// Copyright 2014 The Chromium Authors. All rights reserved. // Use of this source code is governed by a BSD-style license that can be // found in the LICENSE file. #include "ui/gfx/geometry/r_tree_base.h" #include <algorithm> #include "base/logging.h" // Helpers -------------------------------------------------------------------- namespace { // Returns a Vector2d to allow us to do arithmetic on the result such as // computing distances between centers. gfx::Vector2d CenterOfRect(const gfx::Rect& rect) { return rect.OffsetFromOrigin() + gfx::Vector2d(rect.width() / 2, rect.height() / 2); } } namespace gfx { // RTreeBase::NodeBase -------------------------------------------------------- RTreeBase::NodeBase::~NodeBase() { } void RTreeBase::NodeBase::RecomputeBoundsUpToRoot() { RecomputeLocalBounds(); if (parent_) parent_->RecomputeBoundsUpToRoot(); } RTreeBase::NodeBase::NodeBase(const Rect& rect, NodeBase* parent) : rect_(rect), parent_(parent) { } void RTreeBase::NodeBase::RecomputeLocalBounds() { } // RTreeBase::RecordBase ------------------------------------------------------ RTreeBase::RecordBase::RecordBase(const Rect& rect) : NodeBase(rect, NULL) { } RTreeBase::RecordBase::~RecordBase() { } void RTreeBase::RecordBase::AppendIntersectingRecords( const Rect& query_rect, Records* matches_out) const { if (rect().Intersects(query_rect)) matches_out->push_back(this); } void RTreeBase::RecordBase::AppendAllRecords(Records* matches_out) const { matches_out->push_back(this); } scoped_ptr<RTreeBase::NodeBase> RTreeBase::RecordBase::RemoveAndReturnLastChild() { return scoped_ptr<NodeBase>(); } int RTreeBase::RecordBase::Level() const { return -1; } // RTreeBase::Node ------------------------------------------------------------ RTreeBase::Node::Node() : NodeBase(Rect(), NULL), level_(0) { } RTreeBase::Node::~Node() { } scoped_ptr<RTreeBase::Node> RTreeBase::Node::ConstructParent() { DCHECK(!parent()); scoped_ptr<Node> new_parent(new Node(level_ + 1)); new_parent->AddChild(scoped_ptr<NodeBase>(this)); return new_parent.Pass(); } void RTreeBase::Node::AppendIntersectingRecords( const Rect& query_rect, Records* matches_out) const { // Check own bounding box for intersection, can cull all children if no // intersection. if (!rect().Intersects(query_rect)) return; // Conversely if we are completely contained within the query rect we can // confidently skip all bounds checks for ourselves and all our children. if (query_rect.Contains(rect())) { AppendAllRecords(matches_out); return; } // We intersect the query rect but we are not are not contained within it. // We must query each of our children in turn. for (Nodes::const_iterator i = children_.begin(); i != children_.end(); ++i) (*i)->AppendIntersectingRecords(query_rect, matches_out); } void RTreeBase::Node::AppendAllRecords(Records* matches_out) const { for (Nodes::const_iterator i = children_.begin(); i != children_.end(); ++i) (*i)->AppendAllRecords(matches_out); } void RTreeBase::Node::RemoveNodesForReinsert(size_t number_to_remove, Nodes* nodes) { DCHECK_LE(number_to_remove, children_.size()); std::partial_sort(children_.begin(), children_.begin() + number_to_remove, children_.end(), &RTreeBase::Node::CompareCenterDistanceFromParent); // Move the lowest-distance nodes to the returned vector. nodes->insert( nodes->end(), children_.begin(), children_.begin() + number_to_remove); children_.weak_erase(children_.begin(), children_.begin() + number_to_remove); } scoped_ptr<RTreeBase::NodeBase> RTreeBase::Node::RemoveChild( NodeBase* child_node, Nodes* orphans) { DCHECK_EQ(this, child_node->parent()); scoped_ptr<NodeBase> orphan(child_node->RemoveAndReturnLastChild()); while (orphan) { orphans->push_back(orphan.release()); orphan = child_node->RemoveAndReturnLastChild(); } Nodes::iterator i = std::find(children_.begin(), children_.end(), child_node); DCHECK(i != children_.end()); children_.weak_erase(i); return scoped_ptr<NodeBase>(child_node); } scoped_ptr<RTreeBase::NodeBase> RTreeBase::Node::RemoveAndReturnLastChild() { if (children_.empty()) return scoped_ptr<NodeBase>(); scoped_ptr<NodeBase> last_child(children_.back()); children_.weak_erase(children_.end() - 1); last_child->set_parent(NULL); return last_child.Pass(); } RTreeBase::Node* RTreeBase::Node::ChooseSubtree(NodeBase* node) { DCHECK(node); // Should never be called on a node at equal or lower level in the tree than // the node to insert. DCHECK_GT(level_, node->Level()); // If we are a parent of nodes on the provided node level, we are done. if (level_ == node->Level() + 1) return this; // Precompute a vector of expanded rects, used by both LeastOverlapIncrease // and LeastAreaEnlargement. Rects expanded_rects; expanded_rects.reserve(children_.size()); for (Nodes::iterator i = children_.begin(); i != children_.end(); ++i) expanded_rects.push_back(UnionRects(node->rect(), (*i)->rect())); Node* best_candidate = NULL; // For parents of leaf nodes, we pick the node that will cause the least // increase in overlap by the addition of this new node. This may detect a // tie, in which case it will return NULL. if (level_ == 1) best_candidate = LeastOverlapIncrease(node->rect(), expanded_rects); // For non-parents of leaf nodes, or for parents of leaf nodes with ties in // overlap increase, we choose the subtree with least area enlargement caused // by the addition of the new node. if (!best_candidate) best_candidate = LeastAreaEnlargement(node->rect(), expanded_rects); DCHECK(best_candidate); return best_candidate->ChooseSubtree(node); } size_t RTreeBase::Node::AddChild(scoped_ptr<NodeBase> node) { DCHECK(node); // Sanity-check that the level of the child being added is one less than ours. DCHECK_EQ(level_ - 1, node->Level()); node->set_parent(this); set_rect(UnionRects(rect(), node->rect())); children_.push_back(node.release()); return children_.size(); } scoped_ptr<RTreeBase::NodeBase> RTreeBase::Node::Split(size_t min_children, size_t max_children) { // We should have too many children to begin with. DCHECK_EQ(max_children + 1, children_.size()); // Determine if we should split along the horizontal or vertical axis. std::vector<NodeBase*> vertical_sort(children_.get()); std::vector<NodeBase*> horizontal_sort(children_.get()); std::sort(vertical_sort.begin(), vertical_sort.end(), &RTreeBase::Node::CompareVertical); std::sort(horizontal_sort.begin(), horizontal_sort.end(), &RTreeBase::Node::CompareHorizontal); Rects low_vertical_bounds; Rects low_horizontal_bounds; BuildLowBounds(vertical_sort, horizontal_sort, &low_vertical_bounds, &low_horizontal_bounds); Rects high_vertical_bounds; Rects high_horizontal_bounds; BuildHighBounds(vertical_sort, horizontal_sort, &high_vertical_bounds, &high_horizontal_bounds); // Choose |end_index| such that both Nodes after the split will have // min_children <= children_.size() <= max_children. size_t end_index = std::min(max_children, children_.size() - min_children); bool is_vertical_split = SmallestMarginSum(min_children, end_index, low_horizontal_bounds, high_horizontal_bounds) < SmallestMarginSum(min_children, end_index, low_vertical_bounds, high_vertical_bounds); // Choose split index along chosen axis and perform the split. const Rects& low_bounds( is_vertical_split ? low_vertical_bounds : low_horizontal_bounds); const Rects& high_bounds( is_vertical_split ? high_vertical_bounds : high_horizontal_bounds); size_t split_index = ChooseSplitIndex(min_children, end_index, low_bounds, high_bounds); const std::vector<NodeBase*>& sort( is_vertical_split ? vertical_sort : horizontal_sort); return DivideChildren(low_bounds, high_bounds, sort, split_index); } int RTreeBase::Node::Level() const { return level_; } RTreeBase::Node::Node(int level) : NodeBase(Rect(), NULL), level_(level) { } // static bool RTreeBase::Node::CompareVertical(const NodeBase* a, const NodeBase* b) { const Rect& a_rect = a->rect(); const Rect& b_rect = b->rect(); return (a_rect.y() < b_rect.y()) || ((a_rect.y() == b_rect.y()) && (a_rect.height() < b_rect.height())); } // static bool RTreeBase::Node::CompareHorizontal(const NodeBase* a, const NodeBase* b) { const Rect& a_rect = a->rect(); const Rect& b_rect = b->rect(); return (a_rect.x() < b_rect.x()) || ((a_rect.x() == b_rect.x()) && (a_rect.width() < b_rect.width())); } // static bool RTreeBase::Node::CompareCenterDistanceFromParent(const NodeBase* a, const NodeBase* b) { const NodeBase* p = a->parent(); DCHECK(p); DCHECK_EQ(p, b->parent()); Vector2d p_center = CenterOfRect(p->rect()); Vector2d a_center = CenterOfRect(a->rect()); Vector2d b_center = CenterOfRect(b->rect()); // We don't bother with square roots because we are only comparing the two // values for sorting purposes. return (a_center - p_center).LengthSquared() < (b_center - p_center).LengthSquared(); } // static void RTreeBase::Node::BuildLowBounds( const std::vector<NodeBase*>& vertical_sort, const std::vector<NodeBase*>& horizontal_sort, Rects* vertical_bounds, Rects* horizontal_bounds) { Rect vertical_bounds_rect; vertical_bounds->reserve(vertical_sort.size()); for (std::vector<NodeBase*>::const_iterator i = vertical_sort.begin(); i != vertical_sort.end(); ++i) { vertical_bounds_rect.Union((*i)->rect()); vertical_bounds->push_back(vertical_bounds_rect); } Rect horizontal_bounds_rect; horizontal_bounds->reserve(horizontal_sort.size()); for (std::vector<NodeBase*>::const_iterator i = horizontal_sort.begin(); i != horizontal_sort.end(); ++i) { horizontal_bounds_rect.Union((*i)->rect()); horizontal_bounds->push_back(horizontal_bounds_rect); } } // static void RTreeBase::Node::BuildHighBounds( const std::vector<NodeBase*>& vertical_sort, const std::vector<NodeBase*>& horizontal_sort, Rects* vertical_bounds, Rects* horizontal_bounds) { Rect vertical_bounds_rect; vertical_bounds->reserve(vertical_sort.size()); for (std::vector<NodeBase*>::const_reverse_iterator i = vertical_sort.rbegin(); i != vertical_sort.rend(); ++i) { vertical_bounds_rect.Union((*i)->rect()); vertical_bounds->push_back(vertical_bounds_rect); } std::reverse(vertical_bounds->begin(), vertical_bounds->end()); Rect horizontal_bounds_rect; horizontal_bounds->reserve(horizontal_sort.size()); for (std::vector<NodeBase*>::const_reverse_iterator i = horizontal_sort.rbegin(); i != horizontal_sort.rend(); ++i) { horizontal_bounds_rect.Union((*i)->rect()); horizontal_bounds->push_back(horizontal_bounds_rect); } std::reverse(horizontal_bounds->begin(), horizontal_bounds->end()); } size_t RTreeBase::Node::ChooseSplitIndex(size_t start_index, size_t end_index, const Rects& low_bounds, const Rects& high_bounds) { DCHECK_EQ(low_bounds.size(), high_bounds.size()); int smallest_overlap_area = UnionRects( low_bounds[start_index], high_bounds[start_index]).size().GetArea(); int smallest_combined_area = low_bounds[start_index].size().GetArea() + high_bounds[start_index].size().GetArea(); size_t optimal_split_index = start_index; for (size_t p = start_index + 1; p < end_index; ++p) { const int overlap_area = UnionRects(low_bounds[p], high_bounds[p]).size().GetArea(); const int combined_area = low_bounds[p].size().GetArea() + high_bounds[p].size().GetArea(); if ((overlap_area < smallest_overlap_area) || ((overlap_area == smallest_overlap_area) && (combined_area < smallest_combined_area))) { smallest_overlap_area = overlap_area; smallest_combined_area = combined_area; optimal_split_index = p; } } // optimal_split_index currently points at the last element in the first set, // so advance it by 1 to point at the first element in the second set. return optimal_split_index + 1; } // static int RTreeBase::Node::SmallestMarginSum(size_t start_index, size_t end_index, const Rects& low_bounds, const Rects& high_bounds) { DCHECK_EQ(low_bounds.size(), high_bounds.size()); DCHECK_LT(start_index, low_bounds.size()); DCHECK_LE(start_index, end_index); DCHECK_LE(end_index, low_bounds.size()); Rects::const_iterator i(low_bounds.begin() + start_index); Rects::const_iterator j(high_bounds.begin() + start_index); int smallest_sum = i->width() + i->height() + j->width() + j->height(); for (; i != (low_bounds.begin() + end_index); ++i, ++j) { smallest_sum = std::min( smallest_sum, i->width() + i->height() + j->width() + j->height()); } return smallest_sum; } void RTreeBase::Node::RecomputeLocalBounds() { Rect bounds; for (size_t i = 0; i < children_.size(); ++i) bounds.Union(children_[i]->rect()); set_rect(bounds); } int RTreeBase::Node::OverlapIncreaseToAdd(const Rect& rect, const NodeBase* candidate_node, const Rect& expanded_rect) const { DCHECK(candidate_node); // Early-out when |rect| is contained completely within |candidate|. if (candidate_node->rect().Contains(rect)) return 0; int total_original_overlap = 0; int total_expanded_overlap = 0; // Now calculate overlap with all other rects in this node. for (Nodes::const_iterator it = children_.begin(); it != children_.end(); ++it) { // Skip calculating overlap with the candidate rect. if ((*it) == candidate_node) continue; NodeBase* overlap_node = (*it); total_original_overlap += IntersectRects( candidate_node->rect(), overlap_node->rect()).size().GetArea(); Rect expanded_overlap_rect = expanded_rect; expanded_overlap_rect.Intersect(overlap_node->rect()); total_expanded_overlap += expanded_overlap_rect.size().GetArea(); } return total_expanded_overlap - total_original_overlap; } scoped_ptr<RTreeBase::NodeBase> RTreeBase::Node::DivideChildren( const Rects& low_bounds, const Rects& high_bounds, const std::vector<NodeBase*>& sorted_children, size_t split_index) { DCHECK_EQ(low_bounds.size(), high_bounds.size()); DCHECK_EQ(low_bounds.size(), sorted_children.size()); DCHECK_LT(split_index, low_bounds.size()); DCHECK_GT(split_index, 0U); scoped_ptr<Node> sibling(new Node(level_)); sibling->set_parent(parent()); set_rect(low_bounds[split_index - 1]); sibling->set_rect(high_bounds[split_index]); // Our own children_ vector is unsorted, so we wipe it out and divide the // sorted bounds rects between ourselves and our sibling. children_.weak_clear(); children_.insert(children_.end(), sorted_children.begin(), sorted_children.begin() + split_index); sibling->children_.insert(sibling->children_.end(), sorted_children.begin() + split_index, sorted_children.end()); for (size_t i = 0; i < sibling->children_.size(); ++i) sibling->children_[i]->set_parent(sibling.get()); return sibling.PassAs<NodeBase>(); } RTreeBase::Node* RTreeBase::Node::LeastOverlapIncrease( const Rect& node_rect, const Rects& expanded_rects) { NodeBase* best_node = children_.front(); int least_overlap_increase = OverlapIncreaseToAdd(node_rect, children_[0], expanded_rects[0]); for (size_t i = 1; i < children_.size(); ++i) { int overlap_increase = OverlapIncreaseToAdd(node_rect, children_[i], expanded_rects[i]); if (overlap_increase < least_overlap_increase) { least_overlap_increase = overlap_increase; best_node = children_[i]; } else if (overlap_increase == least_overlap_increase) { // If we are tied at zero there is no possible better overlap increase, // so we can report a tie early. if (overlap_increase == 0) return NULL; best_node = NULL; } } // Ensure that our children are always Nodes and not Records. DCHECK_GE(level_, 1); return static_cast<Node*>(best_node); } RTreeBase::Node* RTreeBase::Node::LeastAreaEnlargement( const Rect& node_rect, const Rects& expanded_rects) { DCHECK(!children_.empty()); DCHECK_EQ(children_.size(), expanded_rects.size()); NodeBase* best_node = children_.front(); int least_area_enlargement = expanded_rects[0].size().GetArea() - best_node->rect().size().GetArea(); for (size_t i = 1; i < children_.size(); ++i) { NodeBase* candidate_node = children_[i]; int area_change = expanded_rects[i].size().GetArea() - candidate_node->rect().size().GetArea(); DCHECK_GE(area_change, 0); if (area_change < least_area_enlargement) { best_node = candidate_node; least_area_enlargement = area_change; } else if (area_change == least_area_enlargement && candidate_node->rect().size().GetArea() < best_node->rect().size().GetArea()) { // Ties are broken by choosing the entry with the least area. best_node = candidate_node; } } // Ensure that our children are always Nodes and not Records. DCHECK_GE(level_, 1); return static_cast<Node*>(best_node); } // RTreeBase ------------------------------------------------------------------ RTreeBase::RTreeBase(size_t min_children, size_t max_children) : root_(new Node()), min_children_(min_children), max_children_(max_children) { DCHECK_GE(min_children_, 2U); DCHECK_LE(min_children_, max_children_ / 2U); } RTreeBase::~RTreeBase() { } void RTreeBase::InsertNode( scoped_ptr<NodeBase> node, int* highest_reinsert_level) { // Find the most appropriate parent to insert node into. Node* parent = root_->ChooseSubtree(node.get()); DCHECK(parent); // Verify ChooseSubtree returned a Node at the correct level. DCHECK_EQ(parent->Level(), node->Level() + 1); Node* insert_parent = static_cast<Node*>(parent); NodeBase* needs_bounds_recomputed = insert_parent->parent(); Nodes reinserts; // Attempt to insert the Node, if this overflows the Node we must handle it. while (insert_parent && insert_parent->AddChild(node.Pass()) > max_children_) { // If we have yet to re-insert nodes at this level during this data insert, // and we're not at the root, R*-Tree calls for re-insertion of some of the // nodes, resulting in a better balance on the tree. if (insert_parent->parent() && insert_parent->Level() > *highest_reinsert_level) { insert_parent->RemoveNodesForReinsert(max_children_ / 3, &reinserts); // Adjust highest_reinsert_level to this level. *highest_reinsert_level = insert_parent->Level(); // RemoveNodesForReinsert() does not recompute bounds, so mark it. needs_bounds_recomputed = insert_parent; break; } // Split() will create a sibling to insert_parent both of which will have // valid bounds, but this invalidates their parent's bounds. node = insert_parent->Split(min_children_, max_children_); insert_parent = static_cast<Node*>(insert_parent->parent()); needs_bounds_recomputed = insert_parent; } // If we have a Node to insert, and we hit the root of the current tree, // we create a new root which is the parent of the current root and the // insert_node. Note that we must release() the |root_| since // ConstructParent() will take ownership of it. if (!insert_parent && node) { root_ = root_.release()->ConstructParent(); root_->AddChild(node.Pass()); } // Recompute bounds along insertion path. if (needs_bounds_recomputed) needs_bounds_recomputed->RecomputeBoundsUpToRoot(); // Complete re-inserts, if any. The algorithm only allows for one invocation // of RemoveNodesForReinsert() per level of the tree in an overall call to // Insert(). while (!reinserts.empty()) { Nodes::iterator last_element = reinserts.end() - 1; NodeBase* temp_ptr(*last_element); reinserts.weak_erase(last_element); InsertNode(make_scoped_ptr(temp_ptr), highest_reinsert_level); } } scoped_ptr<RTreeBase::NodeBase> RTreeBase::RemoveNode(NodeBase* node) { // We need to remove this node from its parent. Node* parent = static_cast<Node*>(node->parent()); // Record nodes are never allowed as the root, so we should always have a // parent. DCHECK(parent); // Should always be a leaf that had the record. DCHECK_EQ(0, parent->Level()); Nodes orphans; scoped_ptr<NodeBase> removed_node(parent->RemoveChild(node, &orphans)); // It's possible that by removing |node| from |parent| we have made |parent| // have less than the minimum number of children, in which case we will need // to remove and delete |parent| while reinserting any other children that it // had. We traverse up the tree doing this until we remove a child from a // parent that still has greater than or equal to the minimum number of Nodes. while (parent->count() < min_children_) { NodeBase* child = parent; parent = static_cast<Node*>(parent->parent()); // If we've hit the root, stop. if (!parent) break; parent->RemoveChild(child, &orphans); } // If we stopped deleting nodes up the tree before encountering the root, // we'll need to fix up the bounds from the first parent we didn't delete // up to the root. if (parent) parent->RecomputeBoundsUpToRoot(); else root_->RecomputeBoundsUpToRoot(); while (!orphans.empty()) { Nodes::iterator last_element = orphans.end() - 1; NodeBase* temp_ptr(*last_element); orphans.weak_erase(last_element); int starting_level = -1; InsertNode(make_scoped_ptr(temp_ptr), &starting_level); } return removed_node.Pass(); } void RTreeBase::PruneRootIfNecessary() { if (root()->count() == 1 && root()->Level() > 0) { // Awkward reset(cast(release)) pattern here because there's no better way // to downcast the scoped_ptr from RemoveAndReturnLastChild() from NodeBase // to Node. root_.reset( static_cast<Node*>(root_->RemoveAndReturnLastChild().release())); } } void RTreeBase::ResetRoot() { root_.reset(new Node()); } } // namespace gfx