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* Copyright 2012 Google Inc.
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
#ifndef SkRTree_DEFINED
#define SkRTree_DEFINED
#include "SkRect.h"
#include "SkTDArray.h"
#include "SkChunkAlloc.h"
#include "SkBBoxHierarchy.h"
* An R-Tree implementation. In short, it is a balanced n-ary tree containing a hierarchy of
* bounding rectangles.
* Much like a B-Tree it maintains balance by enforcing minimum and maximum child counts, and
* splitting nodes when they become overfull. Unlike B-trees, however, we're using spatial data; so
* there isn't a canonical ordering to use when choosing insertion locations and splitting
* distributions. A variety of heuristics have been proposed for these problems; here, we're using
* something resembling an R*-tree, which attempts to minimize area and overlap during insertion,
* and aims to minimize a combination of margin, overlap, and area when splitting.
* One detail that is thus far unimplemented that may improve tree quality is attempting to remove
* and reinsert nodes when they become full, instead of immediately splitting (nodes that may have
* been placed well early on may hurt the tree later when more nodes have been added; removing
* and reinserting nodes generally helps reduce overlap and make a better tree). Deletion of nodes
* is also unimplemented.
* For more details see:
* Beckmann, N.; Kriegel, H. P.; Schneider, R.; Seeger, B. (1990). "The R*-tree:
* an efficient and robust access method for points and rectangles"
* It also supports bulk-loading from a batch of bounds and values; if you don't require the tree
* to be usable in its intermediate states while it is being constructed, this is significantly
* quicker than individual insertions and produces more consistent trees.
class SkRTree : public SkBBoxHierarchy {
* Create a new R-Tree with specified min/max child counts.
* The child counts are valid iff:
* - (max + 1) / 2 >= min (splitting an overfull node must be enough to populate 2 nodes)
* - min < max
* - min > 0
* - max < SK_MaxU16
* If you have some prior information about the distribution of bounds you're expecting, you
* can provide an optional aspect ratio parameter. This allows the bulk-load algorithm to create
* better proportioned tiles of rectangles.
static SkRTree* Create(int minChildren, int maxChildren, SkScalar aspectRatio = 1,
bool orderWhenBulkLoading = true);
virtual ~SkRTree();
* Insert a node, consisting of bounds and a data value into the tree, if we don't immediately
* need to use the tree; we may allow the insert to be deferred (this can allow us to bulk-load
* a large batch of nodes at once, which tends to be faster and produce a better tree).
* @param data The data value
* @param bounds The corresponding bounding box
* @param defer Can this insert be deferred? (this may be ignored)
virtual void insert(void* data, const SkIRect& bounds, bool defer = false) SK_OVERRIDE;
* If any inserts have been deferred, this will add them into the tree
virtual void flushDeferredInserts() SK_OVERRIDE;
* Given a query rectangle, populates the passed-in array with the elements it intersects
virtual void search(const SkIRect& query, SkTDArray<void*>* results) const SK_OVERRIDE;
virtual void clear() SK_OVERRIDE;
bool isEmpty() const { return 0 == fCount; }
* Gets the depth of the tree structure
virtual int getDepth() const SK_OVERRIDE {
return this->isEmpty() ? 0 : fRoot.fChild.subtree->fLevel + 1;
* This gets the insertion count (rather than the node count)
virtual int getCount() const SK_OVERRIDE { return fCount; }
virtual void rewindInserts() SK_OVERRIDE;
struct Node;
* A branch of the tree, this may contain a pointer to another interior node, or a data value
struct Branch {
union {
Node* subtree;
void* data;
} fChild;
SkIRect fBounds;
* A node in the tree, has between fMinChildren and fMaxChildren (the root is a special case)
struct Node {
uint16_t fNumChildren;
uint16_t fLevel;
bool isLeaf() { return 0 == fLevel; }
// Since we want to be able to pick min/max child counts at runtime, we assume the creator
// has allocated sufficient space directly after us in memory, and index into that space
Branch* child(size_t index) {
return reinterpret_cast<Branch*>(this + 1) + index;
typedef int32_t SkIRect::*SortSide;
// Helper for sorting our children arrays by sides of their rects
struct RectLessThan {
RectLessThan(SkRTree::SortSide side) : fSide(side) { }
bool operator()(const SkRTree::Branch lhs, const SkRTree::Branch rhs) const {
return lhs.fBounds.*fSide < rhs.fBounds.*fSide;
const SkRTree::SortSide fSide;
struct RectLessX {
bool operator()(const SkRTree::Branch lhs, const SkRTree::Branch rhs) {
return ((lhs.fBounds.fRight - lhs.fBounds.fLeft) >> 1) <
((rhs.fBounds.fRight - lhs.fBounds.fLeft) >> 1);
struct RectLessY {
bool operator()(const SkRTree::Branch lhs, const SkRTree::Branch rhs) {
return ((lhs.fBounds.fBottom - lhs.fBounds.fTop) >> 1) <
((rhs.fBounds.fBottom - lhs.fBounds.fTop) >> 1);
SkRTree(int minChildren, int maxChildren, SkScalar aspectRatio, bool orderWhenBulkLoading);
* Recursively descend the tree to find an insertion position for 'branch', updates
* bounding boxes on the way up.
Branch* insert(Node* root, Branch* branch, uint16_t level = 0);
int chooseSubtree(Node* root, Branch* branch);
SkIRect computeBounds(Node* n);
int distributeChildren(Branch* children);
void search(Node* root, const SkIRect query, SkTDArray<void*>* results) const;
* This performs a bottom-up bulk load using the STR (sort-tile-recursive) algorithm, this
* seems to generally produce better, more consistent trees at significantly lower cost than
* repeated insertions.
* This consumes the input array.
* TODO: Experiment with other bulk-load algorithms (in particular the Hilbert pack variant,
* which groups rects by position on the Hilbert curve, is probably worth a look). There also
* exist top-down bulk load variants (VAMSplit, TopDownGreedy, etc).
Branch bulkLoad(SkTDArray<Branch>* branches, int level = 0);
void validate() const;
int validateSubtree(Node* root, SkIRect bounds, bool isRoot = false) const;
const int fMinChildren;
const int fMaxChildren;
const size_t fNodeSize;
// This is the count of data elements (rather than total nodes in the tree)
int fCount;
Branch fRoot;
SkChunkAlloc fNodes;
SkTDArray<Branch> fDeferredInserts;
SkScalar fAspectRatio;
bool fSortWhenBulkLoading;
Node* allocateNode(uint16_t level);
typedef SkBBoxHierarchy INHERITED;