SQLite

             * 0.5;
    sqlite3_result_double(context, rArea);
    sqlite3_free(p);
  }            
}

/*
** If pPoly is a polygon, compute its bounding box. Then:
**
**    (1) if aCoord!=0 store the bounding box in aCoord, returning NULL
**    (2) otherwise, compute a GeoPoly for the bounding box and return the
**        new GeoPoly
**
** If pPoly is NULL but aCoord is not NULL, then compute a new GeoPoly from
** the bounding box in aCoord and return a pointer to that GeoPoly.
*/
static GeoPoly *geopolyBBox(
  sqlite3_context *context,   /* For recording the error */
  sqlite3_value *pPoly,       /* The polygon */
  RtreeCoord *aCoord,         /* Results here */
  int *pRc                    /* Error code here */
){
  GeoPoly *pOut = 0;
  GeoPoly *p;
  float mnX, mxX, mnY, mxY;
  if( pPoly==0 && aCoord!=0 ){
    p = 0;
    mnX = aCoord[0].f;
    mxX = aCoord[1].f;
    mnY = aCoord[2].f;
    mxY = aCoord[3].f;
    goto geopolyBboxFill;
  }else{
    p = geopolyFuncParam(context, pPoly, pRc);
  }
  if( p ){
    int ii;

    mnX = mxX = p->a[0];
    mnY = mxY = p->a[1];
    for(ii=1; ii<p->nVertex; ii++){
      double r = p->a[ii*2];
      if( r<mnX ) mnX = r;
      else if( r>mxX ) mxX = r;
      r = p->a[ii*2+1];
      if( r<mnY ) mnY = r;
      else if( r>mxY ) mxY = r;
    }
    if( pRc ) *pRc = SQLITE_OK;
    if( aCoord==0 ){
      geopolyBboxFill:
      pOut = sqlite3_realloc(p, sizeof(GeoPoly)+sizeof(GeoCoord)*6);
      if( pOut==0 ){
        sqlite3_free(p);
        if( context ) sqlite3_result_error_nomem(context);
        if( pRc ) *pRc = SQLITE_NOMEM;
        return 0;
      }
      pOut->nVertex = 4;
      ii = 1;
      pOut->hdr[0] = *(unsigned char*)&ii;
      pOut->hdr[1] = 0;
      pOut->hdr[2] = 0;
      pOut->hdr[3] = 4;
      pOut->a[0] = mnX;
      pOut->a[1] = mnY;
      pOut->a[2] = mxX;
      pOut->a[3] = mnY;

  GeoPoly *p = geopolyBBox(context, argv[0], 0, 0);
  if( p ){
    sqlite3_result_blob(context, p->hdr, 
       4+8*p->nVertex, SQLITE_TRANSIENT);
    sqlite3_free(p);
  }
}

/*
** State vector for the geopoly_group_bbox() aggregate function.
*/
typedef struct GeoBBox GeoBBox;
struct GeoBBox {
  int isInit;
  RtreeCoord a[4];
};


/*
** Implementation of the geopoly_group_bbox(X) aggregate SQL function.
*/
static void geopolyBBoxStep(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  RtreeCoord a[4];
  int rc = SQLITE_OK;
  (void)geopolyBBox(context, argv[0], a, &rc);
  if( rc==SQLITE_OK ){
    GeoBBox *pBBox;
    pBBox = (GeoBBox*)sqlite3_aggregate_context(context, sizeof(*pBBox));
    if( pBBox==0 ) return;
    if( pBBox->isInit==0 ){
      pBBox->isInit = 1;
      memcpy(pBBox->a, a, sizeof(RtreeCoord)*4);
    }else{
      if( a[0].f < pBBox->a[0].f ) pBBox->a[0] = a[0];
      if( a[1].f > pBBox->a[1].f ) pBBox->a[1] = a[1];
      if( a[2].f < pBBox->a[2].f ) pBBox->a[2] = a[2];
      if( a[3].f > pBBox->a[3].f ) pBBox->a[3] = a[3];
    }
  }
}
static void geopolyBBoxFinal(
  sqlite3_context *context
){
  GeoPoly *p;
  GeoBBox *pBBox;
  pBBox = (GeoBBox*)sqlite3_aggregate_context(context, 0);
  if( pBBox==0 ) return;
  p = geopolyBBox(context, 0, pBBox->a, 0);
  if( p ){
    sqlite3_result_blob(context, p->hdr, 
       4+8*p->nVertex, SQLITE_TRANSIENT);
    sqlite3_free(p);
  }
}


/*
** Determine if point (x0,y0) is beneath line segment (x1,y1)->(x2,y2).
** Returns:
**
**    +2  x0,y0 is on the line segement
**

  pSql = sqlite3_str_new(db);
  sqlite3_str_appendf(pSql, "CREATE TABLE x(_shape");
  pRtree->nAux = 1;   /* Add one for _shape */
  for(ii=3; ii<argc; ii++){
    pRtree->nAux++;
    sqlite3_str_appendf(pSql, ",%s", argv[ii]);
  }
  sqlite3_str_appendf(pSql, ");");
  zSql = sqlite3_str_finish(pSql);
  if( !zSql ){
    rc = SQLITE_NOMEM;
  }else if( SQLITE_OK!=(rc = sqlite3_declare_vtab(db, zSql)) ){
    *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
  }
  sqlite3_free(zSql);

      }else{
        sqlite3_reset(pCsr->pReadAux);
        if( rc==SQLITE_DONE ) rc = SQLITE_OK;
        return rc;
      }
    }
    sqlite3_result_value(ctx, sqlite3_column_value(pCsr->pReadAux, i+2));


  }
  return SQLITE_OK;
}


/*
** The xUpdate method for GEOPOLY module virtual tables.

     { geopolyWithinFunc,        2,    "geopoly_within"           },
     { geopolyContainsPointFunc, 3,    "geopoly_contains_point"   },
     { geopolyOverlapFunc,       2,    "geopoly_overlap"          },
     { geopolyDebugFunc,         1,    "geopoly_debug"            },
     { geopolyBBoxFunc,          1,    "geopoly_bbox"             },
     { geopolyXformFunc,         7,    "geopoly_xform"            },
  };
  static const struct {
    void (*xStep)(sqlite3_context*,int,sqlite3_value**);
    void (*xFinal)(sqlite3_context*);
    const char *zName;
  } aAgg[] = {
     { geopolyBBoxStep, geopolyBBoxFinal, "geopoly_group_bbox"    },
  };
  int i;
  for(i=0; i<sizeof(aFunc)/sizeof(aFunc[0]) && rc==SQLITE_OK; i++){
    rc = sqlite3_create_function(db, aFunc[i].zName, aFunc[i].nArg,
                                 SQLITE_UTF8, 0,
                                 aFunc[i].xFunc, 0, 0);
  }
  for(i=0; i<sizeof(aAgg)/sizeof(aAgg[0]) && rc==SQLITE_OK; i++){
    rc = sqlite3_create_function(db, aAgg[i].zName, 1, SQLITE_UTF8, 0,
                                 0, aAgg[i].xStep, aAgg[i].xFinal);
  }
  if( rc==SQLITE_OK ){
    rc = sqlite3_create_module_v2(db, "geopoly", &geopolyModule, 0, 0);
  }
  return rc;
}

  FROM geo1, querypoly
 WHERE geopoly_overlap(_shape, poly);
SELECT geopoly_svg(poly, 
         printf('style="fill:%s;fill-opacity:0.5;"',clr)
       )
  FROM querypoly;
.print '</svg>'

.print '<h1>Overlap Query And Result Bounding Box</h1>'
.print '<svg width="1000" height="800" style="border:1px solid black">'
SELECT geopoly_svg(_shape,
         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
       )
  FROM geo1, querypoly
 WHERE geopoly_overlap(_shape, poly);
SELECT geopoly_svg(geopoly_bbox(poly),
         'style="fill:none;stroke:black;stroke-width:3"'
       )
  FROM querypoly;
SELECT geopoly_svg(poly, 
         printf('style="fill:%s;fill-opacity:0.5;"',clr)
       )
  FROM querypoly;
SELECT geopoly_svg(geopoly_group_bbox(_shape),
         'style="fill:none;stroke:red;stroke-width:3"'
       )
  FROM geo1, querypoly
 WHERE geopoly_overlap(_shape, poly);
.print '</svg>'

.print '<h1>Bounding-Box Overlap Query</h1>'
.print '<svg width="1000" height="800" style="border:1px solid black">'
SELECT geopoly_svg(_shape,
         printf('style="fill:none;stroke:%s;stroke-width:1"',geo1.clr)
       ),
       geopoly_svg(geopoly_bbox(_shape),