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Comment:Backport the RTree implementation from the trunk into the 3.6.23 branch. The code for the application-defined query boxes is still present but is disabled. The reason for this backport is to take advantage of recent enhancements to robustness to database corruption.
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Timelines: family | ancestors | descendants | both | branch-3.6.23
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SHA1: 854b23c117c973fcf63f31bda189b7492595c3f9
User & Date: drh 2010-10-01 20:45:09
Context
2010-10-02
01:00
Fix the amalgamation builder so that it works with the rtree updates of the prior check-in. Leaf check-in: 265b0b29 user: drh tags: branch-3.6.23
2010-10-01
20:45
Backport the RTree implementation from the trunk into the 3.6.23 branch. The code for the application-defined query boxes is still present but is disabled. The reason for this backport is to take advantage of recent enhancements to robustness to database corruption. check-in: 854b23c1 user: drh tags: branch-3.6.23
2010-08-24
12:05
Pull the incremental_vacuum bug fix ([255f1eefa373153942c67b18b]) and the R-tree segfault bug fix ([7f2f71cc9e3c39093f09231f44]) into the 3.6.23 branch. Increase the version number to 3.6.23.3. check-in: bcbdecd8 user: drh tags: branch-3.6.23
Changes
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Changes to ext/rtree/rtree.c.

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**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
** This file contains code for implementations of the r-tree and r*-tree
** algorithms packaged as an SQLite virtual table module.
*/








































#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
................................................................................
  #define PickSeeds LinearPickSeeds
  #define AssignCells splitNodeGuttman
#endif
#if VARIANT_RSTARTREE_SPLIT
  #define AssignCells splitNodeStartree
#endif





#ifndef SQLITE_CORE
  #include "sqlite3ext.h"
  SQLITE_EXTENSION_INIT1
#else
  #include "sqlite3.h"
#endif

#include <string.h>
#include <assert.h>

#ifndef SQLITE_AMALGAMATION

typedef sqlite3_int64 i64;
typedef unsigned char u8;
typedef unsigned int u32;
#endif

typedef struct Rtree Rtree;
typedef struct RtreeCursor RtreeCursor;
typedef struct RtreeNode RtreeNode;
typedef struct RtreeCell RtreeCell;
typedef struct RtreeConstraint RtreeConstraint;


typedef union RtreeCoord RtreeCoord;

/* The rtree may have between 1 and RTREE_MAX_DIMENSIONS dimensions. */
#define RTREE_MAX_DIMENSIONS 5

/* Size of hash table Rtree.aHash. This hash table is not expected to
** ever contain very many entries, so a fixed number of buckets is 
................................................................................
** If an R*-tree "Reinsert" operation is required, the same number of
** cells are removed from the overfull node and reinserted into the tree.
*/
#define RTREE_MINCELLS(p) ((((p)->iNodeSize-4)/(p)->nBytesPerCell)/3)
#define RTREE_REINSERT(p) RTREE_MINCELLS(p)
#define RTREE_MAXCELLS 51










/* 
** An rtree cursor object.
*/
struct RtreeCursor {
  sqlite3_vtab_cursor base;
  RtreeNode *pNode;                 /* Node cursor is currently pointing at */
  int iCell;                        /* Index of current cell in pNode */
................................................................................
    ((double)coord.i)                             \
)

/*
** A search constraint.
*/
struct RtreeConstraint {
  int iCoord;                       /* Index of constrained coordinate */
  int op;                           /* Constraining operation */
  double rValue;                    /* Constraint value. */


};

/* Possible values for RtreeConstraint.op */
#define RTREE_EQ 0x41
#define RTREE_LE 0x42
#define RTREE_LT 0x43
#define RTREE_GE 0x44
#define RTREE_GT 0x45


/* 
** An rtree structure node.
**
** Data format (RtreeNode.zData):
**
**   1. If the node is the root node (node 1), then the first 2 bytes
**      of the node contain the tree depth as a big-endian integer.
**      For non-root nodes, the first 2 bytes are left unused.
**
**   2. The next 2 bytes contain the number of entries currently 
**      stored in the node.
**
**   3. The remainder of the node contains the node entries. Each entry
**      consists of a single 8-byte integer followed by an even number
**      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.
*/
struct RtreeNode {
  RtreeNode *pParent;               /* Parent node */
  i64 iNode;
  int nRef;
  int isDirty;
  u8 *zData;
................................................................................
** Structure to store a deserialized rtree record.
*/
struct RtreeCell {
  i64 iRowid;
  RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];
};



































#ifndef MAX
# define MAX(x,y) ((x) < (y) ? (y) : (x))
#endif
#ifndef MIN
# define MIN(x,y) ((x) > (y) ? (y) : (x))
#endif

................................................................................
  }
}

/*
** Clear the content of node p (set all bytes to 0x00).
*/
static void nodeZero(Rtree *pRtree, RtreeNode *p){
  if( p ){
    memset(&p->zData[2], 0, pRtree->iNodeSize-2);
    p->isDirty = 1;
  }
}

/*
** Given a node number iNode, return the corresponding key to use
** in the Rtree.aHash table.
*/
static int nodeHash(i64 iNode){
................................................................................

/*
** Search the node hash table for node iNode. If found, return a pointer
** to it. Otherwise, return 0.
*/
static RtreeNode *nodeHashLookup(Rtree *pRtree, i64 iNode){
  RtreeNode *p;
  assert( iNode!=0 );
  for(p=pRtree->aHash[nodeHash(iNode)]; p && p->iNode!=iNode; p=p->pNext);
  return p;
}

/*
** Add node pNode to the node hash table.
*/
static void nodeHashInsert(Rtree *pRtree, RtreeNode *pNode){
  if( pNode ){
    int iHash;
    assert( pNode->pNext==0 );
    iHash = nodeHash(pNode->iNode);
    pNode->pNext = pRtree->aHash[iHash];
    pRtree->aHash[iHash] = pNode;
  }
}

/*
** Remove node pNode from the node hash table.
*/
static void nodeHashDelete(Rtree *pRtree, RtreeNode *pNode){
  RtreeNode **pp;
................................................................................

/*
** Allocate and return new r-tree node. Initially, (RtreeNode.iNode==0),
** indicating that node has not yet been assigned a node number. It is
** assigned a node number when nodeWrite() is called to write the
** node contents out to the database.
*/
static RtreeNode *nodeNew(Rtree *pRtree, RtreeNode *pParent, int zero){
  RtreeNode *pNode;
  pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);
  if( pNode ){
    memset(pNode, 0, sizeof(RtreeNode) + (zero?pRtree->iNodeSize:0));
    pNode->zData = (u8 *)&pNode[1];
    pNode->nRef = 1;
    pNode->pParent = pParent;
    pNode->isDirty = 1;
    nodeReference(pParent);
  }
  return pNode;
................................................................................
nodeAcquire(
  Rtree *pRtree,             /* R-tree structure */
  i64 iNode,                 /* Node number to load */
  RtreeNode *pParent,        /* Either the parent node or NULL */
  RtreeNode **ppNode         /* OUT: Acquired node */
){
  int rc;

  RtreeNode *pNode;

  /* Check if the requested node is already in the hash table. If so,
  ** increase its reference count and return it.
  */
  if( (pNode = nodeHashLookup(pRtree, iNode)) ){
    assert( !pParent || !pNode->pParent || pNode->pParent==pParent );
................................................................................
      pNode->pParent = pParent;
    }
    pNode->nRef++;
    *ppNode = pNode;
    return SQLITE_OK;
  }






  pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);
  if( !pNode ){
    *ppNode = 0;
    return SQLITE_NOMEM;
  }

  pNode->pParent = pParent;
  pNode->zData = (u8 *)&pNode[1];
  pNode->nRef = 1;
  pNode->iNode = iNode;
  pNode->isDirty = 0;
  pNode->pNext = 0;

  sqlite3_bind_int64(pRtree->pReadNode, 1, iNode);
  rc = sqlite3_step(pRtree->pReadNode);
  if( rc==SQLITE_ROW ){
    const u8 *zBlob = sqlite3_column_blob(pRtree->pReadNode, 0);
    assert( sqlite3_column_bytes(pRtree->pReadNode, 0)==pRtree->iNodeSize );
    memcpy(pNode->zData, zBlob, pRtree->iNodeSize);
    nodeReference(pParent);
  }else{
    sqlite3_free(pNode);
    pNode = 0;
  }

  *ppNode = pNode;

  rc = sqlite3_reset(pRtree->pReadNode);








  if( rc==SQLITE_OK && iNode==1 ){
    pRtree->iDepth = readInt16(pNode->zData);


  }













  if( pNode!=0 ){
    nodeHashInsert(pRtree, pNode);
  }else if( rc==SQLITE_OK ){

    rc = SQLITE_CORRUPT;





  }

  return rc;
}

/*
** Overwrite cell iCell of node pNode with the contents of pCell.
................................................................................
){
  int nCell;                    /* Current number of cells in pNode */
  int nMaxCell;                 /* Maximum number of cells for pNode */

  nMaxCell = (pRtree->iNodeSize-4)/pRtree->nBytesPerCell;
  nCell = NCELL(pNode);

  assert(nCell<=nMaxCell);

  if( nCell<nMaxCell ){
    nodeOverwriteCell(pRtree, pNode, pCell, nCell);
    writeInt16(&pNode->zData[2], nCell+1);
    pNode->isDirty = 1;
  }

  return (nCell==nMaxCell);
................................................................................
    rc = SQLITE_OK;
  }
  *ppCursor = (sqlite3_vtab_cursor *)pCsr;

  return rc;
}




















/* 
** Rtree virtual table module xClose method.
*/
static int rtreeClose(sqlite3_vtab_cursor *cur){
  Rtree *pRtree = (Rtree *)(cur->pVtab);
  int rc;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  sqlite3_free(pCsr->aConstraint);
  rc = nodeRelease(pRtree, pCsr->pNode);
  sqlite3_free(pCsr);
  return rc;
}

/*
** Rtree virtual table module xEof method.
................................................................................
** Return non-zero if the cursor does not currently point to a valid 
** record (i.e if the scan has finished), or zero otherwise.
*/
static int rtreeEof(sqlite3_vtab_cursor *cur){
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  return (pCsr->pNode==0);
}

/* 























** Cursor pCursor currently points to a cell in a non-leaf page.
** Return true if the sub-tree headed by the cell is filtered
** (excluded) by the constraints in the pCursor->aConstraint[] 
** array, or false otherwise.



*/
static int testRtreeCell(Rtree *pRtree, RtreeCursor *pCursor){
  RtreeCell cell;
  int ii;
  int bRes = 0;

  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
  for(ii=0; bRes==0 && ii<pCursor->nConstraint; ii++){
    RtreeConstraint *p = &pCursor->aConstraint[ii];
    double cell_min = DCOORD(cell.aCoord[(p->iCoord>>1)*2]);
    double cell_max = DCOORD(cell.aCoord[(p->iCoord>>1)*2+1]);

    assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
        || p->op==RTREE_GT || p->op==RTREE_EQ
    );

    switch( p->op ){
      case RTREE_LE: case RTREE_LT: bRes = p->rValue<cell_min; break;



      case RTREE_GE: case RTREE_GT: bRes = p->rValue>cell_max; break;



      case RTREE_EQ: 
        bRes = (p->rValue>cell_max || p->rValue<cell_min);
        break;











    }
  }


  return bRes;
}

/* 
** Return true if the cell that cursor pCursor currently points to
** would be filtered (excluded) by the constraints in the 
** pCursor->aConstraint[] array, or false otherwise.





**
** This function assumes that the cell is part of a leaf node.
*/
static int testRtreeEntry(Rtree *pRtree, RtreeCursor *pCursor){
  RtreeCell cell;
  int ii;


  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
  for(ii=0; ii<pCursor->nConstraint; ii++){
    RtreeConstraint *p = &pCursor->aConstraint[ii];
    double coord = DCOORD(cell.aCoord[p->iCoord]);
    int res;
    assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
        || p->op==RTREE_GT || p->op==RTREE_EQ
    );
    switch( p->op ){
      case RTREE_LE: res = (coord<=p->rValue); break;
      case RTREE_LT: res = (coord<p->rValue);  break;
      case RTREE_GE: res = (coord>=p->rValue); break;
      case RTREE_GT: res = (coord>p->rValue);  break;
      case RTREE_EQ: res = (coord==p->rValue); break;






    }




    if( !res ) return 1;


  }


  return 0;
}

/*
** Cursor pCursor currently points at a node that heads a sub-tree of
** height iHeight (if iHeight==0, then the node is a leaf). Descend
** to point to the left-most cell of the sub-tree that matches the 
** configured constraints.
................................................................................

  RtreeNode *pSavedNode = pCursor->pNode;
  int iSavedCell = pCursor->iCell;

  assert( iHeight>=0 );

  if( iHeight==0 ){
    isEof = testRtreeEntry(pRtree, pCursor);
  }else{
    isEof = testRtreeCell(pRtree, pCursor);
  }
  if( isEof || iHeight==0 ){
    *pEof = isEof;
    return SQLITE_OK;
  }

  iRowid = nodeGetRowid(pRtree, pCursor->pNode, pCursor->iCell);
  rc = nodeAcquire(pRtree, iRowid, pCursor->pNode, &pChild);
  if( rc!=SQLITE_OK ){
    return rc;
  }
................................................................................
  return SQLITE_OK;
}

/*
** One of the cells in node pNode is guaranteed to have a 64-bit 
** integer value equal to iRowid. Return the index of this cell.
*/
static int nodeRowidIndex(Rtree *pRtree, RtreeNode *pNode, i64 iRowid){





  int ii;


  for(ii=0; nodeGetRowid(pRtree, pNode, ii)!=iRowid; ii++){
    assert( ii<(NCELL(pNode)-1) );


  }

  return ii;
}

/*
** Return the index of the cell containing a pointer to node pNode
** in its parent. If pNode is the root node, return -1.
*/
static int nodeParentIndex(Rtree *pRtree, RtreeNode *pNode){
  RtreeNode *pParent = pNode->pParent;
  if( pParent ){
    return nodeRowidIndex(pRtree, pParent, pNode->iNode);
  }

  return -1;
}

/* 
** Rtree virtual table module xNext method.
*/
static int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){
  Rtree *pRtree = (Rtree *)(pVtabCursor->pVtab);
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
  int rc = SQLITE_OK;







  if( pCsr->iStrategy==1 ){
    /* This "scan" is a direct lookup by rowid. There is no next entry. */
    nodeRelease(pRtree, pCsr->pNode);
    pCsr->pNode = 0;
  }

  else if( pCsr->pNode ){
    /* Move to the next entry that matches the configured constraints. */
    int iHeight = 0;
    while( pCsr->pNode ){
      RtreeNode *pNode = pCsr->pNode;
      int nCell = NCELL(pNode);
      for(pCsr->iCell++; pCsr->iCell<nCell; pCsr->iCell++){
        int isEof;
        rc = descendToCell(pRtree, pCsr, iHeight, &isEof);
        if( rc!=SQLITE_OK || !isEof ){
          return rc;
        }
      }
      pCsr->pNode = pNode->pParent;
      pCsr->iCell = nodeParentIndex(pRtree, pNode);



      nodeReference(pCsr->pNode);
      nodeRelease(pRtree, pNode);
      iHeight++;
    }
  }

  return rc;
................................................................................
    sqlite3_reset(pRtree->pReadRowid);
  }else{
    rc = sqlite3_reset(pRtree->pReadRowid);
  }
  return rc;
}















































/* 
** Rtree virtual table module xFilter method.
*/
static int rtreeFilter(
  sqlite3_vtab_cursor *pVtabCursor, 
  int idxNum, const char *idxStr,
................................................................................

  RtreeNode *pRoot = 0;
  int ii;
  int rc = SQLITE_OK;

  rtreeReference(pRtree);

  sqlite3_free(pCsr->aConstraint);
  pCsr->aConstraint = 0;
  pCsr->iStrategy = idxNum;

  if( idxNum==1 ){
    /* Special case - lookup by rowid. */
    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */
    i64 iRowid = sqlite3_value_int64(argv[0]);
    rc = findLeafNode(pRtree, iRowid, &pLeaf);
    pCsr->pNode = pLeaf; 

    if( pLeaf && rc==SQLITE_OK ){
      pCsr->iCell = nodeRowidIndex(pRtree, pLeaf, iRowid);
    }
  }else{
    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
    ** with the configured constraints. 
    */
    if( argc>0 ){
      pCsr->aConstraint = sqlite3_malloc(sizeof(RtreeConstraint)*argc);
      pCsr->nConstraint = argc;
      if( !pCsr->aConstraint ){
        rc = SQLITE_NOMEM;
      }else{

        assert( (idxStr==0 && argc==0) || strlen(idxStr)==argc*2 );
        for(ii=0; ii<argc; ii++){
          RtreeConstraint *p = &pCsr->aConstraint[ii];
          p->op = idxStr[ii*2];
          p->iCoord = idxStr[ii*2+1]-'a';










          p->rValue = sqlite3_value_double(argv[ii]);

        }
      }
    }
  
    if( rc==SQLITE_OK ){
      pCsr->pNode = 0;
      rc = nodeAcquire(pRtree, 1, 0, &pRoot);
................................................................................
** Rtree virtual table module xBestIndex method. There are three
** table scan strategies to choose from (in order from most to 
** least desirable):
**
**   idxNum     idxStr        Strategy
**   ------------------------------------------------
**     1        Unused        Direct lookup by rowid.
**     2        See below     R-tree query.
**     3        Unused        Full table scan.
**   ------------------------------------------------
**
** If strategy 1 or 3 is used, then idxStr is not meaningful. If strategy
** 2 is used, idxStr is formatted to contain 2 bytes for each 
** constraint used. The first two bytes of idxStr correspond to 
** the constraint in sqlite3_index_info.aConstraintUsage[] with
** (argvIndex==1) etc.
**
** The first of each pair of bytes in idxStr identifies the constraint
** operator as follows:
................................................................................
**   Operator    Byte Value
**   ----------------------
**      =        0x41 ('A')
**     <=        0x42 ('B')
**      <        0x43 ('C')
**     >=        0x44 ('D')
**      >        0x45 ('E')

**   ----------------------
**
** The second of each pair of bytes identifies the coordinate column
** to which the constraint applies. The leftmost coordinate column
** is 'a', the second from the left 'b' etc.
*/
static int rtreeBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){
................................................................................
      ** considered almost as quick as a direct rowid lookup (for which 
      ** sqlite uses an internal cost of 0.0).
      */ 
      pIdxInfo->estimatedCost = 10.0;
      return SQLITE_OK;
    }

    if( p->usable && p->iColumn>0 ){


      u8 op = 0;
      switch( p->op ){
        case SQLITE_INDEX_CONSTRAINT_EQ: op = RTREE_EQ; break;
        case SQLITE_INDEX_CONSTRAINT_GT: op = RTREE_GT; break;
        case SQLITE_INDEX_CONSTRAINT_LE: op = RTREE_LE; break;
        case SQLITE_INDEX_CONSTRAINT_LT: op = RTREE_LT; break;
        case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;




      }
      if( op ){


        /* Make sure this particular constraint has not been used before.
        ** If it has been used before, ignore it.
        **
        ** A <= or < can be used if there is a prior >= or >.
        ** A >= or > can be used if there is a prior < or <=.
        ** A <= or < is disqualified if there is a prior <=, <, or ==.
        ** A >= or > is disqualified if there is a prior >=, >, or ==.
        ** A == is disqualifed if there is any prior constraint.
        */
        int j, opmsk;
        static const unsigned char compatible[] = { 0, 0, 1, 1, 2, 2 };
        assert( compatible[RTREE_EQ & 7]==0 );
        assert( compatible[RTREE_LT & 7]==1 );
        assert( compatible[RTREE_LE & 7]==1 );
        assert( compatible[RTREE_GT & 7]==2 );
        assert( compatible[RTREE_GE & 7]==2 );
        cCol = p->iColumn - 1 + 'a';
        opmsk = compatible[op & 7];
        for(j=0; j<iIdx; j+=2){
          if( zIdxStr[j+1]==cCol && (compatible[zIdxStr[j] & 7] & opmsk)!=0 ){
            op = 0;
            break;
          }
        }
      }
      if( op ){
        assert( iIdx<sizeof(zIdxStr)-1 );
        zIdxStr[iIdx++] = op;
        zIdxStr[iIdx++] = cCol;
        pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);
................................................................................
  RtreeCell *aCell, 
  int nCell, 
  int iExclude
){
  int ii;
  float overlap = 0.0;
  for(ii=0; ii<nCell; ii++){

    if( ii!=iExclude ){




      int jj;
      float o = 1.0;
      for(jj=0; jj<(pRtree->nDim*2); jj+=2){
        double x1;
        double x2;

        x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[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++){

      float growth;
      float area;
      float overlap = 0.0;
      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);
      }
#endif
      if( (iCell==0) 
       || (overlap<fMinOverlap) 
       || (overlap==fMinOverlap && growth<fMinGrowth)
       || (overlap==fMinOverlap && growth==fMinGrowth && area<fMinArea)
      ){








        fMinOverlap = overlap;
        fMinGrowth = growth;
        fMinArea = area;
        iBest = cell.iRowid;
      }
    }

................................................................................
}

/*
** A cell with the same content as pCell has just been inserted into
** the node pNode. This function updates the bounding box cells in
** all ancestor elements.
*/
static void AdjustTree(
  Rtree *pRtree,                    /* Rtree table */
  RtreeNode *pNode,                 /* Adjust ancestry of this node. */
  RtreeCell *pCell                  /* This cell was just inserted */
){
  RtreeNode *p = pNode;
  while( p->pParent ){
    RtreeCell cell;
    RtreeNode *pParent = p->pParent;



    int iCell = nodeParentIndex(pRtree, p);



    nodeGetCell(pRtree, pParent, iCell, &cell);
    if( !cellContains(pRtree, &cell, pCell) ){
      cellUnion(pRtree, &cell, pCell);
      nodeOverwriteCell(pRtree, pParent, &cell, iCell);
    }
 
    p = pParent;
  }

}

/*
** Write mapping (iRowid->iNode) to the <rtree>_rowid table.
*/
static int rowidWrite(Rtree *pRtree, sqlite3_int64 iRowid, sqlite3_int64 iNode){
  sqlite3_bind_int64(pRtree->pWriteRowid, 1, iRowid);
................................................................................
    nodeGetCell(pRtree, pNode, i, &aCell[i]);
  }
  nodeZero(pRtree, pNode);
  memcpy(&aCell[nCell], pCell, sizeof(RtreeCell));
  nCell++;

  if( pNode->iNode==1 ){
    pRight = nodeNew(pRtree, pNode, 1);
    pLeft = nodeNew(pRtree, pNode, 1);
    pRtree->iDepth++;
    pNode->isDirty = 1;
    writeInt16(pNode->zData, pRtree->iDepth);
  }else{
    pLeft = pNode;
    pRight = nodeNew(pRtree, pLeft->pParent, 1);
    nodeReference(pLeft);
  }

  if( !pLeft || !pRight ){
    rc = SQLITE_NOMEM;
    goto splitnode_out;
  }
................................................................................
  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. */




  if( (0==pRight->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pRight)))
   || (0==pLeft->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pLeft)))
  ){
    goto splitnode_out;
  }

  rightbbox.iRowid = pRight->iNode;
  leftbbox.iRowid = pLeft->iNode;
................................................................................
  if( pNode->iNode==1 ){
    rc = rtreeInsertCell(pRtree, pLeft->pParent, &leftbbox, iHeight+1);
    if( rc!=SQLITE_OK ){
      goto splitnode_out;
    }
  }else{
    RtreeNode *pParent = pLeft->pParent;

    int iCell = nodeParentIndex(pRtree, pLeft);

    nodeOverwriteCell(pRtree, pParent, &leftbbox, iCell);
    AdjustTree(pRtree, pParent, &leftbbox);




  }
  if( (rc = rtreeInsertCell(pRtree, pRight->pParent, &rightbbox, iHeight+1)) ){
    goto splitnode_out;
  }

  for(i=0; i<NCELL(pRight); i++){
    i64 iRowid = nodeGetRowid(pRtree, pRight, i);
................................................................................
splitnode_out:
  nodeRelease(pRtree, pRight);
  nodeRelease(pRtree, pLeft);
  sqlite3_free(aCell);
  return rc;
}












static int fixLeafParent(Rtree *pRtree, RtreeNode *pLeaf){
  int rc = SQLITE_OK;
  if( pLeaf->iNode!=1 && pLeaf->pParent==0 ){



    sqlite3_bind_int64(pRtree->pReadParent, 1, pLeaf->iNode);
    if( sqlite3_step(pRtree->pReadParent)==SQLITE_ROW ){









      i64 iNode = sqlite3_column_int64(pRtree->pReadParent, 0);


      rc = nodeAcquire(pRtree, iNode, 0, &pLeaf->pParent);
    }else{
      rc = SQLITE_ERROR;
    }

    sqlite3_reset(pRtree->pReadParent);
    if( rc==SQLITE_OK ){
      rc = fixLeafParent(pRtree, pLeaf->pParent);
    }


  }
  return rc;
}

static int deleteCell(Rtree *, RtreeNode *, int, int);

static int removeNode(Rtree *pRtree, RtreeNode *pNode, int iHeight){
  int rc;

  RtreeNode *pParent;
  int iCell;

  assert( pNode->nRef==1 );

  /* Remove the entry in the parent cell. */
  iCell = nodeParentIndex(pRtree, pNode);

  pParent = pNode->pParent;
  pNode->pParent = 0;
  if( SQLITE_OK!=(rc = deleteCell(pRtree, pParent, iCell, iHeight+1)) 

   || SQLITE_OK!=(rc = nodeRelease(pRtree, pParent))
  ){




    return rc;
  }

  /* Remove the xxx_node entry. */
  sqlite3_bind_int64(pRtree->pDeleteNode, 1, pNode->iNode);
  sqlite3_step(pRtree->pDeleteNode);
  if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteNode)) ){
................................................................................
  pNode->pNext = pRtree->pDeleted;
  pNode->nRef++;
  pRtree->pDeleted = pNode;

  return SQLITE_OK;
}

static void fixBoundingBox(Rtree *pRtree, RtreeNode *pNode){
  RtreeNode *pParent = pNode->pParent;

  if( pParent ){
    int ii; 
    int nCell = NCELL(pNode);
    RtreeCell box;                            /* Bounding box for pNode */
    nodeGetCell(pRtree, pNode, 0, &box);
    for(ii=1; ii<nCell; ii++){
      RtreeCell cell;
      nodeGetCell(pRtree, pNode, ii, &cell);
      cellUnion(pRtree, &box, &cell);
    }
    box.iRowid = pNode->iNode;
    ii = nodeParentIndex(pRtree, pNode);

    nodeOverwriteCell(pRtree, pParent, &box, ii);
    fixBoundingBox(pRtree, pParent);
  }


}

/*
** Delete the cell at index iCell of node pNode. After removing the
** cell, adjust the r-tree data structure if required.
*/
static int deleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell, int iHeight){

  int rc;

  if( SQLITE_OK!=(rc = fixLeafParent(pRtree, pNode)) ){
    return rc;
  }

  /* Remove the cell from the node. This call just moves bytes around
................................................................................
  nodeDeleteCell(pRtree, pNode, iCell);

  /* If the node is not the tree root and now has less than the minimum
  ** number of cells, remove it from the tree. Otherwise, update the
  ** cell in the parent node so that it tightly contains the updated
  ** node.
  */
  if( pNode->iNode!=1 ){
    RtreeNode *pParent = pNode->pParent;

    if( (pParent->iNode!=1 || NCELL(pParent)!=1) 
     && (NCELL(pNode)<RTREE_MINCELLS(pRtree))
    ){
      rc = removeNode(pRtree, pNode, iHeight);
    }else{
      fixBoundingBox(pRtree, pNode);
    }
  }

  return rc;
}

static int Reinsert(
................................................................................
        rc = rowidWrite(pRtree, p->iRowid, pNode->iNode);
      }else{
        rc = parentWrite(pRtree, p->iRowid, pNode->iNode);
      }
    }
  }
  if( rc==SQLITE_OK ){
    fixBoundingBox(pRtree, pNode);
  }
  for(; rc==SQLITE_OK && ii<nCell; ii++){
    /* Find a node to store this cell in. pNode->iNode currently contains
    ** the height of the sub-tree headed by the cell.
    */
    RtreeNode *pInsert;
    RtreeCell *p = &aCell[aOrder[ii]];
................................................................................
      pRtree->iReinsertHeight = iHeight;
      rc = Reinsert(pRtree, pNode, pCell, iHeight);
    }
#else
    rc = SplitNode(pRtree, pNode, pCell, iHeight);
#endif
  }else{
    AdjustTree(pRtree, pNode, pCell);

    if( iHeight==0 ){
      rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
    }else{
      rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);

    }
  }
  return rc;
}

static int reinsertNodeContent(Rtree *pRtree, RtreeNode *pNode){
  int ii;
................................................................................
){
  Rtree *pRtree = (Rtree *)pVtab;
  int rc = SQLITE_OK;

  rtreeReference(pRtree);

  assert(nData>=1);
  assert(hashIsEmpty(pRtree));

  /* If azData[0] is not an SQL NULL value, it is the rowid of a
  ** record to delete from the r-tree table. The following block does
  ** just that.
  */
  if( sqlite3_value_type(azData[0])!=SQLITE_NULL ){
    i64 iDelete;                /* The rowid to delete */
................................................................................
      iDelete = sqlite3_value_int64(azData[0]);
      rc = findLeafNode(pRtree, iDelete, &pLeaf);
    }

    /* Delete the cell in question from the leaf node. */
    if( rc==SQLITE_OK ){
      int rc2;
      iCell = nodeRowidIndex(pRtree, pLeaf, iDelete);

      rc = deleteCell(pRtree, pLeaf, iCell, 0);

      rc2 = nodeRelease(pRtree, pLeaf);
      if( rc==SQLITE_OK ){
        rc = rc2;
      }
    }

    /* Delete the corresponding entry in the <rtree>_rowid table. */
................................................................................
    ** it, schedule the contents of the child for reinsertion and 
    ** reduce the tree height by one.
    **
    ** This is equivalent to copying the contents of the child into
    ** the root node (the operation that Gutman's paper says to perform 
    ** in this scenario).
    */
    if( rc==SQLITE_OK && pRtree->iDepth>0 ){
      if( rc==SQLITE_OK && NCELL(pRoot)==1 ){
        RtreeNode *pChild;
        i64 iChild = nodeGetRowid(pRtree, pRoot, 0);
        rc = nodeAcquire(pRtree, iChild, pRoot, &pChild);
        if( rc==SQLITE_OK ){
          rc = removeNode(pRtree, pChild, pRtree->iDepth-1);
        }


        if( rc==SQLITE_OK ){
          pRtree->iDepth--;
          writeInt16(pRoot->zData, pRtree->iDepth);
          pRoot->isDirty = 1;
        }
      }
    }

    /* Re-insert the contents of any underfull nodes removed from the tree. */
    for(pLeaf=pRtree->pDeleted; pLeaf; pLeaf=pRtree->pDeleted){
      if( rc==SQLITE_OK ){
        rc = reinsertNodeContent(pRtree, pLeaf);
................................................................................
      if( SQLITE_ROW==sqlite3_step(pRtree->pReadRowid) ){
        sqlite3_reset(pRtree->pReadRowid);
        rc = SQLITE_CONSTRAINT;
        goto constraint;
      }
      rc = sqlite3_reset(pRtree->pReadRowid);
    }


    if( rc==SQLITE_OK ){
      rc = ChooseLeaf(pRtree, &cell, 0, &pLeaf);
    }
    if( rc==SQLITE_OK ){
      int rc2;
      pRtree->iReinsertHeight = -1;
................................................................................
  char **pzErr,                       /* OUT: Error message, if any */
  int isCreate                        /* True for xCreate, false for xConnect */
){
  int rc = SQLITE_OK;
  Rtree *pRtree;
  int nDb;              /* Length of string argv[1] */
  int nName;            /* Length of string argv[2] */
  int eCoordType = (int)pAux;

  const char *aErrMsg[] = {
    0,                                                    /* 0 */
    "Wrong number of columns for an rtree table",         /* 1 */
    "Too few columns for an rtree table",                 /* 2 */
    "Too many columns for an rtree table"                 /* 3 */
  };
................................................................................

/*
** Register the r-tree module with database handle db. This creates the
** virtual table module "rtree" and the debugging/analysis scalar 
** function "rtreenode".
*/
int sqlite3RtreeInit(sqlite3 *db){

  int rc = SQLITE_OK;

  if( rc==SQLITE_OK ){
    int utf8 = SQLITE_UTF8;
    rc = sqlite3_create_function(db, "rtreenode", 2, utf8, 0, rtreenode, 0, 0);
  }
  if( rc==SQLITE_OK ){
    int utf8 = SQLITE_UTF8;
    rc = sqlite3_create_function(db, "rtreedepth", 1, utf8, 0,rtreedepth, 0, 0);
  }
  if( rc==SQLITE_OK ){
    void *c = (void *)RTREE_COORD_REAL32;
    rc = sqlite3_create_module_v2(db, "rtree", &rtreeModule, c, 0);
................................................................................
  if( rc==SQLITE_OK ){
    void *c = (void *)RTREE_COORD_INT32;
    rc = sqlite3_create_module_v2(db, "rtree_i32", &rtreeModule, c, 0);
  }

  return rc;
}




































































#if !SQLITE_CORE
int sqlite3_extension_init(
  sqlite3 *db,
  char **pzErrMsg,
  const sqlite3_api_routines *pApi
){
  SQLITE_EXTENSION_INIT2(pApi)
  return sqlite3RtreeInit(db);
}
#endif

#endif







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**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
** This file contains code for implementations of the r-tree and r*-tree
** algorithms packaged as an SQLite virtual table module.
*/

/*
** Database Format of R-Tree Tables
** --------------------------------
**
** The data structure for a single virtual r-tree table is stored in three 
** native SQLite tables declared as follows. In each case, the '%' character
** in the table name is replaced with the user-supplied name of the r-tree
** table.
**
**   CREATE TABLE %_node(nodeno INTEGER PRIMARY KEY, data BLOB)
**   CREATE TABLE %_parent(nodeno INTEGER PRIMARY KEY, parentnode INTEGER)
**   CREATE TABLE %_rowid(rowid INTEGER PRIMARY KEY, nodeno INTEGER)
**
** The data for each node of the r-tree structure is stored in the %_node
** table. For each node that is not the root node of the r-tree, there is
** an entry in the %_parent table associating the node with its parent.
** And for each row of data in the table, there is an entry in the %_rowid
** table that maps from the entries rowid to the id of the node that it
** is stored on.
**
** The root node of an r-tree always exists, even if the r-tree table is
** empty. The nodeno of the root node is always 1. All other nodes in the
** table must be the same size as the root node. The content of each node
** is formatted as follows:
**
**   1. If the node is the root node (node 1), then the first 2 bytes
**      of the node contain the tree depth as a big-endian integer.
**      For non-root nodes, the first 2 bytes are left unused.
**
**   2. The next 2 bytes contain the number of entries currently 
**      stored in the node.
**
**   3. The remainder of the node contains the node entries. Each entry
**      consists of a single 8-byte integer followed by an even number
**      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
................................................................................
  #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

#include <string.h>
#include <assert.h>

#ifndef SQLITE_AMALGAMATION
#include "sqlite3rtree.h"
typedef sqlite3_int64 i64;
typedef unsigned char u8;
typedef unsigned int u32;
#endif

typedef struct Rtree Rtree;
typedef struct RtreeCursor RtreeCursor;
typedef struct RtreeNode RtreeNode;
typedef struct RtreeCell RtreeCell;
typedef struct RtreeConstraint RtreeConstraint;
typedef struct RtreeMatchArg RtreeMatchArg;
typedef struct RtreeGeomCallback RtreeGeomCallback;
typedef union RtreeCoord RtreeCoord;

/* The rtree may have between 1 and RTREE_MAX_DIMENSIONS dimensions. */
#define RTREE_MAX_DIMENSIONS 5

/* Size of hash table Rtree.aHash. This hash table is not expected to
** ever contain very many entries, so a fixed number of buckets is 
................................................................................
** If an R*-tree "Reinsert" operation is required, the same number of
** cells are removed from the overfull node and reinserted into the tree.
*/
#define RTREE_MINCELLS(p) ((((p)->iNodeSize-4)/(p)->nBytesPerCell)/3)
#define RTREE_REINSERT(p) RTREE_MINCELLS(p)
#define RTREE_MAXCELLS 51

/*
** The smallest possible node-size is (512-64)==448 bytes. And the largest
** supported cell size is 48 bytes (8 byte rowid + ten 4 byte coordinates).
** Therefore all non-root nodes must contain at least 3 entries. Since 
** 2^40 is greater than 2^64, an r-tree structure always has a depth of
** 40 or less.
*/
#define RTREE_MAX_DEPTH 40

/* 
** An rtree cursor object.
*/
struct RtreeCursor {
  sqlite3_vtab_cursor base;
  RtreeNode *pNode;                 /* Node cursor is currently pointing at */
  int iCell;                        /* Index of current cell in pNode */
................................................................................
    ((double)coord.i)                             \
)

/*
** A search constraint.
*/
struct RtreeConstraint {
  int iCoord;                     /* Index of constrained coordinate */
  int op;                         /* Constraining operation */
  double rValue;                  /* Constraint value. */
  int (*xGeom)(sqlite3_rtree_geometry *, int, double *, int *);
  sqlite3_rtree_geometry *pGeom;  /* Constraint callback argument for a MATCH */
};

/* Possible values for RtreeConstraint.op */
#define RTREE_EQ    0x41
#define RTREE_LE    0x42
#define RTREE_LT    0x43
#define RTREE_GE    0x44
#define RTREE_GT    0x45
#define RTREE_MATCH 0x46

/* 
** An rtree structure node.















*/
struct RtreeNode {
  RtreeNode *pParent;               /* Parent node */
  i64 iNode;
  int nRef;
  int isDirty;
  u8 *zData;
................................................................................
** Structure to store a deserialized rtree record.
*/
struct RtreeCell {
  i64 iRowid;
  RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];
};


/*
** Value for the first field of every RtreeMatchArg object. The MATCH
** operator tests that the first field of a blob operand matches this
** value to avoid operating on invalid blobs (which could cause a segfault).
*/
#define RTREE_GEOMETRY_MAGIC 0x891245AB

/*
** An instance of this structure must be supplied as a blob argument to
** the right-hand-side of an SQL MATCH operator used to constrain an
** r-tree query.
*/
struct RtreeMatchArg {
  u32 magic;                      /* Always RTREE_GEOMETRY_MAGIC */
  int (*xGeom)(sqlite3_rtree_geometry *, int, double *, int *);
  void *pContext;
  int nParam;
  double aParam[1];
};

/*
** When a geometry callback is created (see sqlite3_rtree_geometry_callback),
** a single instance of the following structure is allocated. It is used
** as the context for the user-function created by by s_r_g_c(). The object
** is eventually deleted by the destructor mechanism provided by
** sqlite3_create_function_v2() (which is called by s_r_g_c() to create
** the geometry callback function).
*/
struct RtreeGeomCallback {
  int (*xGeom)(sqlite3_rtree_geometry *, int, double *, int *);
  void *pContext;
};

#ifndef MAX
# define MAX(x,y) ((x) < (y) ? (y) : (x))
#endif
#ifndef MIN
# define MIN(x,y) ((x) > (y) ? (y) : (x))
#endif

................................................................................
  }
}

/*
** Clear the content of node p (set all bytes to 0x00).
*/
static void nodeZero(Rtree *pRtree, RtreeNode *p){

  memset(&p->zData[2], 0, pRtree->iNodeSize-2);
  p->isDirty = 1;

}

/*
** Given a node number iNode, return the corresponding key to use
** in the Rtree.aHash table.
*/
static int nodeHash(i64 iNode){
................................................................................

/*
** Search the node hash table for node iNode. If found, return a pointer
** to it. Otherwise, return 0.
*/
static RtreeNode *nodeHashLookup(Rtree *pRtree, i64 iNode){
  RtreeNode *p;

  for(p=pRtree->aHash[nodeHash(iNode)]; p && p->iNode!=iNode; p=p->pNext);
  return p;
}

/*
** Add node pNode to the node hash table.
*/
static void nodeHashInsert(Rtree *pRtree, RtreeNode *pNode){

  int iHash;
  assert( pNode->pNext==0 );
  iHash = nodeHash(pNode->iNode);
  pNode->pNext = pRtree->aHash[iHash];
  pRtree->aHash[iHash] = pNode;

}

/*
** Remove node pNode from the node hash table.
*/
static void nodeHashDelete(Rtree *pRtree, RtreeNode *pNode){
  RtreeNode **pp;
................................................................................

/*
** Allocate and return new r-tree node. Initially, (RtreeNode.iNode==0),
** indicating that node has not yet been assigned a node number. It is
** assigned a node number when nodeWrite() is called to write the
** node contents out to the database.
*/
static RtreeNode *nodeNew(Rtree *pRtree, RtreeNode *pParent){
  RtreeNode *pNode;
  pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);
  if( pNode ){
    memset(pNode, 0, sizeof(RtreeNode) + pRtree->iNodeSize);
    pNode->zData = (u8 *)&pNode[1];
    pNode->nRef = 1;
    pNode->pParent = pParent;
    pNode->isDirty = 1;
    nodeReference(pParent);
  }
  return pNode;
................................................................................
nodeAcquire(
  Rtree *pRtree,             /* R-tree structure */
  i64 iNode,                 /* Node number to load */
  RtreeNode *pParent,        /* Either the parent node or NULL */
  RtreeNode **ppNode         /* OUT: Acquired node */
){
  int rc;
  int rc2 = SQLITE_OK;
  RtreeNode *pNode;

  /* Check if the requested node is already in the hash table. If so,
  ** increase its reference count and return it.
  */
  if( (pNode = nodeHashLookup(pRtree, iNode)) ){
    assert( !pParent || !pNode->pParent || pNode->pParent==pParent );
................................................................................
      pNode->pParent = pParent;
    }
    pNode->nRef++;
    *ppNode = pNode;
    return SQLITE_OK;
  }

  sqlite3_bind_int64(pRtree->pReadNode, 1, iNode);
  rc = sqlite3_step(pRtree->pReadNode);
  if( rc==SQLITE_ROW ){
    const u8 *zBlob = sqlite3_column_blob(pRtree->pReadNode, 0);
    if( pRtree->iNodeSize==sqlite3_column_bytes(pRtree->pReadNode, 0) ){
      pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode)+pRtree->iNodeSize);
      if( !pNode ){

        rc2 = SQLITE_NOMEM;

      }else{
        pNode->pParent = pParent;
        pNode->zData = (u8 *)&pNode[1];
        pNode->nRef = 1;
        pNode->iNode = iNode;
        pNode->isDirty = 0;
        pNode->pNext = 0;






        memcpy(pNode->zData, zBlob, pRtree->iNodeSize);
        nodeReference(pParent);



      }
    }

  }
  rc = sqlite3_reset(pRtree->pReadNode);
  if( rc==SQLITE_OK ) rc = rc2;

  /* If the root node was just loaded, set pRtree->iDepth to the height
  ** of the r-tree structure. A height of zero means all data is stored on
  ** the root node. A height of one means the children of the root node
  ** are the leaves, and so on. If the depth as specified on the root node
  ** is greater than RTREE_MAX_DEPTH, the r-tree structure must be corrupt.
  */
  if( pNode && iNode==1 ){
    pRtree->iDepth = readInt16(pNode->zData);
    if( pRtree->iDepth>RTREE_MAX_DEPTH ){
      rc = SQLITE_CORRUPT;
    }
  }

  /* If no error has occurred so far, check if the "number of entries"
  ** field on the node is too large. If so, set the return code to 
  ** SQLITE_CORRUPT.
  */
  if( pNode && rc==SQLITE_OK ){
    if( NCELL(pNode)>((pRtree->iNodeSize-4)/pRtree->nBytesPerCell) ){
      rc = SQLITE_CORRUPT;
    }
  }

  if( rc==SQLITE_OK ){
    if( pNode!=0 ){
      nodeHashInsert(pRtree, pNode);

    }else{
      rc = SQLITE_CORRUPT;
    }
    *ppNode = pNode;
  }else{
    sqlite3_free(pNode);
    *ppNode = 0;
  }

  return rc;
}

/*
** Overwrite cell iCell of node pNode with the contents of pCell.
................................................................................
){
  int nCell;                    /* Current number of cells in pNode */
  int nMaxCell;                 /* Maximum number of cells for pNode */

  nMaxCell = (pRtree->iNodeSize-4)/pRtree->nBytesPerCell;
  nCell = NCELL(pNode);

  assert( nCell<=nMaxCell );

  if( nCell<nMaxCell ){
    nodeOverwriteCell(pRtree, pNode, pCell, nCell);
    writeInt16(&pNode->zData[2], nCell+1);
    pNode->isDirty = 1;
  }

  return (nCell==nMaxCell);
................................................................................
    rc = SQLITE_OK;
  }
  *ppCursor = (sqlite3_vtab_cursor *)pCsr;

  return rc;
}


/*
** Free the RtreeCursor.aConstraint[] array and its contents.
*/
static void freeCursorConstraints(RtreeCursor *pCsr){
  if( pCsr->aConstraint ){
    int i;                        /* Used to iterate through constraint array */
    for(i=0; i<pCsr->nConstraint; i++){
      sqlite3_rtree_geometry *pGeom = pCsr->aConstraint[i].pGeom;
      if( pGeom ){
        if( pGeom->xDelUser ) pGeom->xDelUser(pGeom->pUser);
        sqlite3_free(pGeom);
      }
    }
    sqlite3_free(pCsr->aConstraint);
    pCsr->aConstraint = 0;
  }
}

/* 
** Rtree virtual table module xClose method.
*/
static int rtreeClose(sqlite3_vtab_cursor *cur){
  Rtree *pRtree = (Rtree *)(cur->pVtab);
  int rc;
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  freeCursorConstraints(pCsr);
  rc = nodeRelease(pRtree, pCsr->pNode);
  sqlite3_free(pCsr);
  return rc;
}

/*
** Rtree virtual table module xEof method.
................................................................................
** Return non-zero if the cursor does not currently point to a valid 
** record (i.e if the scan has finished), or zero otherwise.
*/
static int rtreeEof(sqlite3_vtab_cursor *cur){
  RtreeCursor *pCsr = (RtreeCursor *)cur;
  return (pCsr->pNode==0);
}

/*
** The r-tree constraint passed as the second argument to this function is
** guaranteed to be a MATCH constraint.
*/
static int testRtreeGeom(
  Rtree *pRtree,                  /* R-Tree object */
  RtreeConstraint *pConstraint,   /* MATCH constraint to test */
  RtreeCell *pCell,               /* Cell to test */
  int *pbRes                      /* OUT: Test result */
){
  int i;
  double aCoord[RTREE_MAX_DIMENSIONS*2];
  int nCoord = pRtree->nDim*2;

  assert( pConstraint->op==RTREE_MATCH );
  assert( pConstraint->pGeom );

  for(i=0; i<nCoord; i++){
    aCoord[i] = DCOORD(pCell->aCoord[i]);
  }
  return pConstraint->xGeom(pConstraint->pGeom, nCoord, aCoord, pbRes);
}

/* 
** Cursor pCursor currently points to a cell in a non-leaf page.
** Set *pbEof to true if the sub-tree headed by the cell is filtered
** (excluded) by the constraints in the pCursor->aConstraint[] 
** array, or false otherwise.
**
** Return SQLITE_OK if successful or an SQLite error code if an error
** occurs within a geometry callback.
*/
static int testRtreeCell(Rtree *pRtree, RtreeCursor *pCursor, int *pbEof){
  RtreeCell cell;
  int ii;
  int bRes = 0;

  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
  for(ii=0; bRes==0 && ii<pCursor->nConstraint; ii++){
    RtreeConstraint *p = &pCursor->aConstraint[ii];
    double cell_min = DCOORD(cell.aCoord[(p->iCoord>>1)*2]);
    double cell_max = DCOORD(cell.aCoord[(p->iCoord>>1)*2+1]);

    assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
        || p->op==RTREE_GT || p->op==RTREE_EQ || p->op==RTREE_MATCH
    );

    switch( p->op ){
      case RTREE_LE: case RTREE_LT: 
        bRes = p->rValue<cell_min; 
        break;

      case RTREE_GE: case RTREE_GT: 
        bRes = p->rValue>cell_max; 
        break;

      case RTREE_EQ:
        bRes = (p->rValue>cell_max || p->rValue<cell_min);
        break;

      default: {
        int rc;
        assert( p->op==RTREE_MATCH );
        rc = testRtreeGeom(pRtree, p, &cell, &bRes);
        if( rc!=SQLITE_OK ){
          return rc;
        }
        bRes = !bRes;
        break;
      }
    }
  }

  *pbEof = bRes;
  return SQLITE_OK;
}

/* 
** Test if the cell that cursor pCursor currently points to
** would be filtered (excluded) by the constraints in the 
** pCursor->aConstraint[] array. If so, set *pbEof to true before
** returning. If the cell is not filtered (excluded) by the constraints,
** set pbEof to zero.
**
** Return SQLITE_OK if successful or an SQLite error code if an error
** occurs within a geometry callback.
**
** This function assumes that the cell is part of a leaf node.
*/
static int testRtreeEntry(Rtree *pRtree, RtreeCursor *pCursor, int *pbEof){
  RtreeCell cell;
  int ii;
  *pbEof = 0;

  nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
  for(ii=0; ii<pCursor->nConstraint; ii++){
    RtreeConstraint *p = &pCursor->aConstraint[ii];
    double coord = DCOORD(cell.aCoord[p->iCoord]);
    int res;
    assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE 
        || p->op==RTREE_GT || p->op==RTREE_EQ || p->op==RTREE_MATCH
    );
    switch( p->op ){
      case RTREE_LE: res = (coord<=p->rValue); break;
      case RTREE_LT: res = (coord<p->rValue);  break;
      case RTREE_GE: res = (coord>=p->rValue); break;
      case RTREE_GT: res = (coord>p->rValue);  break;
      case RTREE_EQ: res = (coord==p->rValue); break;
      default: {
        int rc;
        assert( p->op==RTREE_MATCH );
        rc = testRtreeGeom(pRtree, p, &cell, &res);
        if( rc!=SQLITE_OK ){
          return rc;
        }
        break;
      }
    }

    if( !res ){
      *pbEof = 1;
      return SQLITE_OK;
    }
  }

  return SQLITE_OK;
}

/*
** Cursor pCursor currently points at a node that heads a sub-tree of
** height iHeight (if iHeight==0, then the node is a leaf). Descend
** to point to the left-most cell of the sub-tree that matches the 
** configured constraints.
................................................................................

  RtreeNode *pSavedNode = pCursor->pNode;
  int iSavedCell = pCursor->iCell;

  assert( iHeight>=0 );

  if( iHeight==0 ){
    rc = testRtreeEntry(pRtree, pCursor, &isEof);
  }else{
    rc = testRtreeCell(pRtree, pCursor, &isEof);
  }
  if( rc!=SQLITE_OK || isEof || iHeight==0 ){
    *pEof = isEof;
    return rc;
  }

  iRowid = nodeGetRowid(pRtree, pCursor->pNode, pCursor->iCell);
  rc = nodeAcquire(pRtree, iRowid, pCursor->pNode, &pChild);
  if( rc!=SQLITE_OK ){
    return rc;
  }
................................................................................
  return SQLITE_OK;
}

/*
** One of the cells in node pNode is guaranteed to have a 64-bit 
** integer value equal to iRowid. Return the index of this cell.
*/
static int nodeRowidIndex(
  Rtree *pRtree, 
  RtreeNode *pNode, 
  i64 iRowid,
  int *piIndex
){
  int ii;
  int nCell = NCELL(pNode);
  for(ii=0; ii<nCell; ii++){
    if( nodeGetRowid(pRtree, pNode, ii)==iRowid ){

      *piIndex = ii;
      return SQLITE_OK;
    }
  }
  return SQLITE_CORRUPT;
}

/*
** Return the index of the cell containing a pointer to node pNode
** in its parent. If pNode is the root node, return -1.
*/
static int nodeParentIndex(Rtree *pRtree, RtreeNode *pNode, int *piIndex){
  RtreeNode *pParent = pNode->pParent;
  if( pParent ){
    return nodeRowidIndex(pRtree, pParent, pNode->iNode, piIndex);
  }
  *piIndex = -1;
  return SQLITE_OK;
}

/* 
** Rtree virtual table module xNext method.
*/
static int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){
  Rtree *pRtree = (Rtree *)(pVtabCursor->pVtab);
  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
  int rc = SQLITE_OK;

  /* RtreeCursor.pNode must not be NULL. If is is NULL, then this cursor is
  ** already at EOF. It is against the rules to call the xNext() method of
  ** a cursor that has already reached EOF.
  */
  assert( pCsr->pNode );

  if( pCsr->iStrategy==1 ){
    /* This "scan" is a direct lookup by rowid. There is no next entry. */
    nodeRelease(pRtree, pCsr->pNode);
    pCsr->pNode = 0;
  }else{


    /* Move to the next entry that matches the configured constraints. */
    int iHeight = 0;
    while( pCsr->pNode ){
      RtreeNode *pNode = pCsr->pNode;
      int nCell = NCELL(pNode);
      for(pCsr->iCell++; pCsr->iCell<nCell; pCsr->iCell++){
        int isEof;
        rc = descendToCell(pRtree, pCsr, iHeight, &isEof);
        if( rc!=SQLITE_OK || !isEof ){
          return rc;
        }
      }
      pCsr->pNode = pNode->pParent;
      rc = nodeParentIndex(pRtree, pNode, &pCsr->iCell);
      if( rc!=SQLITE_OK ){
        return rc;
      }
      nodeReference(pCsr->pNode);
      nodeRelease(pRtree, pNode);
      iHeight++;
    }
  }

  return rc;
................................................................................
    sqlite3_reset(pRtree->pReadRowid);
  }else{
    rc = sqlite3_reset(pRtree->pReadRowid);
  }
  return rc;
}

/*
** This function is called to configure the RtreeConstraint object passed
** as the second argument for a MATCH constraint. The value passed as the
** first argument to this function is the right-hand operand to the MATCH
** operator.
*/
static int deserializeGeometry(sqlite3_value *pValue, RtreeConstraint *pCons){
  RtreeMatchArg *p;
  sqlite3_rtree_geometry *pGeom;
  int nBlob;

  /* Check that value is actually a blob. */
  if( !sqlite3_value_type(pValue)==SQLITE_BLOB ) return SQLITE_ERROR;

  /* Check that the blob is roughly the right size. */
  nBlob = sqlite3_value_bytes(pValue);
  if( nBlob<sizeof(RtreeMatchArg) 
   || ((nBlob-sizeof(RtreeMatchArg))%sizeof(double))!=0
  ){
    return SQLITE_ERROR;
  }

  pGeom = (sqlite3_rtree_geometry *)sqlite3_malloc(
      sizeof(sqlite3_rtree_geometry) + nBlob
  );
  if( !pGeom ) return SQLITE_NOMEM;
  memset(pGeom, 0, sizeof(sqlite3_rtree_geometry));
  p = (RtreeMatchArg *)&pGeom[1];

  memcpy(p, sqlite3_value_blob(pValue), nBlob);
  if( p->magic!=RTREE_GEOMETRY_MAGIC 
   || nBlob!=(sizeof(RtreeMatchArg) + (p->nParam-1)*sizeof(double))
  ){
    sqlite3_free(pGeom);
    return SQLITE_ERROR;
  }

  pGeom->pContext = p->pContext;
  pGeom->nParam = p->nParam;
  pGeom->aParam = p->aParam;

  pCons->xGeom = p->xGeom;
  pCons->pGeom = pGeom;
  return SQLITE_OK;
}

/* 
** Rtree virtual table module xFilter method.
*/
static int rtreeFilter(
  sqlite3_vtab_cursor *pVtabCursor, 
  int idxNum, const char *idxStr,
................................................................................

  RtreeNode *pRoot = 0;
  int ii;
  int rc = SQLITE_OK;

  rtreeReference(pRtree);

  freeCursorConstraints(pCsr);

  pCsr->iStrategy = idxNum;

  if( idxNum==1 ){
    /* Special case - lookup by rowid. */
    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */
    i64 iRowid = sqlite3_value_int64(argv[0]);
    rc = findLeafNode(pRtree, iRowid, &pLeaf);
    pCsr->pNode = pLeaf; 
    if( pLeaf ){
      assert( rc==SQLITE_OK );
      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &pCsr->iCell);
    }
  }else{
    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
    ** with the configured constraints. 
    */
    if( argc>0 ){
      pCsr->aConstraint = sqlite3_malloc(sizeof(RtreeConstraint)*argc);
      pCsr->nConstraint = argc;
      if( !pCsr->aConstraint ){
        rc = SQLITE_NOMEM;
      }else{
        memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*argc);
        assert( (idxStr==0 && argc==0) || strlen(idxStr)==argc*2 );
        for(ii=0; ii<argc; ii++){
          RtreeConstraint *p = &pCsr->aConstraint[ii];
          p->op = idxStr[ii*2];
          p->iCoord = idxStr[ii*2+1]-'a';
          if( p->op==RTREE_MATCH ){
            /* A MATCH operator. The right-hand-side must be a blob that
            ** can be cast into an RtreeMatchArg object. One created using
            ** an sqlite3_rtree_geometry_callback() SQL user function.
            */
            rc = deserializeGeometry(argv[ii], p);
            if( rc!=SQLITE_OK ){
              break;
            }
          }else{
            p->rValue = sqlite3_value_double(argv[ii]);
          }
        }
      }
    }
  
    if( rc==SQLITE_OK ){
      pCsr->pNode = 0;
      rc = nodeAcquire(pRtree, 1, 0, &pRoot);
................................................................................
** Rtree virtual table module xBestIndex method. There are three
** table scan strategies to choose from (in order from most to 
** least desirable):
**
**   idxNum     idxStr        Strategy
**   ------------------------------------------------
**     1        Unused        Direct lookup by rowid.
**     2        See below     R-tree query or full-table scan.

**   ------------------------------------------------
**
** If strategy 1 is used, then idxStr is not meaningful. If strategy
** 2 is used, idxStr is formatted to contain 2 bytes for each 
** constraint used. The first two bytes of idxStr correspond to 
** the constraint in sqlite3_index_info.aConstraintUsage[] with
** (argvIndex==1) etc.
**
** The first of each pair of bytes in idxStr identifies the constraint
** operator as follows:
................................................................................
**   Operator    Byte Value
**   ----------------------
**      =        0x41 ('A')
**     <=        0x42 ('B')
**      <        0x43 ('C')
**     >=        0x44 ('D')
**      >        0x45 ('E')
**   MATCH       0x46 ('F')
**   ----------------------
**
** The second of each pair of bytes identifies the coordinate column
** to which the constraint applies. The leftmost coordinate column
** is 'a', the second from the left 'b' etc.
*/
static int rtreeBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){
................................................................................
      ** considered almost as quick as a direct rowid lookup (for which 
      ** sqlite uses an internal cost of 0.0).
      */ 
      pIdxInfo->estimatedCost = 10.0;
      return SQLITE_OK;
    }

    if( p->usable && (p->iColumn>0 || p->op==SQLITE_INDEX_CONSTRAINT_MATCH) ){
      int j, opmsk;
      static const unsigned char compatible[] = { 0, 0, 1, 1, 2, 2 };
      u8 op = 0;
      switch( p->op ){
        case SQLITE_INDEX_CONSTRAINT_EQ: op = RTREE_EQ; break;
        case SQLITE_INDEX_CONSTRAINT_GT: op = RTREE_GT; break;
        case SQLITE_INDEX_CONSTRAINT_LE: op = RTREE_LE; break;
        case SQLITE_INDEX_CONSTRAINT_LT: op = RTREE_LT; break;
        case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;
        default:
          assert( p->op==SQLITE_INDEX_CONSTRAINT_MATCH );
          op = RTREE_MATCH; 
          break;
      }

      assert( op!=0 );

      /* Make sure this particular constraint has not been used before.
      ** If it has been used before, ignore it.
      **
      ** A <= or < can be used if there is a prior >= or >.
      ** A >= or > can be used if there is a prior < or <=.
      ** A <= or < is disqualified if there is a prior <=, <, or ==.
      ** A >= or > is disqualified if there is a prior >=, >, or ==.
      ** A == is disqualifed if there is any prior constraint.
      */


      assert( compatible[RTREE_EQ & 7]==0 );
      assert( compatible[RTREE_LT & 7]==1 );
      assert( compatible[RTREE_LE & 7]==1 );
      assert( compatible[RTREE_GT & 7]==2 );
      assert( compatible[RTREE_GE & 7]==2 );
      cCol = p->iColumn - 1 + 'a';
      opmsk = compatible[op & 7];
      for(j=0; j<iIdx; j+=2){
        if( zIdxStr[j+1]==cCol && (compatible[zIdxStr[j] & 7] & opmsk)!=0 ){
          op = 0;
          break;

        }
      }
      if( op ){
        assert( iIdx<sizeof(zIdxStr)-1 );
        zIdxStr[iIdx++] = op;
        zIdxStr[iIdx++] = cCol;
        pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);
................................................................................
  RtreeCell *aCell, 
  int nCell, 
  int iExclude
){
  int ii;
  float overlap = 0.0;
  for(ii=0; ii<nCell; ii++){
#if VARIANT_RSTARTREE_CHOOSESUBTREE
    if( ii!=iExclude )
#else
    assert( iExclude==-1 );
#endif
    {
      int jj;
      float o = 1.0;
      for(jj=0; jj<(pRtree->nDim*2); jj+=2){
        double x1;
        double x2;

        x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[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;
      float growth;
      float area;
      float overlap = 0.0;
      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);
      }

      if( (iCell==0) 
       || (overlap<fMinOverlap) 
       || (overlap==fMinOverlap && growth<fMinGrowth)
       || (overlap==fMinOverlap && growth==fMinGrowth && area<fMinArea)
      ){
        bBest = 1;
      }
#else
      if( iCell==0||growth<fMinGrowth||(growth==fMinGrowth && area<fMinArea) ){
        bBest = 1;
      }
#endif
      if( bBest ){
        fMinOverlap = overlap;
        fMinGrowth = growth;
        fMinArea = area;
        iBest = cell.iRowid;
      }
    }

................................................................................
}

/*
** A cell with the same content as pCell has just been inserted into
** the node pNode. This function updates the bounding box cells in
** all ancestor elements.
*/
static int AdjustTree(
  Rtree *pRtree,                    /* Rtree table */
  RtreeNode *pNode,                 /* Adjust ancestry of this node. */
  RtreeCell *pCell                  /* This cell was just inserted */
){
  RtreeNode *p = pNode;
  while( p->pParent ){

    RtreeNode *pParent = p->pParent;
    RtreeCell cell;
    int iCell;

    if( nodeParentIndex(pRtree, p, &iCell) ){
      return SQLITE_CORRUPT;
    }

    nodeGetCell(pRtree, pParent, iCell, &cell);
    if( !cellContains(pRtree, &cell, pCell) ){
      cellUnion(pRtree, &cell, pCell);
      nodeOverwriteCell(pRtree, pParent, &cell, iCell);
    }
 
    p = pParent;
  }
  return SQLITE_OK;
}

/*
** Write mapping (iRowid->iNode) to the <rtree>_rowid table.
*/
static int rowidWrite(Rtree *pRtree, sqlite3_int64 iRowid, sqlite3_int64 iNode){
  sqlite3_bind_int64(pRtree->pWriteRowid, 1, iRowid);
................................................................................
    nodeGetCell(pRtree, pNode, i, &aCell[i]);
  }
  nodeZero(pRtree, pNode);
  memcpy(&aCell[nCell], pCell, sizeof(RtreeCell));
  nCell++;

  if( pNode->iNode==1 ){
    pRight = nodeNew(pRtree, pNode);
    pLeft = nodeNew(pRtree, pNode);
    pRtree->iDepth++;
    pNode->isDirty = 1;
    writeInt16(pNode->zData, pRtree->iDepth);
  }else{
    pLeft = pNode;
    pRight = nodeNew(pRtree, pLeft->pParent);
    nodeReference(pLeft);
  }

  if( !pLeft || !pRight ){
    rc = SQLITE_NOMEM;
    goto splitnode_out;
  }
................................................................................
  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.
  ** In this case avoid the all to nodeWrite().
  */
  if( SQLITE_OK!=(rc = nodeWrite(pRtree, pRight))
   || (0==pLeft->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pLeft)))
  ){
    goto splitnode_out;
  }

  rightbbox.iRowid = pRight->iNode;
  leftbbox.iRowid = pLeft->iNode;
................................................................................
  if( pNode->iNode==1 ){
    rc = rtreeInsertCell(pRtree, pLeft->pParent, &leftbbox, iHeight+1);
    if( rc!=SQLITE_OK ){
      goto splitnode_out;
    }
  }else{
    RtreeNode *pParent = pLeft->pParent;
    int iCell;
    rc = nodeParentIndex(pRtree, pLeft, &iCell);
    if( rc==SQLITE_OK ){
      nodeOverwriteCell(pRtree, pParent, &leftbbox, iCell);
      rc = AdjustTree(pRtree, pParent, &leftbbox);
    }
    if( rc!=SQLITE_OK ){
      goto splitnode_out;
    }
  }
  if( (rc = rtreeInsertCell(pRtree, pRight->pParent, &rightbbox, iHeight+1)) ){
    goto splitnode_out;
  }

  for(i=0; i<NCELL(pRight); i++){
    i64 iRowid = nodeGetRowid(pRtree, pRight, i);
................................................................................
splitnode_out:
  nodeRelease(pRtree, pRight);
  nodeRelease(pRtree, pLeft);
  sqlite3_free(aCell);
  return rc;
}

/*
** If node pLeaf is not the root of the r-tree and its pParent pointer is 
** still NULL, load all ancestor nodes of pLeaf into memory and populate
** the pLeaf->pParent chain all the way up to the root node.
**
** This operation is required when a row is deleted (or updated - an update
** is implemented as a delete followed by an insert). SQLite provides the
** rowid of the row to delete, which can be used to find the leaf on which
** the entry resides (argument pLeaf). Once the leaf is located, this 
** function is called to determine its ancestry.
*/
static int fixLeafParent(Rtree *pRtree, RtreeNode *pLeaf){
  int rc = SQLITE_OK;

  RtreeNode *pChild = pLeaf;
  while( rc==SQLITE_OK && pChild->iNode!=1 && pChild->pParent==0 ){
    int rc2 = SQLITE_OK;          /* sqlite3_reset() return code */
    sqlite3_bind_int64(pRtree->pReadParent, 1, pChild->iNode);
    rc = sqlite3_step(pRtree->pReadParent);
    if( rc==SQLITE_ROW ){
      RtreeNode *pTest;           /* Used to test for reference loops */
      i64 iNode;                  /* Node number of parent node */

      /* Before setting pChild->pParent, test that we are not creating a
      ** loop of references (as we would if, say, pChild==pParent). We don't
      ** want to do this as it leads to a memory leak when trying to delete
      ** the referenced counted node structures.
      */
      iNode = sqlite3_column_int64(pRtree->pReadParent, 0);
      for(pTest=pLeaf; pTest && pTest->iNode!=iNode; pTest=pTest->pParent);
      if( !pTest ){
        rc2 = nodeAcquire(pRtree, iNode, 0, &pChild->pParent);


      }
    }
    rc = sqlite3_reset(pRtree->pReadParent);
    if( rc==SQLITE_OK ) rc = rc2;


    if( rc==SQLITE_OK && !pChild->pParent ) rc = SQLITE_CORRUPT;
    pChild = pChild->pParent;
  }
  return rc;
}

static int deleteCell(Rtree *, RtreeNode *, int, int);

static int removeNode(Rtree *pRtree, RtreeNode *pNode, int iHeight){
  int rc;
  int rc2;
  RtreeNode *pParent;
  int iCell;

  assert( pNode->nRef==1 );

  /* Remove the entry in the parent cell. */
  rc = nodeParentIndex(pRtree, pNode, &iCell);
  if( rc==SQLITE_OK ){
    pParent = pNode->pParent;
    pNode->pParent = 0;
    rc = deleteCell(pRtree, pParent, iCell, iHeight+1);
  }
  rc2 = nodeRelease(pRtree, pParent);

  if( rc==SQLITE_OK ){
    rc = rc2;
  }
  if( rc!=SQLITE_OK ){
    return rc;
  }

  /* Remove the xxx_node entry. */
  sqlite3_bind_int64(pRtree->pDeleteNode, 1, pNode->iNode);
  sqlite3_step(pRtree->pDeleteNode);
  if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteNode)) ){
................................................................................
  pNode->pNext = pRtree->pDeleted;
  pNode->nRef++;
  pRtree->pDeleted = pNode;

  return SQLITE_OK;
}

static int fixBoundingBox(Rtree *pRtree, RtreeNode *pNode){
  RtreeNode *pParent = pNode->pParent;
  int rc = SQLITE_OK; 
  if( pParent ){
    int ii; 
    int nCell = NCELL(pNode);
    RtreeCell box;                            /* Bounding box for pNode */
    nodeGetCell(pRtree, pNode, 0, &box);
    for(ii=1; ii<nCell; ii++){
      RtreeCell cell;
      nodeGetCell(pRtree, pNode, ii, &cell);
      cellUnion(pRtree, &box, &cell);
    }
    box.iRowid = pNode->iNode;
    rc = nodeParentIndex(pRtree, pNode, &ii);
    if( rc==SQLITE_OK ){
      nodeOverwriteCell(pRtree, pParent, &box, ii);
      rc = fixBoundingBox(pRtree, pParent);
    }
  }
  return rc;
}

/*
** Delete the cell at index iCell of node pNode. After removing the
** cell, adjust the r-tree data structure if required.
*/
static int deleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell, int iHeight){
  RtreeNode *pParent;
  int rc;

  if( SQLITE_OK!=(rc = fixLeafParent(pRtree, pNode)) ){
    return rc;
  }

  /* Remove the cell from the node. This call just moves bytes around
................................................................................
  nodeDeleteCell(pRtree, pNode, iCell);

  /* If the node is not the tree root and now has less than the minimum
  ** number of cells, remove it from the tree. Otherwise, update the
  ** cell in the parent node so that it tightly contains the updated
  ** node.
  */

  pParent = pNode->pParent;
  assert( pParent || pNode->iNode==1 );
  if( pParent ){
    if( NCELL(pNode)<RTREE_MINCELLS(pRtree) ){

      rc = removeNode(pRtree, pNode, iHeight);
    }else{
      rc = fixBoundingBox(pRtree, pNode);
    }
  }

  return rc;
}

static int Reinsert(
................................................................................
        rc = rowidWrite(pRtree, p->iRowid, pNode->iNode);
      }else{
        rc = parentWrite(pRtree, p->iRowid, pNode->iNode);
      }
    }
  }
  if( rc==SQLITE_OK ){
    rc = fixBoundingBox(pRtree, pNode);
  }
  for(; rc==SQLITE_OK && ii<nCell; ii++){
    /* Find a node to store this cell in. pNode->iNode currently contains
    ** the height of the sub-tree headed by the cell.
    */
    RtreeNode *pInsert;
    RtreeCell *p = &aCell[aOrder[ii]];
................................................................................
      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);
      }
    }
  }
  return rc;
}

static int reinsertNodeContent(Rtree *pRtree, RtreeNode *pNode){
  int ii;
................................................................................
){
  Rtree *pRtree = (Rtree *)pVtab;
  int rc = SQLITE_OK;

  rtreeReference(pRtree);

  assert(nData>=1);


  /* If azData[0] is not an SQL NULL value, it is the rowid of a
  ** record to delete from the r-tree table. The following block does
  ** just that.
  */
  if( sqlite3_value_type(azData[0])!=SQLITE_NULL ){
    i64 iDelete;                /* The rowid to delete */
................................................................................
      iDelete = sqlite3_value_int64(azData[0]);
      rc = findLeafNode(pRtree, iDelete, &pLeaf);
    }

    /* Delete the cell in question from the leaf node. */
    if( rc==SQLITE_OK ){
      int rc2;
      rc = nodeRowidIndex(pRtree, pLeaf, iDelete, &iCell);
      if( rc==SQLITE_OK ){
        rc = deleteCell(pRtree, pLeaf, iCell, 0);
      }
      rc2 = nodeRelease(pRtree, pLeaf);
      if( rc==SQLITE_OK ){
        rc = rc2;
      }
    }

    /* Delete the corresponding entry in the <rtree>_rowid table. */
................................................................................
    ** it, schedule the contents of the child for reinsertion and 
    ** reduce the tree height by one.
    **
    ** This is equivalent to copying the contents of the child into
    ** the root node (the operation that Gutman's paper says to perform 
    ** in this scenario).
    */
    if( rc==SQLITE_OK && pRtree->iDepth>0 && NCELL(pRoot)==1 ){
      int rc2;
      RtreeNode *pChild;
      i64 iChild = nodeGetRowid(pRtree, pRoot, 0);
      rc = nodeAcquire(pRtree, iChild, pRoot, &pChild);
      if( rc==SQLITE_OK ){
        rc = removeNode(pRtree, pChild, pRtree->iDepth-1);
      }
      rc2 = nodeRelease(pRtree, pChild);
      if( rc==SQLITE_OK ) rc = rc2;
      if( rc==SQLITE_OK ){
        pRtree->iDepth--;
        writeInt16(pRoot->zData, pRtree->iDepth);
        pRoot->isDirty = 1;

      }
    }

    /* Re-insert the contents of any underfull nodes removed from the tree. */
    for(pLeaf=pRtree->pDeleted; pLeaf; pLeaf=pRtree->pDeleted){
      if( rc==SQLITE_OK ){
        rc = reinsertNodeContent(pRtree, pLeaf);
................................................................................
      if( SQLITE_ROW==sqlite3_step(pRtree->pReadRowid) ){
        sqlite3_reset(pRtree->pReadRowid);
        rc = SQLITE_CONSTRAINT;
        goto constraint;
      }
      rc = sqlite3_reset(pRtree->pReadRowid);
    }
    *pRowid = cell.iRowid;

    if( rc==SQLITE_OK ){
      rc = ChooseLeaf(pRtree, &cell, 0, &pLeaf);
    }
    if( rc==SQLITE_OK ){
      int rc2;
      pRtree->iReinsertHeight = -1;
................................................................................
  char **pzErr,                       /* OUT: Error message, if any */
  int isCreate                        /* True for xCreate, false for xConnect */
){
  int rc = SQLITE_OK;
  Rtree *pRtree;
  int nDb;              /* Length of string argv[1] */
  int nName;            /* Length of string argv[2] */
  int eCoordType = (pAux ? RTREE_COORD_INT32 : RTREE_COORD_REAL32);

  const char *aErrMsg[] = {
    0,                                                    /* 0 */
    "Wrong number of columns for an rtree table",         /* 1 */
    "Too few columns for an rtree table",                 /* 2 */
    "Too many columns for an rtree table"                 /* 3 */
  };
................................................................................

/*
** Register the r-tree module with database handle db. This creates the
** virtual table module "rtree" and the debugging/analysis scalar 
** function "rtreenode".
*/
int sqlite3RtreeInit(sqlite3 *db){
  const int utf8 = SQLITE_UTF8;
  int rc;



  rc = sqlite3_create_function(db, "rtreenode", 2, utf8, 0, rtreenode, 0, 0);

  if( rc==SQLITE_OK ){
    int utf8 = SQLITE_UTF8;
    rc = sqlite3_create_function(db, "rtreedepth", 1, utf8, 0,rtreedepth, 0, 0);
  }
  if( rc==SQLITE_OK ){
    void *c = (void *)RTREE_COORD_REAL32;
    rc = sqlite3_create_module_v2(db, "rtree", &rtreeModule, c, 0);
................................................................................
  if( rc==SQLITE_OK ){
    void *c = (void *)RTREE_COORD_INT32;
    rc = sqlite3_create_module_v2(db, "rtree_i32", &rtreeModule, c, 0);
  }

  return rc;
}

/*
** A version of sqlite3_free() that can be used as a callback. This is used
** in two places - as the destructor for the blob value returned by the
** invocation of a geometry function, and as the destructor for the geometry
** functions themselves.
*/
static void doSqlite3Free(void *p){
  sqlite3_free(p);
}

/*
** Each call to sqlite3_rtree_geometry_callback() creates an ordinary SQLite
** scalar user function. This C function is the callback used for all such
** registered SQL functions.
**
** The scalar user functions return a blob that is interpreted by r-tree
** table MATCH operators.
*/
static void geomCallback(sqlite3_context *ctx, int nArg, sqlite3_value **aArg){
  RtreeGeomCallback *pGeomCtx = (RtreeGeomCallback *)sqlite3_user_data(ctx);
  RtreeMatchArg *pBlob;
  int nBlob;

  nBlob = sizeof(RtreeMatchArg) + (nArg-1)*sizeof(double);
  pBlob = (RtreeMatchArg *)sqlite3_malloc(nBlob);
  if( !pBlob ){
    sqlite3_result_error_nomem(ctx);
  }else{
    int i;
    pBlob->magic = RTREE_GEOMETRY_MAGIC;
    pBlob->xGeom = pGeomCtx->xGeom;
    pBlob->pContext = pGeomCtx->pContext;
    pBlob->nParam = nArg;
    for(i=0; i<nArg; i++){
      pBlob->aParam[i] = sqlite3_value_double(aArg[i]);
    }
    sqlite3_result_blob(ctx, pBlob, nBlob, doSqlite3Free);
  }
}

/*
** Register a new geometry function for use with the r-tree MATCH operator.
*/
int sqlite3_rtree_geometry_callback(
  sqlite3 *db,
  const char *zGeom,
  int (*xGeom)(sqlite3_rtree_geometry *, int, double *, int *),
  void *pContext
){
#if 0
  RtreeGeomCallback *pGeomCtx;      /* Context object for new user-function */

  /* Allocate and populate the context object. */
  pGeomCtx = (RtreeGeomCallback *)sqlite3_malloc(sizeof(RtreeGeomCallback));
  if( !pGeomCtx ) return SQLITE_NOMEM;
  pGeomCtx->xGeom = xGeom;
  pGeomCtx->pContext = pContext;

  /* Create the new user-function. Register a destructor function to delete
  ** the context object when it is no longer required.  */
  return sqlite3_create_function_v2(db, zGeom, -1, SQLITE_ANY, 
      (void *)pGeomCtx, geomCallback, 0, 0, doSqlite3Free
  );
#endif
  return SQLITE_MISUSE;
}

#if !SQLITE_CORE
int sqlite3_extension_init(
  sqlite3 *db,
  char **pzErrMsg,
  const sqlite3_api_routines *pApi
){
  SQLITE_EXTENSION_INIT2(pApi)
  return sqlite3RtreeInit(db);
}
#endif

#endif

Added ext/rtree/sqlite3rtree.h.

















































































































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/*
** 2010 August 30
**
** The author disclaims copyright to this source code.  In place of
** a legal notice, here is a blessing:
**
**    May you do good and not evil.
**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
*/

#ifndef _SQLITE3RTREE_H_
#define _SQLITE3RTREE_H_

#include <sqlite3.h>

#ifdef __cplusplus
extern "C" {
#endif

typedef struct sqlite3_rtree_geometry sqlite3_rtree_geometry;

/*
** Register a geometry callback named zGeom that can be used as part of an
** R-Tree geometry query as follows:
**
**   SELECT ... FROM <rtree> WHERE <rtree col> MATCH $zGeom(... params ...)
*/
int sqlite3_rtree_geometry_callback(
  sqlite3 *db,
  const char *zGeom,
  int (*xGeom)(sqlite3_rtree_geometry *, int nCoord, double *aCoord, int *pRes),
  void *pContext
);


/*
** A pointer to a structure of the following type is passed as the first
** argument to callbacks registered using rtree_geometry_callback().
*/
struct sqlite3_rtree_geometry {
  void *pContext;                 /* Copy of pContext passed to s_r_g_c() */
  int nParam;                     /* Size of array aParam[] */
  double *aParam;                 /* Parameters passed to SQL geom function */
  void *pUser;                    /* Callback implementation user data */
  void (*xDelUser)(void *);       /* Called by SQLite to clean up pUser */
};


#ifdef __cplusplus
}  /* end of the 'extern "C"' block */
#endif

#endif  /* ifndef _SQLITE3RTREE_H_ */