }
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::balanceTopdown() {
  if (root_node != NULL_NODE) {
    Node* leaves = new Node[n_leaves];
    Node* leaves_ = leaves;
    extractLeaves(root_node, leaves_);
    root_node = NULL_NODE;
    std::copy(leaves, leaves + n_leaves, nodes);
    freelist = n_leaves;
    n_nodes = n_leaves;
    for (size_t i = n_leaves; i < n_nodes_alloc; ++i) nodes[i].next = i + 1;
    nodes[n_nodes_alloc - 1].next = NULL_NODE;
 
    size_t* ids = new size_t[n_leaves];
    for (size_t i = 0; i < n_leaves; ++i) ids[i] = i;
 
    root_node = topdown(ids, ids + n_leaves);
    delete[] ids;
  }
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::balanceIncremental(int iterations) {
  if (iterations < 0) iterations = (int)n_leaves;
  if ((root_node != NULL_NODE) && (iterations > 0)) {
    for (int i = 0; i < iterations; ++i) {
      size_t node = root_node;
      unsigned int bit = 0;
      while (!nodes[node].isLeaf()) {
        node = nodes[node].children[(opath >> bit) & 1];
        bit = (bit + 1) & (sizeof(unsigned int) * 8 - 1);
      }
      update(node);
      ++opath;
    }
  }
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::refit() {
  if (root_node != NULL_NODE) recurseRefit(root_node);
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::extractLeaves(size_t root, Node*& leaves) const {
  if (!nodes[root].isLeaf()) {
    extractLeaves(nodes[root].children[0], leaves);
    extractLeaves(nodes[root].children[1], leaves);
  } else {
    *leaves = nodes[root];
    leaves++;
  }
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::size() const {
  return n_leaves;
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::getRoot() const {
  return root_node;
}
 
//==============================================================================
template <typename BV>
typename HierarchyTree<BV>::Node* HierarchyTree<BV>::getNodes() const {
  return nodes;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::print(size_t root, int depth) {
  for (int i = 0; i < depth; ++i) std::cout << " ";
  Node* n = nodes + root;
  std::cout << " (" << n->bv.min_[0] << ", " << n->bv.min_[1] << ", "
            << n->bv.min_[2] << "; " << n->bv.max_[0] << ", " << n->bv.max_[1]
            << ", " << n->bv.max_[2] << ")" << std::endl;
  if (n->isLeaf()) {
  } else {
    print(n->children[0], depth + 1);
    print(n->children[1], depth + 1);
  }
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::getMaxHeight(size_t node) const {
  if (!nodes[node].isLeaf()) {
    size_t height1 = getMaxHeight(nodes[node].children[0]);
    size_t height2 = getMaxHeight(nodes[node].children[1]);
    return std::max(height1, height2) + 1;
  } else
    return 0;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::getMaxDepth(size_t node, size_t depth,
                                    size_t& max_depth) const {
  if (!nodes[node].isLeaf()) {
    getMaxDepth(nodes[node].children[0], depth + 1, max_depth);
    getmaxDepth(nodes[node].children[1], depth + 1, max_depth);
  } else
    max_depth = std::max(max_depth, depth);
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::bottomup(size_t* lbeg, size_t* lend) {
  size_t* lcur_end = lend;
  while (lbeg < lcur_end - 1) {
    size_t *min_it1 = nullptr, *min_it2 = nullptr;
    Scalar min_size = (std::numeric_limits<Scalar>::max)();
    for (size_t* it1 = lbeg; it1 < lcur_end; ++it1) {
      for (size_t* it2 = it1 + 1; it2 < lcur_end; ++it2) {
        Scalar cur_size = (nodes[*it1].bv + nodes[*it2].bv).size();
        if (cur_size < min_size) {
          min_size = cur_size;
          min_it1 = it1;
          min_it2 = it2;
        }
      }
    }
 
    size_t p =
        createNode(NULL_NODE, nodes[*min_it1].bv, nodes[*min_it2].bv, nullptr);
    nodes[p].children[0] = *min_it1;
    nodes[p].children[1] = *min_it2;
    nodes[*min_it1].parent = p;
    nodes[*min_it2].parent = p;
    *min_it1 = p;
    size_t tmp = *min_it2;
    lcur_end--;
    *min_it2 = *lcur_end;
    *lcur_end = tmp;
  }
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::topdown(size_t* lbeg, size_t* lend) {
  switch (topdown_level) {
    case 0:
      return topdown_0(lbeg, lend);
      break;
    case 1:
      return topdown_1(lbeg, lend);
      break;
    default:
      return topdown_0(lbeg, lend);
  }
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::topdown_0(size_t* lbeg, size_t* lend) {
  long num_leaves = lend - lbeg;
  if (num_leaves > 1) {
    if (num_leaves > bu_threshold) {
      BV vol = nodes[*lbeg].bv;
      for (size_t* i = lbeg + 1; i < lend; ++i) vol += nodes[*i].bv;
 
      size_t best_axis = 0;
      Scalar extent[3] = {vol.width(), vol.height(), vol.depth()};
      if (extent[1] > extent[0]) best_axis = 1;
      if (extent[2] > extent[best_axis]) best_axis = 2;
 
      nodeBaseLess<BV> comp(nodes, best_axis);
      size_t* lcenter = lbeg + num_leaves / 2;
      std::nth_element(lbeg, lcenter, lend, comp);
 
      size_t node = createNode(NULL_NODE, vol, nullptr);
      nodes[node].children[0] = topdown_0(lbeg, lcenter);
      nodes[node].children[1] = topdown_0(lcenter, lend);
      nodes[nodes[node].children[0]].parent = node;
      nodes[nodes[node].children[1]].parent = node;
      return node;
    } else {
      bottomup(lbeg, lend);
      return *lbeg;
    }
  }
  return *lbeg;
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::topdown_1(size_t* lbeg, size_t* lend) {
  long num_leaves = lend - lbeg;
  if (num_leaves > 1) {
    if (num_leaves > bu_threshold) {
      Vec3s split_p = nodes[*lbeg].bv.center();
      BV vol = nodes[*lbeg].bv;
      for (size_t* i = lbeg + 1; i < lend; ++i) {
        split_p += nodes[*i].bv.center();
        vol += nodes[*i].bv;
      }
      split_p /= static_cast<Scalar>(num_leaves);
      int best_axis = -1;
      int bestmidp = (int)num_leaves;
      int splitcount[3][2] = {{0, 0}, {0, 0}, {0, 0}};
      for (size_t* i = lbeg; i < lend; ++i) {
        Vec3s x = nodes[*i].bv.center() - split_p;
        for (int j = 0; j < 3; ++j) ++splitcount[j][x[j] > 0 ? 1 : 0];
      }
 
      for (size_t i = 0; i < 3; ++i) {
        if ((splitcount[i][0] > 0) && (splitcount[i][1] > 0)) {
          int midp = std::abs(splitcount[i][0] - splitcount[i][1]);
          if (midp < bestmidp) {
            best_axis = (int)i;
            bestmidp = midp;
          }
        }
      }
 
      if (best_axis < 0) best_axis = 0;
 
      Scalar split_value = split_p[best_axis];
      size_t* lcenter = lbeg;
      for (size_t* i = lbeg; i < lend; ++i) {
        if (nodes[*i].bv.center()[best_axis] < split_value) {
          size_t temp = *i;
          *i = *lcenter;
          *lcenter = temp;
          ++lcenter;
        }
      }
 
      size_t node = createNode(NULL_NODE, vol, nullptr);
      nodes[node].children[0] = topdown_1(lbeg, lcenter);
      nodes[node].children[1] = topdown_1(lcenter, lend);
      nodes[nodes[node].children[0]].parent = node;
      nodes[nodes[node].children[1]].parent = node;
      return node;
    } else {
      bottomup(lbeg, lend);
      return *lbeg;
    }
  }
  return *lbeg;
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::mortonRecurse_0(size_t* lbeg, size_t* lend,
                                          const uint32_t& split, int bits) {
  long num_leaves = lend - lbeg;
  if (num_leaves > 1) {
    if (bits > 0) {
      const SortByMorton comp{nodes, split};
      size_t* lcenter = std::lower_bound(lbeg, lend, NULL_NODE, comp);
 
      if (lcenter == lbeg) {
        uint32_t split2 = split | (1 << (bits - 1));
        return mortonRecurse_0(lbeg, lend, split2, bits - 1);
      } else if (lcenter == lend) {
        uint32_t split1 = (split & (~(1 << bits))) | (1 << (bits - 1));
        return mortonRecurse_0(lbeg, lend, split1, bits - 1);
      } else {
        uint32_t split1 = (split & (~(1 << bits))) | (1 << (bits - 1));
        uint32_t split2 = split | (1 << (bits - 1));
 
        size_t child1 = mortonRecurse_0(lbeg, lcenter, split1, bits - 1);
        size_t child2 = mortonRecurse_0(lcenter, lend, split2, bits - 1);
        size_t node = createNode(NULL_NODE, nullptr);
        nodes[node].children[0] = child1;
        nodes[node].children[1] = child2;
        nodes[child1].parent = node;
        nodes[child2].parent = node;
        return node;
      }
    } else {
      size_t node = topdown(lbeg, lend);
      return node;
    }
  } else
    return *lbeg;
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::mortonRecurse_1(size_t* lbeg, size_t* lend,
                                          const uint32_t& split, int bits) {
  long num_leaves = lend - lbeg;
  if (num_leaves > 1) {
    if (bits > 0) {
      const SortByMorton comp{nodes, split};
      size_t* lcenter = std::lower_bound(lbeg, lend, NULL_NODE, comp);
 
      if (lcenter == lbeg) {
        uint32_t split2 = split | (1 << (bits - 1));
        return mortonRecurse_1(lbeg, lend, split2, bits - 1);
      } else if (lcenter == lend) {
        uint32_t split1 = (split & (~(1 << bits))) | (1 << (bits - 1));
        return mortonRecurse_1(lbeg, lend, split1, bits - 1);
      } else {
        uint32_t split1 = (split & (~(1 << bits))) | (1 << (bits - 1));
        uint32_t split2 = split | (1 << (bits - 1));
 
        size_t child1 = mortonRecurse_1(lbeg, lcenter, split1, bits - 1);
        size_t child2 = mortonRecurse_1(lcenter, lend, split2, bits - 1);
        size_t node = createNode(NULL_NODE, nullptr);
        nodes[node].children[0] = child1;
        nodes[node].children[1] = child2;
        nodes[child1].parent = node;
        nodes[child2].parent = node;
        return node;
      }
    } else {
      size_t child1 = mortonRecurse_1(lbeg, lbeg + num_leaves / 2, 0, bits - 1);
      size_t child2 = mortonRecurse_1(lbeg + num_leaves / 2, lend, 0, bits - 1);
      size_t node = createNode(NULL_NODE, nullptr);
      nodes[node].children[0] = child1;
      nodes[node].children[1] = child2;
      nodes[child1].parent = node;
      nodes[child2].parent = node;
      return node;
    }
  } else
    return *lbeg;
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::mortonRecurse_2(size_t* lbeg, size_t* lend) {
  long num_leaves = lend - lbeg;
  if (num_leaves > 1) {
    size_t child1 = mortonRecurse_2(lbeg, lbeg + num_leaves / 2);
    size_t child2 = mortonRecurse_2(lbeg + num_leaves / 2, lend);
    size_t node = createNode(NULL_NODE, nullptr);
    nodes[node].children[0] = child1;
    nodes[node].children[1] = child2;
    nodes[child1].parent = node;
    nodes[child2].parent = node;
    return node;
  } else
    return *lbeg;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::insertLeaf(size_t root, size_t leaf) {
  if (root_node == NULL_NODE) {
    root_node = leaf;
    nodes[leaf].parent = NULL_NODE;
  } else {
    if (!nodes[root].isLeaf()) {
      do {
        root = nodes[root].children[select(leaf, nodes[root].children[0],
                                           nodes[root].children[1], nodes)];
      } while (!nodes[root].isLeaf());
    }
 
    size_t prev = nodes[root].parent;
    size_t node = createNode(prev, nodes[leaf].bv, nodes[root].bv, nullptr);
    if (prev != NULL_NODE) {
      nodes[prev].children[indexOf(root)] = node;
      nodes[node].children[0] = root;
      nodes[root].parent = node;
      nodes[node].children[1] = leaf;
      nodes[leaf].parent = node;
      do {
        if (!nodes[prev].bv.contain(nodes[node].bv))
          nodes[prev].bv = nodes[nodes[prev].children[0]].bv +
                           nodes[nodes[prev].children[1]].bv;
        else
          break;
        node = prev;
      } while (NULL_NODE != (prev = nodes[node].parent));
    } else {
      nodes[node].children[0] = root;
      nodes[root].parent = node;
      nodes[node].children[1] = leaf;
      nodes[leaf].parent = node;
      root_node = node;
    }
  }
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::removeLeaf(size_t leaf) {
  if (leaf == root_node) {
    root_node = NULL_NODE;
    return NULL_NODE;
  } else {
    size_t parent = nodes[leaf].parent;
    size_t prev = nodes[parent].parent;
    size_t sibling = nodes[parent].children[1 - indexOf(leaf)];
 
    if (prev != NULL_NODE) {
      nodes[prev].children[indexOf(parent)] = sibling;
      nodes[sibling].parent = prev;
      deleteNode(parent);
      while (prev != NULL_NODE) {
        BV new_bv = nodes[nodes[prev].children[0]].bv +
                    nodes[nodes[prev].children[1]].bv;
        if (!(new_bv == nodes[prev].bv)) {
          nodes[prev].bv = new_bv;
          prev = nodes[prev].parent;
        } else
          break;
      }
 
      return (prev != NULL_NODE) ? prev : root_node;
    } else {
      root_node = sibling;
      nodes[sibling].parent = NULL_NODE;
      deleteNode(parent);
      return root_node;
    }
  }
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::update_(size_t leaf, const BV& bv) {
  size_t root = removeLeaf(leaf);
  if (root != NULL_NODE) {
    if (max_lookahead_level >= 0) {
      for (int i = 0;
           (i < max_lookahead_level) && (nodes[root].parent != NULL_NODE); ++i)
        root = nodes[root].parent;
    }
 
    nodes[leaf].bv = bv;
    insertLeaf(root, leaf);
  }
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::indexOf(size_t node) {
  return (nodes[nodes[node].parent].children[1] == node);
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::allocateNode() {
  if (freelist == NULL_NODE) {
    Node* old_nodes = nodes;
    n_nodes_alloc *= 2;
    nodes = new Node[n_nodes_alloc];
    std::copy(old_nodes, old_nodes + n_nodes, nodes);
    delete[] old_nodes;
 
    for (size_t i = n_nodes; i < n_nodes_alloc - 1; ++i) nodes[i].next = i + 1;
    nodes[n_nodes_alloc - 1].next = NULL_NODE;
    freelist = n_nodes;
  }
 
  size_t node_id = freelist;
  freelist = nodes[node_id].next;
  nodes[node_id].parent = NULL_NODE;
  nodes[node_id].children[0] = NULL_NODE;
  nodes[node_id].children[1] = NULL_NODE;
  ++n_nodes;
  return node_id;
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::createNode(size_t parent, const BV& bv1,
                                     const BV& bv2, void* data) {
  size_t node = allocateNode();
  nodes[node].parent = parent;
  nodes[node].data = data;
  nodes[node].bv = bv1 + bv2;
  return node;
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::createNode(size_t parent, const BV& bv, void* data) {
  size_t node = allocateNode();
  nodes[node].parent = parent;
  nodes[node].data = data;
  nodes[node].bv = bv;
  return node;
}
 
//==============================================================================
template <typename BV>
size_t HierarchyTree<BV>::createNode(size_t parent, void* data) {
  size_t node = allocateNode();
  nodes[node].parent = parent;
  nodes[node].data = data;
  return node;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::deleteNode(size_t node) {
  nodes[node].next = freelist;
  freelist = node;
  --n_nodes;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::recurseRefit(size_t node) {
  if (!nodes[node].isLeaf()) {
    recurseRefit(nodes[node].children[0]);
    recurseRefit(nodes[node].children[1]);
    nodes[node].bv =
        nodes[nodes[node].children[0]].bv + nodes[nodes[node].children[1]].bv;
  } else
    return;
}
 
//==============================================================================
template <typename BV>
void HierarchyTree<BV>::fetchLeaves(size_t root, Node*& leaves, int depth) {
  if ((!nodes[root].isLeaf()) && depth) {
    fetchLeaves(nodes[root].children[0], leaves, depth - 1);
    fetchLeaves(nodes[root].children[1], leaves, depth - 1);
    deleteNode(root);
  } else {
    *leaves = nodes[root];
    leaves++;
  }
}
 
//==============================================================================
template <typename BV>
nodeBaseLess<BV>::nodeBaseLess(const NodeBase<BV>* nodes_, size_t d_)
    : nodes(nodes_), d(d_) {
  // Do nothing
}
 
//==============================================================================
template <typename BV>
bool nodeBaseLess<BV>::operator()(size_t i, size_t j) const {
  if (nodes[i].bv.center()[(int)d] < nodes[j].bv.center()[(int)d]) return true;
 
  return false;
}
 
//==============================================================================
template <typename S, typename BV>
struct SelectImpl {
  static bool run(size_t query, size_t node1, size_t node2,
                  NodeBase<BV>* nodes) {
    COAL_UNUSED_VARIABLE(query);
    COAL_UNUSED_VARIABLE(node1);
    COAL_UNUSED_VARIABLE(node2);
    COAL_UNUSED_VARIABLE(nodes);
 
    return 0;
  }
 
  static bool run(const BV& query, size_t node1, size_t node2,
                  NodeBase<BV>* nodes) {
    COAL_UNUSED_VARIABLE(query);
    COAL_UNUSED_VARIABLE(node1);
    COAL_UNUSED_VARIABLE(node2);
    COAL_UNUSED_VARIABLE(nodes);
 
    return 0;
  }
};
 
//==============================================================================
template <typename BV>
size_t select(size_t query, size_t node1, size_t node2, NodeBase<BV>* nodes) {
  return SelectImpl<Scalar, BV>::run(query, node1, node2, nodes);
}
 
//==============================================================================
template <typename BV>
size_t select(const BV& query, size_t node1, size_t node2,
              NodeBase<BV>* nodes) {
  return SelectImpl<Scalar, BV>::run(query, node1, node2, nodes);
}
 
//==============================================================================
template <typename S>
struct SelectImpl<S, AABB> {
  static bool run(size_t query, size_t node1, size_t node2,
                  NodeBase<AABB>* nodes) {
    const AABB& bv = nodes[query].bv;
    const AABB& bv1 = nodes[node1].bv;
    const AABB& bv2 = nodes[node2].bv;
    Vec3s v = bv.min_ + bv.max_;
    Vec3s v1 = v - (bv1.min_ + bv1.max_);
    Vec3s v2 = v - (bv2.min_ + bv2.max_);
    Scalar d1 = fabs(v1[0]) + fabs(v1[1]) + fabs(v1[2]);
    Scalar d2 = fabs(v2[0]) + fabs(v2[1]) + fabs(v2[2]);
    return (d1 < d2) ? 0 : 1;
  }
 
  static bool run(const AABB& query, size_t node1, size_t node2,
                  NodeBase<AABB>* nodes) {
    const AABB& bv = query;
    const AABB& bv1 = nodes[node1].bv;
    const AABB& bv2 = nodes[node2].bv;
    Vec3s v = bv.min_ + bv.max_;
    Vec3s v1 = v - (bv1.min_ + bv1.max_);
    Vec3s v2 = v - (bv2.min_ + bv2.max_);
    Scalar d1 = fabs(v1[0]) + fabs(v1[1]) + fabs(v1[2]);
    Scalar d2 = fabs(v2[0]) + fabs(v2[1]) + fabs(v2[2]);
    return (d1 < d2) ? 0 : 1;
  }
};
 
}  // namespace implementation_array
}  // namespace detail
}  // namespace coal
 
#endif