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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.
*/
#include "SkRTree.h"
#include "SkTSort.h"
static inline uint32_t get_area(const SkIRect& rect);
static inline uint32_t get_overlap(const SkIRect& rect1, const SkIRect& rect2);
static inline uint32_t get_margin(const SkIRect& rect);
static inline uint32_t get_overlap_increase(const SkIRect& rect1, const SkIRect& rect2,
SkIRect expandBy);
static inline uint32_t get_area_increase(const SkIRect& rect1, SkIRect rect2);
static inline void join_no_empty_check(const SkIRect& joinWith, SkIRect* out);
///////////////////////////////////////////////////////////////////////////////////////////////////
SK_DEFINE_INST_COUNT(SkRTree)
SkRTree* SkRTree::Create(int minChildren, int maxChildren, SkScalar aspectRatio) {
if (minChildren < maxChildren && (maxChildren + 1) / 2 >= minChildren &&
minChildren > 0 && maxChildren < static_cast<int>(SK_MaxU16)) {
return new SkRTree(minChildren, maxChildren, aspectRatio);
}
return NULL;
}
SkRTree::SkRTree(int minChildren, int maxChildren, SkScalar aspectRatio)
: fMinChildren(minChildren)
, fMaxChildren(maxChildren)
, fNodeSize(sizeof(Node) + sizeof(Branch) * maxChildren)
, fCount(0)
, fNodes(fNodeSize * 256)
, fAspectRatio(aspectRatio) {
SkASSERT(minChildren < maxChildren && minChildren > 0 && maxChildren <
static_cast<int>(SK_MaxU16));
SkASSERT((maxChildren + 1) / 2 >= minChildren);
this->validate();
}
SkRTree::~SkRTree() {
this->clear();
}
void SkRTree::insert(void* data, const SkIRect& bounds, bool defer) {
this->validate();
if (bounds.isEmpty()) {
SkASSERT(false);
return;
}
Branch newBranch;
newBranch.fBounds = bounds;
newBranch.fChild.data = data;
if (this->isEmpty()) {
// since a bulk-load into an existing tree is as of yet unimplemented (and arguably not
// of vital importance right now), we only batch up inserts if the tree is empty.
if (defer) {
fDeferredInserts.push(newBranch);
return;
} else {
fRoot.fChild.subtree = allocateNode(0);
fRoot.fChild.subtree->fNumChildren = 0;
}
}
Branch* newSibling = insert(fRoot.fChild.subtree, &newBranch);
fRoot.fBounds = this->computeBounds(fRoot.fChild.subtree);
if (NULL != newSibling) {
Node* oldRoot = fRoot.fChild.subtree;
Node* newRoot = this->allocateNode(oldRoot->fLevel + 1);
newRoot->fNumChildren = 2;
*newRoot->child(0) = fRoot;
*newRoot->child(1) = *newSibling;
fRoot.fChild.subtree = newRoot;
fRoot.fBounds = this->computeBounds(fRoot.fChild.subtree);
}
++fCount;
this->validate();
}
void SkRTree::flushDeferredInserts() {
this->validate();
if (this->isEmpty() && fDeferredInserts.count() > 0) {
fCount = fDeferredInserts.count();
if (1 == fCount) {
fRoot.fChild.subtree = allocateNode(0);
fRoot.fChild.subtree->fNumChildren = 0;
this->insert(fRoot.fChild.subtree, &fDeferredInserts[0]);
fRoot.fBounds = fDeferredInserts[0].fBounds;
} else {
fRoot = this->bulkLoad(&fDeferredInserts);
}
} else {
// TODO: some algorithm for bulk loading into an already populated tree
SkASSERT(0 == fDeferredInserts.count());
}
fDeferredInserts.rewind();
this->validate();
}
void SkRTree::search(const SkIRect& query, SkTDArray<void*>* results) {
this->validate();
if (0 != fDeferredInserts.count()) {
this->flushDeferredInserts();
}
if (!this->isEmpty() && SkIRect::IntersectsNoEmptyCheck(fRoot.fBounds, query)) {
this->search(fRoot.fChild.subtree, query, results);
}
this->validate();
}
void SkRTree::clear() {
this->validate();
fNodes.reset();
fDeferredInserts.rewind();
fCount = 0;
this->validate();
}
SkRTree::Node* SkRTree::allocateNode(uint16_t level) {
Node* out = static_cast<Node*>(fNodes.allocThrow(fNodeSize));
out->fNumChildren = 0;
out->fLevel = level;
return out;
}
SkRTree::Branch* SkRTree::insert(Node* root, Branch* branch, uint16_t level) {
Branch* toInsert = branch;
if (root->fLevel != level) {
int childIndex = this->chooseSubtree(root, branch);
toInsert = this->insert(root->child(childIndex)->fChild.subtree, branch, level);
root->child(childIndex)->fBounds = this->computeBounds(
root->child(childIndex)->fChild.subtree);
}
if (NULL != toInsert) {
if (root->fNumChildren == fMaxChildren) {
// handle overflow by splitting. TODO: opportunistic reinsertion
// decide on a distribution to divide with
Node* newSibling = this->allocateNode(root->fLevel);
Branch* toDivide = SkNEW_ARRAY(Branch, fMaxChildren + 1);
for (int i = 0; i < fMaxChildren; ++i) {
toDivide[i] = *root->child(i);
}
toDivide[fMaxChildren] = *toInsert;
int splitIndex = this->distributeChildren(toDivide);
// divide up the branches
root->fNumChildren = splitIndex;
newSibling->fNumChildren = fMaxChildren + 1 - splitIndex;
for (int i = 0; i < splitIndex; ++i) {
*root->child(i) = toDivide[i];
}
for (int i = splitIndex; i < fMaxChildren + 1; ++i) {
*newSibling->child(i - splitIndex) = toDivide[i];
}
SkDELETE_ARRAY(toDivide);
// pass the new sibling branch up to the parent
branch->fChild.subtree = newSibling;
branch->fBounds = this->computeBounds(newSibling);
return branch;
} else {
*root->child(root->fNumChildren) = *toInsert;
++root->fNumChildren;
return NULL;
}
}
return NULL;
}
int SkRTree::chooseSubtree(Node* root, Branch* branch) {
SkASSERT(!root->isLeaf());
if (1 < root->fLevel) {
// root's child pointers do not point to leaves, so minimize area increase
int32_t minAreaIncrease = SK_MaxS32;
int32_t minArea = SK_MaxS32;
int32_t bestSubtree = -1;
for (int i = 0; i < root->fNumChildren; ++i) {
const SkIRect& subtreeBounds = root->child(i)->fBounds;
int32_t areaIncrease = get_area_increase(subtreeBounds, branch->fBounds);
// break ties in favor of subtree with smallest area
if (areaIncrease < minAreaIncrease || (areaIncrease == minAreaIncrease &&
static_cast<int32_t>(get_area(subtreeBounds)) < minArea)) {
minAreaIncrease = areaIncrease;
minArea = get_area(subtreeBounds);
bestSubtree = i;
}
}
SkASSERT(-1 != bestSubtree);
return bestSubtree;
} else if (1 == root->fLevel) {
// root's child pointers do point to leaves, so minimize overlap increase
int32_t minOverlapIncrease = SK_MaxS32;
int32_t minAreaIncrease = SK_MaxS32;
int32_t bestSubtree = -1;
for (int32_t i = 0; i < root->fNumChildren; ++i) {
const SkIRect& subtreeBounds = root->child(i)->fBounds;
SkIRect expandedBounds = subtreeBounds;
join_no_empty_check(branch->fBounds, &expandedBounds);
int32_t overlap = 0;
for (int32_t j = 0; j < root->fNumChildren; ++j) {
if (j == i) continue;
// Note: this would be more correct if we subtracted the original pre-expanded
// overlap, but computing overlaps is expensive and omitting it doesn't seem to
// hurt query performance. See get_overlap_increase()
overlap += get_overlap(expandedBounds, root->child(j)->fBounds);
}
// break ties with lowest area increase
if (overlap < minOverlapIncrease || (overlap == minOverlapIncrease &&
static_cast<int32_t>(get_area_increase(branch->fBounds, subtreeBounds)) <
minAreaIncrease)) {
minOverlapIncrease = overlap;
minAreaIncrease = get_area_increase(branch->fBounds, subtreeBounds);
bestSubtree = i;
}
}
return bestSubtree;
} else {
SkASSERT(false);
return 0;
}
}
SkIRect SkRTree::computeBounds(Node* n) {
SkIRect r = n->child(0)->fBounds;
for (int i = 1; i < n->fNumChildren; ++i) {
join_no_empty_check(n->child(i)->fBounds, &r);
}
return r;
}
int SkRTree::distributeChildren(Branch* children) {
// We have two sides to sort by on each of two axes:
const static SortSide sorts[2][2] = {
{&SkIRect::fLeft, &SkIRect::fRight},
{&SkIRect::fTop, &SkIRect::fBottom}
};
// We want to choose an axis to split on, then a distribution along that axis; we'll need
// three pieces of info: the split axis, the side to sort by on that axis, and the index
// to split the sorted array on.
int32_t sortSide = -1;
int32_t k = -1;
int32_t axis = -1;
int32_t bestS = SK_MaxS32;
// Evaluate each axis, we want the min summed margin-value (s) over all distributions
for (int i = 0; i < 2; ++i) {
int32_t minOverlap = SK_MaxS32;
int32_t minArea = SK_MaxS32;
int32_t axisBestK = 0;
int32_t axisBestSide = 0;
int32_t s = 0;
// Evaluate each sort
for (int j = 0; j < 2; ++j) {
SkTQSort(children, children + fMaxChildren, RectLessThan(sorts[i][j]));
// Evaluate each split index
for (int32_t k = 1; k <= fMaxChildren - 2 * fMinChildren + 2; ++k) {
SkIRect r1 = children[0].fBounds;
SkIRect r2 = children[fMinChildren + k - 1].fBounds;
for (int32_t l = 1; l < fMinChildren - 1 + k; ++l) {
join_no_empty_check(children[l].fBounds, &r1);
}
for (int32_t l = fMinChildren + k; l < fMaxChildren + 1; ++l) {
join_no_empty_check(children[l].fBounds, &r2);
}
int32_t area = get_area(r1) + get_area(r2);
int32_t overlap = get_overlap(r1, r2);
s += get_margin(r1) + get_margin(r2);
if (overlap < minOverlap || (overlap == minOverlap && area < minArea)) {
minOverlap = overlap;
minArea = area;
axisBestSide = j;
axisBestK = k;
}
}
}
if (s < bestS) {
bestS = s;
axis = i;
sortSide = axisBestSide;
k = axisBestK;
}
}
// replicate the sort of the winning distribution, (we can skip this if the last
// sort ended up being best)
if (!(axis == 1 && sortSide == 1)) {
SkTQSort(children, children + fMaxChildren, RectLessThan(sorts[axis][sortSide]));
}
return fMinChildren - 1 + k;
}
void SkRTree::search(Node* root, const SkIRect query, SkTDArray<void*>* results) const {
for (int i = 0; i < root->fNumChildren; ++i) {
if (SkIRect::IntersectsNoEmptyCheck(root->child(i)->fBounds, query)) {
if (root->isLeaf()) {
results->push(root->child(i)->fChild.data);
} else {
this->search(root->child(i)->fChild.subtree, query, results);
}
}
}
}
SkRTree::Branch SkRTree::bulkLoad(SkTDArray<Branch>* branches, int level) {
if (branches->count() == 1) {
// Only one branch: it will be the root
Branch out = (*branches)[0];
branches->rewind();
return out;
} else {
// First we sort the whole list by y coordinates
SkTQSort(branches->begin(), branches->end() - 1, RectLessY());
int numBranches = branches->count() / fMaxChildren;
int remainder = branches->count() % fMaxChildren;
int newBranches = 0;
if (0 != remainder) {
++numBranches;
// If the remainder isn't enough to fill a node, we'll need to add fewer nodes to
// some other branches to make up for it
if (remainder >= fMinChildren) {
remainder = 0;
} else {
remainder = fMinChildren - remainder;
}
}
int numStrips = SkScalarCeil(SkScalarSqrt(SkIntToScalar(numBranches) *
SkScalarInvert(fAspectRatio)));
int numTiles = SkScalarCeil(SkIntToScalar(numBranches) /
SkIntToScalar(numStrips));
int currentBranch = 0;
for (int i = 0; i < numStrips; ++i) {
int begin = currentBranch;
int end = currentBranch + numTiles * fMaxChildren - SkMin32(remainder,
(fMaxChildren - fMinChildren) * numTiles);
if (end > branches->count()) {
end = branches->count();
}
// Now we sort horizontal strips of rectangles by their x coords
SkTQSort(branches->begin() + begin, branches->begin() + end - 1, RectLessX());
for (int j = 0; j < numTiles && currentBranch < branches->count(); ++j) {
int incrementBy = fMaxChildren;
if (remainder != 0) {
// if need be, omit some nodes to make up for remainder
if (remainder <= fMaxChildren - fMinChildren) {
incrementBy -= remainder;
remainder = 0;
} else {
incrementBy = fMinChildren;
remainder -= fMaxChildren - fMinChildren;
}
}
Node* n = allocateNode(level);
n->fNumChildren = 1;
*n->child(0) = (*branches)[currentBranch];
Branch b;
b.fBounds = (*branches)[currentBranch].fBounds;
b.fChild.subtree = n;
++currentBranch;
for (int k = 1; k < incrementBy && currentBranch < branches->count(); ++k) {
b.fBounds.join((*branches)[currentBranch].fBounds);
*n->child(k) = (*branches)[currentBranch];
++n->fNumChildren;
++currentBranch;
}
(*branches)[newBranches] = b;
++newBranches;
}
}
branches->setCount(newBranches);
return this->bulkLoad(branches, level + 1);
}
}
void SkRTree::validate() {
#ifdef SK_DEBUG
if (this->isEmpty()) {
return;
}
SkASSERT(fCount == (size_t)this->validateSubtree(fRoot.fChild.subtree, fRoot.fBounds, true));
#endif
}
int SkRTree::validateSubtree(Node* root, SkIRect bounds, bool isRoot) {
// make sure the pointer is pointing to a valid place
SkASSERT(fNodes.contains(static_cast<void*>(root)));
if (isRoot) {
// If the root of this subtree is the overall root, we have looser standards:
if (root->isLeaf()) {
SkASSERT(root->fNumChildren >= 1 && root->fNumChildren <= fMaxChildren);
} else {
SkASSERT(root->fNumChildren >= 2 && root->fNumChildren <= fMaxChildren);
}
} else {
SkASSERT(root->fNumChildren >= fMinChildren && root->fNumChildren <= fMaxChildren);
}
for (int i = 0; i < root->fNumChildren; ++i) {
SkASSERT(bounds.contains(root->child(i)->fBounds));
}
if (root->isLeaf()) {
SkASSERT(0 == root->fLevel);
return root->fNumChildren;
} else {
int childCount = 0;
for (int i = 0; i < root->fNumChildren; ++i) {
SkASSERT(root->child(i)->fChild.subtree->fLevel == root->fLevel - 1);
childCount += this->validateSubtree(root->child(i)->fChild.subtree,
root->child(i)->fBounds);
}
return childCount;
}
}
///////////////////////////////////////////////////////////////////////////////////////////////////
static inline uint32_t get_area(const SkIRect& rect) {
return rect.width() * rect.height();
}
static inline uint32_t get_overlap(const SkIRect& rect1, const SkIRect& rect2) {
// I suspect there's a more efficient way of computing this...
return SkMax32(0, SkMin32(rect1.fRight, rect2.fRight) - SkMax32(rect1.fLeft, rect2.fLeft)) *
SkMax32(0, SkMin32(rect1.fBottom, rect2.fBottom) - SkMax32(rect1.fTop, rect2.fTop));
}
// Get the margin (aka perimeter)
static inline uint32_t get_margin(const SkIRect& rect) {
return 2 * (rect.width() + rect.height());
}
static inline uint32_t get_overlap_increase(const SkIRect& rect1, const SkIRect& rect2,
SkIRect expandBy) {
join_no_empty_check(rect1, &expandBy);
return get_overlap(expandBy, rect2) - get_overlap(rect1, rect2);
}
static inline uint32_t get_area_increase(const SkIRect& rect1, SkIRect rect2) {
join_no_empty_check(rect1, &rect2);
return get_area(rect2) - get_area(rect1);
}
// Expand 'out' to include 'joinWith'
static inline void join_no_empty_check(const SkIRect& joinWith, SkIRect* out) {
// since we check for empty bounds on insert, we know we'll never have empty rects
// and we can save the empty check that SkIRect::join requires
if (joinWith.fLeft < out->fLeft) { out->fLeft = joinWith.fLeft; }
if (joinWith.fTop < out->fTop) { out->fTop = joinWith.fTop; }
if (joinWith.fRight > out->fRight) { out->fRight = joinWith.fRight; }
if (joinWith.fBottom > out->fBottom) { out->fBottom = joinWith.fBottom; }
}