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** of 4-byte coordinates. For leaf nodes the integer is the rowid
** of a record. For internal nodes it is the node number of a
** child page.
*/
#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_RTREE)
/*
** This file contains an implementation of a couple of different variants
** of the r-tree algorithm. See the README file for further details. The
** same data-structure is used for all, but the algorithms for insert and
** delete operations vary. The variants used are selected at compile time
** by defining the following symbols:
*/
/* Either, both or none of the following may be set to activate
** r*tree variant algorithms.
*/
#define VARIANT_RSTARTREE_CHOOSESUBTREE 0
#define VARIANT_RSTARTREE_REINSERT 1
/*
** Exactly one of the following must be set to 1.
*/
#define VARIANT_GUTTMAN_QUADRATIC_SPLIT 0
#define VARIANT_GUTTMAN_LINEAR_SPLIT 0
#define VARIANT_RSTARTREE_SPLIT 1
#define VARIANT_GUTTMAN_SPLIT \
(VARIANT_GUTTMAN_LINEAR_SPLIT||VARIANT_GUTTMAN_QUADRATIC_SPLIT)
#if VARIANT_GUTTMAN_QUADRATIC_SPLIT
#define PickNext QuadraticPickNext
#define PickSeeds QuadraticPickSeeds
#define AssignCells splitNodeGuttman
#endif
#if VARIANT_GUTTMAN_LINEAR_SPLIT
#define PickNext LinearPickNext
#define PickSeeds LinearPickSeeds
#define AssignCells splitNodeGuttman
#endif
#if VARIANT_RSTARTREE_SPLIT
#define AssignCells splitNodeStartree
#endif
#if !defined(NDEBUG) && !defined(SQLITE_DEBUG)
# define NDEBUG 1
#endif
#ifndef SQLITE_CORE
#include "sqlite3ext.h"
SQLITE_EXTENSION_INIT1
#else
#include "sqlite3.h"
#endif
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** of 4-byte coordinates. For leaf nodes the integer is the rowid
** of a record. For internal nodes it is the node number of a
** child page.
*/
#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_RTREE)
#ifndef SQLITE_CORE
#include "sqlite3ext.h"
SQLITE_EXTENSION_INIT1
#else
#include "sqlite3.h"
#endif
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RtreeCell cell;
memcpy(&cell, p, sizeof(RtreeCell));
area = cellArea(pRtree, &cell);
cellUnion(pRtree, &cell, pCell);
return (cellArea(pRtree, &cell)-area);
}
#if VARIANT_RSTARTREE_CHOOSESUBTREE || VARIANT_RSTARTREE_SPLIT
static RtreeDValue cellOverlap(
Rtree *pRtree,
RtreeCell *p,
RtreeCell *aCell,
int nCell,
int iExclude
){
int ii;
RtreeDValue overlap = 0.0;
for(ii=0; ii<nCell; ii++){
#if VARIANT_RSTARTREE_CHOOSESUBTREE
if( ii!=iExclude )
#else
assert( iExclude==-1 );
UNUSED_PARAMETER(iExclude);
#endif
{
int jj;
RtreeDValue o = (RtreeDValue)1;
for(jj=0; jj<(pRtree->nDim*2); jj+=2){
RtreeDValue x1, x2;
x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[jj]));
x2 = MIN(DCOORD(p->aCoord[jj+1]), DCOORD(aCell[ii].aCoord[jj+1]));
if( x2<x1 ){
o = 0.0;
break;
}else{
o = o * (x2-x1);
}
}
overlap += o;
}
}
return overlap;
}
#endif
#if VARIANT_RSTARTREE_CHOOSESUBTREE
static RtreeDValue cellOverlapEnlargement(
Rtree *pRtree,
RtreeCell *p,
RtreeCell *pInsert,
RtreeCell *aCell,
int nCell,
int iExclude
){
RtreeDValue before, after;
before = cellOverlap(pRtree, p, aCell, nCell, iExclude);
cellUnion(pRtree, p, pInsert);
after = cellOverlap(pRtree, p, aCell, nCell, iExclude);
return (after-before);
}
#endif
/*
** This function implements the ChooseLeaf algorithm from Gutman[84].
** ChooseSubTree in r*tree terminology.
*/
static int ChooseLeaf(
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RtreeCell cell;
memcpy(&cell, p, sizeof(RtreeCell));
area = cellArea(pRtree, &cell);
cellUnion(pRtree, &cell, pCell);
return (cellArea(pRtree, &cell)-area);
}
static RtreeDValue cellOverlap(
Rtree *pRtree,
RtreeCell *p,
RtreeCell *aCell,
int nCell
){
int ii;
RtreeDValue overlap = 0.0;
for(ii=0; ii<nCell; ii++){
int jj;
RtreeDValue o = (RtreeDValue)1;
for(jj=0; jj<(pRtree->nDim*2); jj+=2){
RtreeDValue x1, x2;
x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[jj]));
x2 = MIN(DCOORD(p->aCoord[jj+1]), DCOORD(aCell[ii].aCoord[jj+1]));
if( x2<x1 ){
o = (RtreeDValue)0;
break;
}else{
o = o * (x2-x1);
}
}
overlap += o;
}
return overlap;
}
/*
** This function implements the ChooseLeaf algorithm from Gutman[84].
** ChooseSubTree in r*tree terminology.
*/
static int ChooseLeaf(
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for(ii=0; rc==SQLITE_OK && ii<(pRtree->iDepth-iHeight); ii++){
int iCell;
sqlite3_int64 iBest = 0;
RtreeDValue fMinGrowth = 0.0;
RtreeDValue fMinArea = 0.0;
#if VARIANT_RSTARTREE_CHOOSESUBTREE
RtreeDValue fMinOverlap = 0.0;
RtreeDValue overlap;
#endif
int nCell = NCELL(pNode);
RtreeCell cell;
RtreeNode *pChild;
RtreeCell *aCell = 0;
#if VARIANT_RSTARTREE_CHOOSESUBTREE
if( ii==(pRtree->iDepth-1) ){
int jj;
aCell = sqlite3_malloc(sizeof(RtreeCell)*nCell);
if( !aCell ){
rc = SQLITE_NOMEM;
nodeRelease(pRtree, pNode);
pNode = 0;
continue;
}
for(jj=0; jj<nCell; jj++){
nodeGetCell(pRtree, pNode, jj, &aCell[jj]);
}
}
#endif
/* Select the child node which will be enlarged the least if pCell
** is inserted into it. Resolve ties by choosing the entry with
** the smallest area.
*/
for(iCell=0; iCell<nCell; iCell++){
int bBest = 0;
RtreeDValue growth;
RtreeDValue area;
nodeGetCell(pRtree, pNode, iCell, &cell);
growth = cellGrowth(pRtree, &cell, pCell);
area = cellArea(pRtree, &cell);
#if VARIANT_RSTARTREE_CHOOSESUBTREE
if( ii==(pRtree->iDepth-1) ){
overlap = cellOverlapEnlargement(pRtree,&cell,pCell,aCell,nCell,iCell);
}else{
overlap = 0.0;
}
if( (iCell==0)
|| (overlap<fMinOverlap)
|| (overlap==fMinOverlap && growth<fMinGrowth)
|| (overlap==fMinOverlap && growth==fMinGrowth && area<fMinArea)
){
bBest = 1;
fMinOverlap = overlap;
}
#else
if( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){
bBest = 1;
}
#endif
if( bBest ){
fMinGrowth = growth;
fMinArea = area;
iBest = cell.iRowid;
}
}
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for(ii=0; rc==SQLITE_OK && ii<(pRtree->iDepth-iHeight); ii++){
int iCell;
sqlite3_int64 iBest = 0;
RtreeDValue fMinGrowth = 0.0;
RtreeDValue fMinArea = 0.0;
int nCell = NCELL(pNode);
RtreeCell cell;
RtreeNode *pChild;
RtreeCell *aCell = 0;
/* Select the child node which will be enlarged the least if pCell
** is inserted into it. Resolve ties by choosing the entry with
** the smallest area.
*/
for(iCell=0; iCell<nCell; iCell++){
int bBest = 0;
RtreeDValue growth;
RtreeDValue area;
nodeGetCell(pRtree, pNode, iCell, &cell);
growth = cellGrowth(pRtree, &cell, pCell);
area = cellArea(pRtree, &cell);
if( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){
bBest = 1;
}
if( bBest ){
fMinGrowth = growth;
fMinArea = area;
iBest = cell.iRowid;
}
}
|
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sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);
sqlite3_step(pRtree->pWriteParent);
return sqlite3_reset(pRtree->pWriteParent);
}
static int rtreeInsertCell(Rtree *, RtreeNode *, RtreeCell *, int);
#if VARIANT_GUTTMAN_LINEAR_SPLIT
/*
** Implementation of the linear variant of the PickNext() function from
** Guttman[84].
*/
static RtreeCell *LinearPickNext(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
RtreeCell *pLeftBox,
RtreeCell *pRightBox,
int *aiUsed
){
int ii;
for(ii=0; aiUsed[ii]; ii++);
aiUsed[ii] = 1;
return &aCell[ii];
}
/*
** Implementation of the linear variant of the PickSeeds() function from
** Guttman[84].
*/
static void LinearPickSeeds(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
int *piLeftSeed,
int *piRightSeed
){
int i;
int iLeftSeed = 0;
int iRightSeed = 1;
RtreeDValue maxNormalInnerWidth = (RtreeDValue)0;
/* Pick two "seed" cells from the array of cells. The algorithm used
** here is the LinearPickSeeds algorithm from Gutman[1984]. The
** indices of the two seed cells in the array are stored in local
** variables iLeftSeek and iRightSeed.
*/
for(i=0; i<pRtree->nDim; i++){
RtreeDValue x1 = DCOORD(aCell[0].aCoord[i*2]);
RtreeDValue x2 = DCOORD(aCell[0].aCoord[i*2+1]);
RtreeDValue x3 = x1;
RtreeDValue x4 = x2;
int jj;
int iCellLeft = 0;
int iCellRight = 0;
for(jj=1; jj<nCell; jj++){
RtreeDValue left = DCOORD(aCell[jj].aCoord[i*2]);
RtreeDValue right = DCOORD(aCell[jj].aCoord[i*2+1]);
if( left<x1 ) x1 = left;
if( right>x4 ) x4 = right;
if( left>x3 ){
x3 = left;
iCellRight = jj;
}
if( right<x2 ){
x2 = right;
iCellLeft = jj;
}
}
if( x4!=x1 ){
RtreeDValue normalwidth = (x3 - x2) / (x4 - x1);
if( normalwidth>maxNormalInnerWidth ){
iLeftSeed = iCellLeft;
iRightSeed = iCellRight;
}
}
}
*piLeftSeed = iLeftSeed;
*piRightSeed = iRightSeed;
}
#endif /* VARIANT_GUTTMAN_LINEAR_SPLIT */
#if VARIANT_GUTTMAN_QUADRATIC_SPLIT
/*
** Implementation of the quadratic variant of the PickNext() function from
** Guttman[84].
*/
static RtreeCell *QuadraticPickNext(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
RtreeCell *pLeftBox,
RtreeCell *pRightBox,
int *aiUsed
){
#define FABS(a) ((a)<0.0?-1.0*(a):(a))
int iSelect = -1;
RtreeDValue fDiff;
int ii;
for(ii=0; ii<nCell; ii++){
if( aiUsed[ii]==0 ){
RtreeDValue left = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
RtreeDValue right = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
RtreeDValue diff = FABS(right-left);
if( iSelect<0 || diff>fDiff ){
fDiff = diff;
iSelect = ii;
}
}
}
aiUsed[iSelect] = 1;
return &aCell[iSelect];
}
/*
** Implementation of the quadratic variant of the PickSeeds() function from
** Guttman[84].
*/
static void QuadraticPickSeeds(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
int *piLeftSeed,
int *piRightSeed
){
int ii;
int jj;
int iLeftSeed = 0;
int iRightSeed = 1;
RtreeDValue fWaste = 0.0;
for(ii=0; ii<nCell; ii++){
for(jj=ii+1; jj<nCell; jj++){
RtreeDValue right = cellArea(pRtree, &aCell[jj]);
RtreeDValue growth = cellGrowth(pRtree, &aCell[ii], &aCell[jj]);
RtreeDValue waste = growth - right;
if( waste>fWaste ){
iLeftSeed = ii;
iRightSeed = jj;
fWaste = waste;
}
}
}
*piLeftSeed = iLeftSeed;
*piRightSeed = iRightSeed;
}
#endif /* VARIANT_GUTTMAN_QUADRATIC_SPLIT */
/*
** Arguments aIdx, aDistance and aSpare all point to arrays of size
** nIdx. The aIdx array contains the set of integers from 0 to
** (nIdx-1) in no particular order. This function sorts the values
** in aIdx according to the indexed values in aDistance. For
** example, assuming the inputs:
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sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);
sqlite3_step(pRtree->pWriteParent);
return sqlite3_reset(pRtree->pWriteParent);
}
static int rtreeInsertCell(Rtree *, RtreeNode *, RtreeCell *, int);
/*
** Arguments aIdx, aDistance and aSpare all point to arrays of size
** nIdx. The aIdx array contains the set of integers from 0 to
** (nIdx-1) in no particular order. This function sorts the values
** in aIdx according to the indexed values in aDistance. For
** example, assuming the inputs:
|
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assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );
}
}
#endif
}
}
#if VARIANT_RSTARTREE_SPLIT
/*
** Implementation of the R*-tree variant of SplitNode from Beckman[1990].
*/
static int splitNodeStartree(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
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assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );
}
}
#endif
}
}
/*
** Implementation of the R*-tree variant of SplitNode from Beckman[1990].
*/
static int splitNodeStartree(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
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cellUnion(pRtree, &left, &aCell[aaSorted[ii][kk]]);
}else{
cellUnion(pRtree, &right, &aCell[aaSorted[ii][kk]]);
}
}
margin += cellMargin(pRtree, &left);
margin += cellMargin(pRtree, &right);
overlap = cellOverlap(pRtree, &left, &right, 1, -1);
area = cellArea(pRtree, &left) + cellArea(pRtree, &right);
if( (nLeft==RTREE_MINCELLS(pRtree))
|| (overlap<fBestOverlap)
|| (overlap==fBestOverlap && area<fBestArea)
){
iBestLeft = nLeft;
fBestOverlap = overlap;
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cellUnion(pRtree, &left, &aCell[aaSorted[ii][kk]]);
}else{
cellUnion(pRtree, &right, &aCell[aaSorted[ii][kk]]);
}
}
margin += cellMargin(pRtree, &left);
margin += cellMargin(pRtree, &right);
overlap = cellOverlap(pRtree, &left, &right, 1);
area = cellArea(pRtree, &left) + cellArea(pRtree, &right);
if( (nLeft==RTREE_MINCELLS(pRtree))
|| (overlap<fBestOverlap)
|| (overlap==fBestOverlap && area<fBestArea)
){
iBestLeft = nLeft;
fBestOverlap = overlap;
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2151
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2153
2154
2155
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2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
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2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
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2191
2192
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2194
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2196
2197
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2199
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2201
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2206
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2208
2209
2210
2211
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|
nodeInsertCell(pRtree, pTarget, pCell);
cellUnion(pRtree, pBbox, pCell);
}
sqlite3_free(aaSorted);
return SQLITE_OK;
}
#endif
#if VARIANT_GUTTMAN_SPLIT
/*
** Implementation of the regular R-tree SplitNode from Guttman[1984].
*/
static int splitNodeGuttman(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
RtreeNode *pLeft,
RtreeNode *pRight,
RtreeCell *pBboxLeft,
RtreeCell *pBboxRight
){
int iLeftSeed = 0;
int iRightSeed = 1;
int *aiUsed;
int i;
aiUsed = sqlite3_malloc(sizeof(int)*nCell);
if( !aiUsed ){
return SQLITE_NOMEM;
}
memset(aiUsed, 0, sizeof(int)*nCell);
PickSeeds(pRtree, aCell, nCell, &iLeftSeed, &iRightSeed);
memcpy(pBboxLeft, &aCell[iLeftSeed], sizeof(RtreeCell));
memcpy(pBboxRight, &aCell[iRightSeed], sizeof(RtreeCell));
nodeInsertCell(pRtree, pLeft, &aCell[iLeftSeed]);
nodeInsertCell(pRtree, pRight, &aCell[iRightSeed]);
aiUsed[iLeftSeed] = 1;
aiUsed[iRightSeed] = 1;
for(i=nCell-2; i>0; i--){
RtreeCell *pNext;
pNext = PickNext(pRtree, aCell, nCell, pBboxLeft, pBboxRight, aiUsed);
RtreeDValue diff =
cellGrowth(pRtree, pBboxLeft, pNext) -
cellGrowth(pRtree, pBboxRight, pNext)
;
if( (RTREE_MINCELLS(pRtree)-NCELL(pRight)==i)
|| (diff>0.0 && (RTREE_MINCELLS(pRtree)-NCELL(pLeft)!=i))
){
nodeInsertCell(pRtree, pRight, pNext);
cellUnion(pRtree, pBboxRight, pNext);
}else{
nodeInsertCell(pRtree, pLeft, pNext);
cellUnion(pRtree, pBboxLeft, pNext);
}
}
sqlite3_free(aiUsed);
return SQLITE_OK;
}
#endif
static int updateMapping(
Rtree *pRtree,
i64 iRowid,
RtreeNode *pNode,
int iHeight
){
|
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
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<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
<
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<
<
<
|
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
|
nodeInsertCell(pRtree, pTarget, pCell);
cellUnion(pRtree, pBbox, pCell);
}
sqlite3_free(aaSorted);
return SQLITE_OK;
}
static int updateMapping(
Rtree *pRtree,
i64 iRowid,
RtreeNode *pNode,
int iHeight
){
|
︙ | | | ︙ | |
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
|
rc = SQLITE_NOMEM;
goto splitnode_out;
}
memset(pLeft->zData, 0, pRtree->iNodeSize);
memset(pRight->zData, 0, pRtree->iNodeSize);
rc = AssignCells(pRtree, aCell, nCell, pLeft, pRight, &leftbbox, &rightbbox);
if( rc!=SQLITE_OK ){
goto splitnode_out;
}
/* Ensure both child nodes have node numbers assigned to them by calling
** nodeWrite(). Node pRight always needs a node number, as it was created
** by nodeNew() above. But node pLeft sometimes already has a node number.
|
|
|
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
|
rc = SQLITE_NOMEM;
goto splitnode_out;
}
memset(pLeft->zData, 0, pRtree->iNodeSize);
memset(pRight->zData, 0, pRtree->iNodeSize);
rc = splitNodeStartree(pRtree, aCell, nCell, pLeft, pRight,&leftbbox,&rightbbox);
if( rc!=SQLITE_OK ){
goto splitnode_out;
}
/* Ensure both child nodes have node numbers assigned to them by calling
** nodeWrite(). Node pRight always needs a node number, as it was created
** by nodeNew() above. But node pLeft sometimes already has a node number.
|
︙ | | | ︙ | |
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
|
if( pChild ){
nodeRelease(pRtree, pChild->pParent);
nodeReference(pNode);
pChild->pParent = pNode;
}
}
if( nodeInsertCell(pRtree, pNode, pCell) ){
#if VARIANT_RSTARTREE_REINSERT
if( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){
rc = SplitNode(pRtree, pNode, pCell, iHeight);
}else{
pRtree->iReinsertHeight = iHeight;
rc = Reinsert(pRtree, pNode, pCell, iHeight);
}
#else
rc = SplitNode(pRtree, pNode, pCell, iHeight);
#endif
}else{
rc = AdjustTree(pRtree, pNode, pCell);
if( rc==SQLITE_OK ){
if( iHeight==0 ){
rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
}else{
rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);
|
<
<
<
<
|
2316
2317
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2319
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2321
2322
2323
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2325
2326
2327
2328
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2330
2331
2332
2333
2334
2335
|
if( pChild ){
nodeRelease(pRtree, pChild->pParent);
nodeReference(pNode);
pChild->pParent = pNode;
}
}
if( nodeInsertCell(pRtree, pNode, pCell) ){
if( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){
rc = SplitNode(pRtree, pNode, pCell, iHeight);
}else{
pRtree->iReinsertHeight = iHeight;
rc = Reinsert(pRtree, pNode, pCell, iHeight);
}
}else{
rc = AdjustTree(pRtree, pNode, pCell);
if( rc==SQLITE_OK ){
if( iHeight==0 ){
rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
}else{
rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);
|
︙ | | | ︙ | |