Adding upstream version 3.40.1.upstream/3.40.1upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 1814 insertions, 0 deletions

diff --git a/ext/rtree/geopoly.c b/ext/rtree/geopoly.c
new file mode 100644
index 0000000..7b41e79
--- /dev/null
+++ b/ext/rtree/geopoly.c
@@ -0,0 +1,1814 @@
+/*
+** 2018-05-25
+**
+** 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.
+**
+******************************************************************************
+**
+** This file implements an alternative R-Tree virtual table that
+** uses polygons to express the boundaries of 2-dimensional objects.
+**
+** This file is #include-ed onto the end of "rtree.c" so that it has
+** access to all of the R-Tree internals.
+*/
+#include <stdlib.h>
+
+/* Enable -DGEOPOLY_ENABLE_DEBUG for debugging facilities */
+#ifdef GEOPOLY_ENABLE_DEBUG
+  static int geo_debug = 0;
+# define GEODEBUG(X) if(geo_debug)printf X
+#else
+# define GEODEBUG(X)
+#endif
+
+/* Character class routines */
+#ifdef sqlite3Isdigit
+   /* Use the SQLite core versions if this routine is part of the
+   ** SQLite amalgamation */
+#  define safe_isdigit(x)  sqlite3Isdigit(x)
+#  define safe_isalnum(x)  sqlite3Isalnum(x)
+#  define safe_isxdigit(x) sqlite3Isxdigit(x)
+#else
+   /* Use the standard library for separate compilation */
+#include <ctype.h>  /* amalgamator: keep */
+#  define safe_isdigit(x)  isdigit((unsigned char)(x))
+#  define safe_isalnum(x)  isalnum((unsigned char)(x))
+#  define safe_isxdigit(x) isxdigit((unsigned char)(x))
+#endif
+
+#ifndef JSON_NULL   /* The following stuff repeats things found in json1 */
+/*
+** Growing our own isspace() routine this way is twice as fast as
+** the library isspace() function.
+*/
+static const char geopolyIsSpace[] = {
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 1, 1, 0, 0, 1, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  1, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+  0, 0, 0, 0, 0, 0, 0, 0,     0, 0, 0, 0, 0, 0, 0, 0,
+};
+#define fast_isspace(x) (geopolyIsSpace[(unsigned char)x])
+#endif /* JSON NULL - back to original code */
+
+/* Compiler and version */
+#ifndef GCC_VERSION
+#if defined(__GNUC__) && !defined(SQLITE_DISABLE_INTRINSIC)
+# define GCC_VERSION (__GNUC__*1000000+__GNUC_MINOR__*1000+__GNUC_PATCHLEVEL__)
+#else
+# define GCC_VERSION 0
+#endif
+#endif
+#ifndef MSVC_VERSION
+#if defined(_MSC_VER) && !defined(SQLITE_DISABLE_INTRINSIC)
+# define MSVC_VERSION _MSC_VER
+#else
+# define MSVC_VERSION 0
+#endif
+#endif
+
+/* Datatype for coordinates
+*/
+typedef float GeoCoord;
+
+/*
+** Internal representation of a polygon.
+**
+** The polygon consists of a sequence of vertexes.  There is a line
+** segment between each pair of vertexes, and one final segment from
+** the last vertex back to the first.  (This differs from the GeoJSON
+** standard in which the final vertex is a repeat of the first.)
+**
+** The polygon follows the right-hand rule.  The area to the right of
+** each segment is "outside" and the area to the left is "inside".
+**
+** The on-disk representation consists of a 4-byte header followed by
+** the values.  The 4-byte header is:
+**
+**      encoding    (1 byte)   0=big-endian, 1=little-endian
+**      nvertex     (3 bytes)  Number of vertexes as a big-endian integer
+**
+** Enough space is allocated for 4 coordinates, to work around over-zealous
+** warnings coming from some compiler (notably, clang). In reality, the size
+** of each GeoPoly memory allocate is adjusted as necessary so that the
+** GeoPoly.a[] array at the end is the appropriate size.
+*/
+typedef struct GeoPoly GeoPoly;
+struct GeoPoly {
+  int nVertex;          /* Number of vertexes */
+  unsigned char hdr[4]; /* Header for on-disk representation */
+  GeoCoord a[8];        /* 2*nVertex values. X (longitude) first, then Y */
+};
+
+/* The size of a memory allocation needed for a GeoPoly object sufficient
+** to hold N coordinate pairs.
+*/
+#define GEOPOLY_SZ(N)  (sizeof(GeoPoly) + sizeof(GeoCoord)*2*((N)-4))
+
+/* Macros to access coordinates of a GeoPoly.
+** We have to use these macros, rather than just say p->a[i] in order
+** to silence (incorrect) UBSAN warnings if the array index is too large.
+*/
+#define GeoX(P,I)  (((GeoCoord*)(P)->a)[(I)*2])
+#define GeoY(P,I)  (((GeoCoord*)(P)->a)[(I)*2+1])
+
+
+/*
+** State of a parse of a GeoJSON input.
+*/
+typedef struct GeoParse GeoParse;
+struct GeoParse {
+  const unsigned char *z;   /* Unparsed input */
+  int nVertex;              /* Number of vertexes in a[] */
+  int nAlloc;               /* Space allocated to a[] */
+  int nErr;                 /* Number of errors encountered */
+  GeoCoord *a;          /* Array of vertexes.  From sqlite3_malloc64() */
+};
+
+/* Do a 4-byte byte swap */
+static void geopolySwab32(unsigned char *a){
+  unsigned char t = a[0];
+  a[0] = a[3];
+  a[3] = t;
+  t = a[1];
+  a[1] = a[2];
+  a[2] = t;
+}
+
+/* Skip whitespace.  Return the next non-whitespace character. */
+static char geopolySkipSpace(GeoParse *p){
+  while( fast_isspace(p->z[0]) ) p->z++;
+  return p->z[0];
+}
+
+/* Parse out a number.  Write the value into *pVal if pVal!=0.
+** return non-zero on success and zero if the next token is not a number.
+*/
+static int geopolyParseNumber(GeoParse *p, GeoCoord *pVal){
+  char c = geopolySkipSpace(p);
+  const unsigned char *z = p->z;
+  int j = 0;
+  int seenDP = 0;
+  int seenE = 0;
+  if( c=='-' ){
+    j = 1;
+    c = z[j];
+  }
+  if( c=='0' && z[j+1]>='0' && z[j+1]<='9' ) return 0;
+  for(;; j++){
+    c = z[j];
+    if( safe_isdigit(c) ) continue;
+    if( c=='.' ){
+      if( z[j-1]=='-' ) return 0;
+      if( seenDP ) return 0;
+      seenDP = 1;
+      continue;
+    }
+    if( c=='e' || c=='E' ){
+      if( z[j-1]<'0' ) return 0;
+      if( seenE ) return -1;
+      seenDP = seenE = 1;
+      c = z[j+1];
+      if( c=='+' || c=='-' ){
+        j++;
+        c = z[j+1];
+      }
+      if( c<'0' || c>'9' ) return 0;
+      continue;
+    }
+    break;
+  }
+  if( z[j-1]<'0' ) return 0;
+  if( pVal ){
+#ifdef SQLITE_AMALGAMATION
+     /* The sqlite3AtoF() routine is much much faster than atof(), if it
+     ** is available */
+     double r;
+     (void)sqlite3AtoF((const char*)p->z, &r, j, SQLITE_UTF8);
+     *pVal = r;
+#else
+     *pVal = (GeoCoord)atof((const char*)p->z);
+#endif
+  }
+  p->z += j;
+  return 1;
+}
+
+/*
+** If the input is a well-formed JSON array of coordinates with at least
+** four coordinates and where each coordinate is itself a two-value array,
+** then convert the JSON into a GeoPoly object and return a pointer to
+** that object.
+**
+** If any error occurs, return NULL.
+*/
+static GeoPoly *geopolyParseJson(const unsigned char *z, int *pRc){
+  GeoParse s;
+  int rc = SQLITE_OK;
+  memset(&s, 0, sizeof(s));
+  s.z = z;
+  if( geopolySkipSpace(&s)=='[' ){
+    s.z++;
+    while( geopolySkipSpace(&s)=='[' ){
+      int ii = 0;
+      char c;
+      s.z++;
+      if( s.nVertex>=s.nAlloc ){
+        GeoCoord *aNew;
+        s.nAlloc = s.nAlloc*2 + 16;
+        aNew = sqlite3_realloc64(s.a, s.nAlloc*sizeof(GeoCoord)*2 );
+        if( aNew==0 ){
+          rc = SQLITE_NOMEM;
+          s.nErr++;
+          break;
+        }
+        s.a = aNew;
+      }
+      while( geopolyParseNumber(&s, ii<=1 ? &s.a[s.nVertex*2+ii] : 0) ){
+        ii++;
+        if( ii==2 ) s.nVertex++;
+        c = geopolySkipSpace(&s);
+        s.z++;
+        if( c==',' ) continue;
+        if( c==']' && ii>=2 ) break;
+        s.nErr++;
+        rc = SQLITE_ERROR;
+        goto parse_json_err;
+      }
+      if( geopolySkipSpace(&s)==',' ){
+        s.z++;
+        continue;
+      }
+      break;
+    }
+    if( geopolySkipSpace(&s)==']'
+     && s.nVertex>=4
+     && s.a[0]==s.a[s.nVertex*2-2]
+     && s.a[1]==s.a[s.nVertex*2-1]
+     && (s.z++, geopolySkipSpace(&s)==0)
+    ){
+      GeoPoly *pOut;
+      int x = 1;
+      s.nVertex--;  /* Remove the redundant vertex at the end */
+      pOut = sqlite3_malloc64( GEOPOLY_SZ((sqlite3_int64)s.nVertex) );
+      x = 1;
+      if( pOut==0 ) goto parse_json_err;
+      pOut->nVertex = s.nVertex;
+      memcpy(pOut->a, s.a, s.nVertex*2*sizeof(GeoCoord));
+      pOut->hdr[0] = *(unsigned char*)&x;
+      pOut->hdr[1] = (s.nVertex>>16)&0xff;
+      pOut->hdr[2] = (s.nVertex>>8)&0xff;
+      pOut->hdr[3] = s.nVertex&0xff;
+      sqlite3_free(s.a);
+      if( pRc ) *pRc = SQLITE_OK;
+      return pOut;
+    }else{
+      s.nErr++;
+      rc = SQLITE_ERROR;
+    }
+  }
+parse_json_err:
+  if( pRc ) *pRc = rc;
+  sqlite3_free(s.a);
+  return 0;
+}
+
+/*
+** Given a function parameter, try to interpret it as a polygon, either
+** in the binary format or JSON text.  Compute a GeoPoly object and
+** return a pointer to that object.  Or if the input is not a well-formed
+** polygon, put an error message in sqlite3_context and return NULL.
+*/
+static GeoPoly *geopolyFuncParam(
+  sqlite3_context *pCtx,      /* Context for error messages */
+  sqlite3_value *pVal,        /* The value to decode */
+  int *pRc                    /* Write error here */
+){
+  GeoPoly *p = 0;
+  int nByte;
+  testcase( pCtx==0 );
+  if( sqlite3_value_type(pVal)==SQLITE_BLOB
+   && (nByte = sqlite3_value_bytes(pVal))>=(4+6*sizeof(GeoCoord))
+  ){
+    const unsigned char *a = sqlite3_value_blob(pVal);
+    int nVertex;
+    if( a==0 ){
+      if( pCtx ) sqlite3_result_error_nomem(pCtx);
+      return 0;
+    }
+    nVertex = (a[1]<<16) + (a[2]<<8) + a[3];
+    if( (a[0]==0 || a[0]==1)
+     && (nVertex*2*sizeof(GeoCoord) + 4)==(unsigned int)nByte
+    ){
+      p = sqlite3_malloc64( sizeof(*p) + (nVertex-1)*2*sizeof(GeoCoord) );
+      if( p==0 ){
+        if( pRc ) *pRc = SQLITE_NOMEM;
+        if( pCtx ) sqlite3_result_error_nomem(pCtx);
+      }else{
+        int x = 1;
+        p->nVertex = nVertex;
+        memcpy(p->hdr, a, nByte);
+        if( a[0] != *(unsigned char*)&x ){
+          int ii;
+          for(ii=0; ii<nVertex; ii++){
+            geopolySwab32((unsigned char*)&GeoX(p,ii));
+            geopolySwab32((unsigned char*)&GeoY(p,ii));
+          }
+          p->hdr[0] ^= 1;
+        }
+      }
+    }
+    if( pRc ) *pRc = SQLITE_OK;
+    return p;
+  }else if( sqlite3_value_type(pVal)==SQLITE_TEXT ){
+    const unsigned char *zJson = sqlite3_value_text(pVal);
+    if( zJson==0 ){
+      if( pRc ) *pRc = SQLITE_NOMEM;
+      return 0;
+    }
+    return geopolyParseJson(zJson, pRc);
+  }else{
+    if( pRc ) *pRc = SQLITE_ERROR;
+    return 0;
+  }
+}
+
+/*
+** Implementation of the geopoly_blob(X) function.
+**
+** If the input is a well-formed Geopoly BLOB or JSON string
+** then return the BLOB representation of the polygon.  Otherwise
+** return NULL.
+*/
+static void geopolyBlobFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
+  if( p ){
+    sqlite3_result_blob(context, p->hdr, 
+       4+8*p->nVertex, SQLITE_TRANSIENT);
+    sqlite3_free(p);
+  }
+}
+
+/*
+** SQL function:     geopoly_json(X)
+**
+** Interpret X as a polygon and render it as a JSON array
+** of coordinates.  Or, if X is not a valid polygon, return NULL.
+*/
+static void geopolyJsonFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
+  if( p ){
+    sqlite3 *db = sqlite3_context_db_handle(context);
+    sqlite3_str *x = sqlite3_str_new(db);
+    int i;
+    sqlite3_str_append(x, "[", 1);
+    for(i=0; i<p->nVertex; i++){
+      sqlite3_str_appendf(x, "[%!g,%!g],", GeoX(p,i), GeoY(p,i));
+    }
+    sqlite3_str_appendf(x, "[%!g,%!g]]", GeoX(p,0), GeoY(p,0));
+    sqlite3_result_text(context, sqlite3_str_finish(x), -1, sqlite3_free);
+    sqlite3_free(p);
+  }
+}
+
+/*
+** SQL function:     geopoly_svg(X, ....)
+**
+** Interpret X as a polygon and render it as a SVG <polyline>.
+** Additional arguments are added as attributes to the <polyline>.
+*/
+static void geopolySvgFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p;
+  if( argc<1 ) return;
+  p = geopolyFuncParam(context, argv[0], 0);
+  if( p ){
+    sqlite3 *db = sqlite3_context_db_handle(context);
+    sqlite3_str *x = sqlite3_str_new(db);
+    int i;
+    char cSep = '\'';
+    sqlite3_str_appendf(x, "<polyline points=");
+    for(i=0; i<p->nVertex; i++){
+      sqlite3_str_appendf(x, "%c%g,%g", cSep, GeoX(p,i), GeoY(p,i));
+      cSep = ' ';
+    }
+    sqlite3_str_appendf(x, " %g,%g'", GeoX(p,0), GeoY(p,0));
+    for(i=1; i<argc; i++){
+      const char *z = (const char*)sqlite3_value_text(argv[i]);
+      if( z && z[0] ){
+        sqlite3_str_appendf(x, " %s", z);
+      }
+    }
+    sqlite3_str_appendf(x, "></polyline>");
+    sqlite3_result_text(context, sqlite3_str_finish(x), -1, sqlite3_free);
+    sqlite3_free(p);
+  }
+}
+
+/*
+** SQL Function:      geopoly_xform(poly, A, B, C, D, E, F)
+**
+** Transform and/or translate a polygon as follows:
+**
+**      x1 = A*x0 + B*y0 + E
+**      y1 = C*x0 + D*y0 + F
+**
+** For a translation:
+**
+**      geopoly_xform(poly, 1, 0, 0, 1, x-offset, y-offset)
+**
+** Rotate by R around the point (0,0):
+**
+**      geopoly_xform(poly, cos(R), sin(R), -sin(R), cos(R), 0, 0)
+*/
+static void geopolyXformFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
+  double A = sqlite3_value_double(argv[1]);
+  double B = sqlite3_value_double(argv[2]);
+  double C = sqlite3_value_double(argv[3]);
+  double D = sqlite3_value_double(argv[4]);
+  double E = sqlite3_value_double(argv[5]);
+  double F = sqlite3_value_double(argv[6]);
+  GeoCoord x1, y1, x0, y0;
+  int ii;
+  if( p ){
+    for(ii=0; ii<p->nVertex; ii++){
+      x0 = GeoX(p,ii);
+      y0 = GeoY(p,ii);
+      x1 = (GeoCoord)(A*x0 + B*y0 + E);
+      y1 = (GeoCoord)(C*x0 + D*y0 + F);
+      GeoX(p,ii) = x1;
+      GeoY(p,ii) = y1;
+    }
+    sqlite3_result_blob(context, p->hdr, 
+       4+8*p->nVertex, SQLITE_TRANSIENT);
+    sqlite3_free(p);
+  }
+}
+
+/*
+** Compute the area enclosed by the polygon.
+**
+** This routine can also be used to detect polygons that rotate in
+** the wrong direction.  Polygons are suppose to be counter-clockwise (CCW).
+** This routine returns a negative value for clockwise (CW) polygons.
+*/
+static double geopolyArea(GeoPoly *p){
+  double rArea = 0.0;
+  int ii;
+  for(ii=0; ii<p->nVertex-1; ii++){
+    rArea += (GeoX(p,ii) - GeoX(p,ii+1))           /* (x0 - x1) */
+              * (GeoY(p,ii) + GeoY(p,ii+1))        /* (y0 + y1) */
+              * 0.5;
+  }
+  rArea += (GeoX(p,ii) - GeoX(p,0))                /* (xN - x0) */
+           * (GeoY(p,ii) + GeoY(p,0))              /* (yN + y0) */
+           * 0.5;
+  return rArea;
+}
+
+/*
+** Implementation of the geopoly_area(X) function.
+**
+** If the input is a well-formed Geopoly BLOB then return the area
+** enclosed by the polygon.  If the polygon circulates clockwise instead
+** of counterclockwise (as it should) then return the negative of the
+** enclosed area.  Otherwise return NULL.
+*/
+static void geopolyAreaFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
+  if( p ){
+    sqlite3_result_double(context, geopolyArea(p));
+    sqlite3_free(p);
+  }            
+}
+
+/*
+** Implementation of the geopoly_ccw(X) function.
+**
+** If the rotation of polygon X is clockwise (incorrect) instead of
+** counter-clockwise (the correct winding order according to RFC7946)
+** then reverse the order of the vertexes in polygon X.  
+**
+** In other words, this routine returns a CCW polygon regardless of the
+** winding order of its input.
+**
+** Use this routine to sanitize historical inputs that that sometimes
+** contain polygons that wind in the wrong direction.
+*/
+static void geopolyCcwFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
+  if( p ){
+    if( geopolyArea(p)<0.0 ){
+      int ii, jj;
+      for(ii=1, jj=p->nVertex-1; ii<jj; ii++, jj--){
+        GeoCoord t = GeoX(p,ii);
+        GeoX(p,ii) = GeoX(p,jj);
+        GeoX(p,jj) = t;
+        t = GeoY(p,ii);
+        GeoY(p,ii) = GeoY(p,jj);
+        GeoY(p,jj) = t;
+      }
+    }
+    sqlite3_result_blob(context, p->hdr, 
+       4+8*p->nVertex, SQLITE_TRANSIENT);
+    sqlite3_free(p);
+  }            
+}
+
+#define GEOPOLY_PI 3.1415926535897932385
+
+/* Fast approximation for sine(X) for X between -0.5*pi and 2*pi
+*/
+static double geopolySine(double r){
+  assert( r>=-0.5*GEOPOLY_PI && r<=2.0*GEOPOLY_PI );
+  if( r>=1.5*GEOPOLY_PI ){
+    r -= 2.0*GEOPOLY_PI;
+  }
+  if( r>=0.5*GEOPOLY_PI ){
+    return -geopolySine(r-GEOPOLY_PI);
+  }else{
+    double r2 = r*r;
+    double r3 = r2*r;
+    double r5 = r3*r2;
+    return 0.9996949*r - 0.1656700*r3 + 0.0075134*r5;
+  }
+}
+
+/*
+** Function:   geopoly_regular(X,Y,R,N)
+**
+** Construct a simple, convex, regular polygon centered at X, Y
+** with circumradius R and with N sides.
+*/
+static void geopolyRegularFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  double x = sqlite3_value_double(argv[0]);
+  double y = sqlite3_value_double(argv[1]);
+  double r = sqlite3_value_double(argv[2]);
+  int n = sqlite3_value_int(argv[3]);
+  int i;
+  GeoPoly *p;
+
+  if( n<3 || r<=0.0 ) return;
+  if( n>1000 ) n = 1000;
+  p = sqlite3_malloc64( sizeof(*p) + (n-1)*2*sizeof(GeoCoord) );
+  if( p==0 ){
+    sqlite3_result_error_nomem(context);
+    return;
+  }
+  i = 1;
+  p->hdr[0] = *(unsigned char*)&i;
+  p->hdr[1] = 0;
+  p->hdr[2] = (n>>8)&0xff;
+  p->hdr[3] = n&0xff;
+  for(i=0; i<n; i++){
+    double rAngle = 2.0*GEOPOLY_PI*i/n;
+    GeoX(p,i) = x - r*geopolySine(rAngle-0.5*GEOPOLY_PI);
+    GeoY(p,i) = y + r*geopolySine(rAngle);
+  }
+  sqlite3_result_blob(context, p->hdr, 4+8*n, SQLITE_TRANSIENT);
+  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 = GeoX(p,0);
+    mnY = mxY = GeoY(p,0);
+    for(ii=1; ii<p->nVertex; ii++){
+      double r = GeoX(p,ii);
+      if( r<mnX ) mnX = (float)r;
+      else if( r>mxX ) mxX = (float)r;
+      r = GeoY(p,ii);
+      if( r<mnY ) mnY = (float)r;
+      else if( r>mxY ) mxY = (float)r;
+    }
+    if( pRc ) *pRc = SQLITE_OK;
+    if( aCoord==0 ){
+      geopolyBboxFill:
+      pOut = sqlite3_realloc64(p, GEOPOLY_SZ(4));
+      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;
+      GeoX(pOut,0) = mnX;
+      GeoY(pOut,0) = mnY;
+      GeoX(pOut,1) = mxX;
+      GeoY(pOut,1) = mnY;
+      GeoX(pOut,2) = mxX;
+      GeoY(pOut,2) = mxY;
+      GeoX(pOut,3) = mnX;
+      GeoY(pOut,3) = mxY;
+    }else{
+      sqlite3_free(p);
+      aCoord[0].f = mnX;
+      aCoord[1].f = mxX;
+      aCoord[2].f = mnY;
+      aCoord[3].f = mxY;
+    }
+  }else if( aCoord ){
+    memset(aCoord, 0, sizeof(RtreeCoord)*4);
+  }
+  return pOut;
+}
+
+/*
+** Implementation of the geopoly_bbox(X) SQL function.
+*/
+static void geopolyBBoxFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  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
+**
+**    +1  x0,y0 is beneath line segment
+**
+**    0   x0,y0 is not on or beneath the line segment or the line segment
+**        is vertical and x0,y0 is not on the line segment
+**
+** The left-most coordinate min(x1,x2) is not considered to be part of
+** the line segment for the purposes of this analysis.
+*/
+static int pointBeneathLine(
+  double x0, double y0,
+  double x1, double y1,
+  double x2, double y2
+){
+  double y;
+  if( x0==x1 && y0==y1 ) return 2;
+  if( x1<x2 ){
+    if( x0<=x1 || x0>x2 ) return 0;
+  }else if( x1>x2 ){
+    if( x0<=x2 || x0>x1 ) return 0;
+  }else{
+    /* Vertical line segment */
+    if( x0!=x1 ) return 0;
+    if( y0<y1 && y0<y2 ) return 0;
+    if( y0>y1 && y0>y2 ) return 0;
+    return 2;
+  }
+  y = y1 + (y2-y1)*(x0-x1)/(x2-x1);
+  if( y0==y ) return 2;
+  if( y0<y ) return 1;
+  return 0;
+}
+
+/*
+** SQL function:    geopoly_contains_point(P,X,Y)
+**
+** Return +2 if point X,Y is within polygon P.
+** Return +1 if point X,Y is on the polygon boundary.
+** Return 0 if point X,Y is outside the polygon
+*/
+static void geopolyContainsPointFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p1 = geopolyFuncParam(context, argv[0], 0);
+  double x0 = sqlite3_value_double(argv[1]);
+  double y0 = sqlite3_value_double(argv[2]);
+  int v = 0;
+  int cnt = 0;
+  int ii;
+  if( p1==0 ) return;
+  for(ii=0; ii<p1->nVertex-1; ii++){
+    v = pointBeneathLine(x0,y0,GeoX(p1,ii), GeoY(p1,ii),
+                               GeoX(p1,ii+1),GeoY(p1,ii+1));
+    if( v==2 ) break;
+    cnt += v;
+  }
+  if( v!=2 ){
+    v = pointBeneathLine(x0,y0,GeoX(p1,ii), GeoY(p1,ii),
+                               GeoX(p1,0),  GeoY(p1,0));
+  }
+  if( v==2 ){
+    sqlite3_result_int(context, 1);
+  }else if( ((v+cnt)&1)==0 ){
+    sqlite3_result_int(context, 0);
+  }else{
+    sqlite3_result_int(context, 2);
+  }
+  sqlite3_free(p1);
+}
+
+/* Forward declaration */
+static int geopolyOverlap(GeoPoly *p1, GeoPoly *p2);
+
+/*
+** SQL function:    geopoly_within(P1,P2)
+**
+** Return +2 if P1 and P2 are the same polygon
+** Return +1 if P2 is contained within P1
+** Return 0 if any part of P2 is on the outside of P1
+**
+*/
+static void geopolyWithinFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p1 = geopolyFuncParam(context, argv[0], 0);
+  GeoPoly *p2 = geopolyFuncParam(context, argv[1], 0);
+  if( p1 && p2 ){
+    int x = geopolyOverlap(p1, p2);
+    if( x<0 ){
+      sqlite3_result_error_nomem(context);
+    }else{
+      sqlite3_result_int(context, x==2 ? 1 : x==4 ? 2 : 0);
+    }
+  }
+  sqlite3_free(p1);
+  sqlite3_free(p2);
+}
+
+/* Objects used by the overlap algorihm. */
+typedef struct GeoEvent GeoEvent;
+typedef struct GeoSegment GeoSegment;
+typedef struct GeoOverlap GeoOverlap;
+struct GeoEvent {
+  double x;              /* X coordinate at which event occurs */
+  int eType;             /* 0 for ADD, 1 for REMOVE */
+  GeoSegment *pSeg;      /* The segment to be added or removed */
+  GeoEvent *pNext;       /* Next event in the sorted list */
+};
+struct GeoSegment {
+  double C, B;           /* y = C*x + B */
+  double y;              /* Current y value */
+  float y0;              /* Initial y value */
+  unsigned char side;    /* 1 for p1, 2 for p2 */
+  unsigned int idx;      /* Which segment within the side */
+  GeoSegment *pNext;     /* Next segment in a list sorted by y */
+};
+struct GeoOverlap {
+  GeoEvent *aEvent;          /* Array of all events */
+  GeoSegment *aSegment;      /* Array of all segments */
+  int nEvent;                /* Number of events */
+  int nSegment;              /* Number of segments */
+};
+
+/*
+** Add a single segment and its associated events.
+*/
+static void geopolyAddOneSegment(
+  GeoOverlap *p,
+  GeoCoord x0,
+  GeoCoord y0,
+  GeoCoord x1,
+  GeoCoord y1,
+  unsigned char side,
+  unsigned int idx
+){
+  GeoSegment *pSeg;
+  GeoEvent *pEvent;
+  if( x0==x1 ) return;  /* Ignore vertical segments */
+  if( x0>x1 ){
+    GeoCoord t = x0;
+    x0 = x1;
+    x1 = t;
+    t = y0;
+    y0 = y1;
+    y1 = t;
+  }
+  pSeg = p->aSegment + p->nSegment;
+  p->nSegment++;
+  pSeg->C = (y1-y0)/(x1-x0);
+  pSeg->B = y1 - x1*pSeg->C;
+  pSeg->y0 = y0;
+  pSeg->side = side;
+  pSeg->idx = idx;
+  pEvent = p->aEvent + p->nEvent;
+  p->nEvent++;
+  pEvent->x = x0;
+  pEvent->eType = 0;
+  pEvent->pSeg = pSeg;
+  pEvent = p->aEvent + p->nEvent;
+  p->nEvent++;
+  pEvent->x = x1;
+  pEvent->eType = 1;
+  pEvent->pSeg = pSeg;
+}
+  
+
+
+/*
+** Insert all segments and events for polygon pPoly.
+*/
+static void geopolyAddSegments(
+  GeoOverlap *p,          /* Add segments to this Overlap object */
+  GeoPoly *pPoly,         /* Take all segments from this polygon */
+  unsigned char side      /* The side of pPoly */
+){
+  unsigned int i;
+  GeoCoord *x;
+  for(i=0; i<(unsigned)pPoly->nVertex-1; i++){
+    x = &GeoX(pPoly,i);
+    geopolyAddOneSegment(p, x[0], x[1], x[2], x[3], side, i);
+  }
+  x = &GeoX(pPoly,i);
+  geopolyAddOneSegment(p, x[0], x[1], pPoly->a[0], pPoly->a[1], side, i);
+}
+
+/*
+** Merge two lists of sorted events by X coordinate
+*/
+static GeoEvent *geopolyEventMerge(GeoEvent *pLeft, GeoEvent *pRight){
+  GeoEvent head, *pLast;
+  head.pNext = 0;
+  pLast = &head;
+  while( pRight && pLeft ){
+    if( pRight->x <= pLeft->x ){
+      pLast->pNext = pRight;
+      pLast = pRight;
+      pRight = pRight->pNext;
+    }else{
+      pLast->pNext = pLeft;
+      pLast = pLeft;
+      pLeft = pLeft->pNext;
+    }
+  }
+  pLast->pNext = pRight ? pRight : pLeft;
+  return head.pNext;  
+}
+
+/*
+** Sort an array of nEvent event objects into a list.
+*/
+static GeoEvent *geopolySortEventsByX(GeoEvent *aEvent, int nEvent){
+  int mx = 0;
+  int i, j;
+  GeoEvent *p;
+  GeoEvent *a[50];
+  for(i=0; i<nEvent; i++){
+    p = &aEvent[i];
+    p->pNext = 0;
+    for(j=0; j<mx && a[j]; j++){
+      p = geopolyEventMerge(a[j], p);
+      a[j] = 0;
+    }
+    a[j] = p;
+    if( j>=mx ) mx = j+1;
+  }
+  p = 0;
+  for(i=0; i<mx; i++){
+    p = geopolyEventMerge(a[i], p);
+  }
+  return p;
+}
+
+/*
+** Merge two lists of sorted segments by Y, and then by C.
+*/
+static GeoSegment *geopolySegmentMerge(GeoSegment *pLeft, GeoSegment *pRight){
+  GeoSegment head, *pLast;
+  head.pNext = 0;
+  pLast = &head;
+  while( pRight && pLeft ){
+    double r = pRight->y - pLeft->y;
+    if( r==0.0 ) r = pRight->C - pLeft->C;
+    if( r<0.0 ){
+      pLast->pNext = pRight;
+      pLast = pRight;
+      pRight = pRight->pNext;
+    }else{
+      pLast->pNext = pLeft;
+      pLast = pLeft;
+      pLeft = pLeft->pNext;
+    }
+  }
+  pLast->pNext = pRight ? pRight : pLeft;
+  return head.pNext;  
+}
+
+/*
+** Sort a list of GeoSegments in order of increasing Y and in the event of
+** a tie, increasing C (slope).
+*/
+static GeoSegment *geopolySortSegmentsByYAndC(GeoSegment *pList){
+  int mx = 0;
+  int i;
+  GeoSegment *p;
+  GeoSegment *a[50];
+  while( pList ){
+    p = pList;
+    pList = pList->pNext;
+    p->pNext = 0;
+    for(i=0; i<mx && a[i]; i++){
+      p = geopolySegmentMerge(a[i], p);
+      a[i] = 0;
+    }
+    a[i] = p;
+    if( i>=mx ) mx = i+1;
+  }
+  p = 0;
+  for(i=0; i<mx; i++){
+    p = geopolySegmentMerge(a[i], p);
+  }
+  return p;
+}
+
+/*
+** Determine the overlap between two polygons
+*/
+static int geopolyOverlap(GeoPoly *p1, GeoPoly *p2){
+  sqlite3_int64 nVertex = p1->nVertex + p2->nVertex + 2;
+  GeoOverlap *p;
+  sqlite3_int64 nByte;
+  GeoEvent *pThisEvent;
+  double rX;
+  int rc = 0;
+  int needSort = 0;
+  GeoSegment *pActive = 0;
+  GeoSegment *pSeg;
+  unsigned char aOverlap[4];
+
+  nByte = sizeof(GeoEvent)*nVertex*2 
+           + sizeof(GeoSegment)*nVertex 
+           + sizeof(GeoOverlap);
+  p = sqlite3_malloc64( nByte );
+  if( p==0 ) return -1;
+  p->aEvent = (GeoEvent*)&p[1];
+  p->aSegment = (GeoSegment*)&p->aEvent[nVertex*2];
+  p->nEvent = p->nSegment = 0;
+  geopolyAddSegments(p, p1, 1);
+  geopolyAddSegments(p, p2, 2);
+  pThisEvent = geopolySortEventsByX(p->aEvent, p->nEvent);
+  rX = pThisEvent && pThisEvent->x==0.0 ? -1.0 : 0.0;
+  memset(aOverlap, 0, sizeof(aOverlap));
+  while( pThisEvent ){
+    if( pThisEvent->x!=rX ){
+      GeoSegment *pPrev = 0;
+      int iMask = 0;
+      GEODEBUG(("Distinct X: %g\n", pThisEvent->x));
+      rX = pThisEvent->x;
+      if( needSort ){
+        GEODEBUG(("SORT\n"));
+        pActive = geopolySortSegmentsByYAndC(pActive);
+        needSort = 0;
+      }
+      for(pSeg=pActive; pSeg; pSeg=pSeg->pNext){
+        if( pPrev ){
+          if( pPrev->y!=pSeg->y ){
+            GEODEBUG(("MASK: %d\n", iMask));
+            aOverlap[iMask] = 1;
+          }
+        }
+        iMask ^= pSeg->side;
+        pPrev = pSeg;
+      }
+      pPrev = 0;
+      for(pSeg=pActive; pSeg; pSeg=pSeg->pNext){
+        double y = pSeg->C*rX + pSeg->B;
+        GEODEBUG(("Segment %d.%d %g->%g\n", pSeg->side, pSeg->idx, pSeg->y, y));
+        pSeg->y = y;
+        if( pPrev ){
+          if( pPrev->y>pSeg->y && pPrev->side!=pSeg->side ){
+            rc = 1;
+            GEODEBUG(("Crossing: %d.%d and %d.%d\n",
+                    pPrev->side, pPrev->idx,
+                    pSeg->side, pSeg->idx));
+            goto geopolyOverlapDone;
+          }else if( pPrev->y!=pSeg->y ){
+            GEODEBUG(("MASK: %d\n", iMask));
+            aOverlap[iMask] = 1;
+          }
+        }
+        iMask ^= pSeg->side;
+        pPrev = pSeg;
+      }
+    }
+    GEODEBUG(("%s %d.%d C=%g B=%g\n",
+      pThisEvent->eType ? "RM " : "ADD",
+      pThisEvent->pSeg->side, pThisEvent->pSeg->idx,
+      pThisEvent->pSeg->C,
+      pThisEvent->pSeg->B));
+    if( pThisEvent->eType==0 ){
+      /* Add a segment */
+      pSeg = pThisEvent->pSeg;
+      pSeg->y = pSeg->y0;
+      pSeg->pNext = pActive;
+      pActive = pSeg;
+      needSort = 1;
+    }else{
+      /* Remove a segment */
+      if( pActive==pThisEvent->pSeg ){
+        pActive = ALWAYS(pActive) ? pActive->pNext : 0;
+      }else{
+        for(pSeg=pActive; pSeg; pSeg=pSeg->pNext){
+          if( pSeg->pNext==pThisEvent->pSeg ){
+            pSeg->pNext = ALWAYS(pSeg->pNext) ? pSeg->pNext->pNext : 0;
+            break;
+          }
+        }
+      }
+    }
+    pThisEvent = pThisEvent->pNext;
+  }
+  if( aOverlap[3]==0 ){
+    rc = 0;
+  }else if( aOverlap[1]!=0 && aOverlap[2]==0 ){
+    rc = 3;
+  }else if( aOverlap[1]==0 && aOverlap[2]!=0 ){
+    rc = 2;
+  }else if( aOverlap[1]==0 && aOverlap[2]==0 ){
+    rc = 4;
+  }else{
+    rc = 1;
+  }
+
+geopolyOverlapDone:
+  sqlite3_free(p);
+  return rc;
+}
+
+/*
+** SQL function:    geopoly_overlap(P1,P2)
+**
+** Determine whether or not P1 and P2 overlap. Return value:
+**
+**   0     The two polygons are disjoint
+**   1     They overlap
+**   2     P1 is completely contained within P2
+**   3     P2 is completely contained within P1
+**   4     P1 and P2 are the same polygon
+**   NULL  Either P1 or P2 or both are not valid polygons
+*/
+static void geopolyOverlapFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  GeoPoly *p1 = geopolyFuncParam(context, argv[0], 0);
+  GeoPoly *p2 = geopolyFuncParam(context, argv[1], 0);
+  if( p1 && p2 ){
+    int x = geopolyOverlap(p1, p2);
+    if( x<0 ){
+      sqlite3_result_error_nomem(context);
+    }else{
+      sqlite3_result_int(context, x);
+    }
+  }
+  sqlite3_free(p1);
+  sqlite3_free(p2);
+}
+
+/*
+** Enable or disable debugging output
+*/
+static void geopolyDebugFunc(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+#ifdef GEOPOLY_ENABLE_DEBUG
+  geo_debug = sqlite3_value_int(argv[0]);
+#endif
+}
+
+/* 
+** This function is the implementation of both the xConnect and xCreate
+** methods of the geopoly virtual table.
+**
+**   argv[0]   -> module name
+**   argv[1]   -> database name
+**   argv[2]   -> table name
+**   argv[...] -> column names...
+*/
+static int geopolyInit(
+  sqlite3 *db,                        /* Database connection */
+  void *pAux,                         /* One of the RTREE_COORD_* constants */
+  int argc, const char *const*argv,   /* Parameters to CREATE TABLE statement */
+  sqlite3_vtab **ppVtab,              /* OUT: New virtual table */
+  char **pzErr,                       /* OUT: Error message, if any */
+  int isCreate                        /* True for xCreate, false for xConnect */
+){
+  int rc = SQLITE_OK;
+  Rtree *pRtree;
+  sqlite3_int64 nDb;              /* Length of string argv[1] */
+  sqlite3_int64 nName;            /* Length of string argv[2] */
+  sqlite3_str *pSql;
+  char *zSql;
+  int ii;
+
+  sqlite3_vtab_config(db, SQLITE_VTAB_CONSTRAINT_SUPPORT, 1);
+
+  /* Allocate the sqlite3_vtab structure */
+  nDb = strlen(argv[1]);
+  nName = strlen(argv[2]);
+  pRtree = (Rtree *)sqlite3_malloc64(sizeof(Rtree)+nDb+nName+2);
+  if( !pRtree ){
+    return SQLITE_NOMEM;
+  }
+  memset(pRtree, 0, sizeof(Rtree)+nDb+nName+2);
+  pRtree->nBusy = 1;
+  pRtree->base.pModule = &rtreeModule;
+  pRtree->zDb = (char *)&pRtree[1];
+  pRtree->zName = &pRtree->zDb[nDb+1];
+  pRtree->eCoordType = RTREE_COORD_REAL32;
+  pRtree->nDim = 2;
+  pRtree->nDim2 = 4;
+  memcpy(pRtree->zDb, argv[1], nDb);
+  memcpy(pRtree->zName, argv[2], nName);
+
+
+  /* Create/Connect to the underlying relational database schema. If
+  ** that is successful, call sqlite3_declare_vtab() to configure
+  ** the r-tree table schema.
+  */
+  pSql = sqlite3_str_new(db);
+  sqlite3_str_appendf(pSql, "CREATE TABLE x(_shape");
+  pRtree->nAux = 1;         /* Add one for _shape */
+  pRtree->nAuxNotNull = 1;  /* The _shape column is always not-null */
+  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);
+  if( rc ) goto geopolyInit_fail;
+  pRtree->nBytesPerCell = 8 + pRtree->nDim2*4;
+
+  /* Figure out the node size to use. */
+  rc = getNodeSize(db, pRtree, isCreate, pzErr);
+  if( rc ) goto geopolyInit_fail;
+  rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate);
+  if( rc ){
+    *pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
+    goto geopolyInit_fail;
+  }
+
+  *ppVtab = (sqlite3_vtab *)pRtree;
+  return SQLITE_OK;
+
+geopolyInit_fail:
+  if( rc==SQLITE_OK ) rc = SQLITE_ERROR;
+  assert( *ppVtab==0 );
+  assert( pRtree->nBusy==1 );
+  rtreeRelease(pRtree);
+  return rc;
+}
+
+
+/* 
+** GEOPOLY virtual table module xCreate method.
+*/
+static int geopolyCreate(
+  sqlite3 *db,
+  void *pAux,
+  int argc, const char *const*argv,
+  sqlite3_vtab **ppVtab,
+  char **pzErr
+){
+  return geopolyInit(db, pAux, argc, argv, ppVtab, pzErr, 1);
+}
+
+/* 
+** GEOPOLY virtual table module xConnect method.
+*/
+static int geopolyConnect(
+  sqlite3 *db,
+  void *pAux,
+  int argc, const char *const*argv,
+  sqlite3_vtab **ppVtab,
+  char **pzErr
+){
+  return geopolyInit(db, pAux, argc, argv, ppVtab, pzErr, 0);
+}
+
+
+/* 
+** GEOPOLY virtual table module xFilter method.
+**
+** Query plans:
+**
+**      1         rowid lookup
+**      2         search for objects overlapping the same bounding box
+**                that contains polygon argv[0]
+**      3         search for objects overlapping the same bounding box
+**                that contains polygon argv[0]
+**      4         full table scan
+*/
+static int geopolyFilter(
+  sqlite3_vtab_cursor *pVtabCursor,     /* The cursor to initialize */
+  int idxNum,                           /* Query plan */
+  const char *idxStr,                   /* Not Used */
+  int argc, sqlite3_value **argv        /* Parameters to the query plan */
+){
+  Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
+  RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
+  RtreeNode *pRoot = 0;
+  int rc = SQLITE_OK;
+  int iCell = 0;
+
+  rtreeReference(pRtree);
+
+  /* Reset the cursor to the same state as rtreeOpen() leaves it in. */
+  resetCursor(pCsr);
+
+  pCsr->iStrategy = idxNum;
+  if( idxNum==1 ){
+    /* Special case - lookup by rowid. */
+    RtreeNode *pLeaf;        /* Leaf on which the required cell resides */
+    RtreeSearchPoint *p;     /* Search point for the leaf */
+    i64 iRowid = sqlite3_value_int64(argv[0]);
+    i64 iNode = 0;
+    rc = findLeafNode(pRtree, iRowid, &pLeaf, &iNode);
+    if( rc==SQLITE_OK && pLeaf!=0 ){
+      p = rtreeSearchPointNew(pCsr, RTREE_ZERO, 0);
+      assert( p!=0 );  /* Always returns pCsr->sPoint */
+      pCsr->aNode[0] = pLeaf;
+      p->id = iNode;
+      p->eWithin = PARTLY_WITHIN;
+      rc = nodeRowidIndex(pRtree, pLeaf, iRowid, &iCell);
+      p->iCell = (u8)iCell;
+      RTREE_QUEUE_TRACE(pCsr, "PUSH-F1:");
+    }else{
+      pCsr->atEOF = 1;
+    }
+  }else{
+    /* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array 
+    ** with the configured constraints. 
+    */
+    rc = nodeAcquire(pRtree, 1, 0, &pRoot);
+    if( rc==SQLITE_OK && idxNum<=3 ){
+      RtreeCoord bbox[4];
+      RtreeConstraint *p;
+      assert( argc==1 );
+      assert( argv[0]!=0 );
+      geopolyBBox(0, argv[0], bbox, &rc);
+      if( rc ){
+        goto geopoly_filter_end;
+      }
+      pCsr->aConstraint = p = sqlite3_malloc(sizeof(RtreeConstraint)*4);
+      pCsr->nConstraint = 4;
+      if( p==0 ){
+        rc = SQLITE_NOMEM;
+      }else{
+        memset(pCsr->aConstraint, 0, sizeof(RtreeConstraint)*4);
+        memset(pCsr->anQueue, 0, sizeof(u32)*(pRtree->iDepth + 1));
+        if( idxNum==2 ){
+          /* Overlap query */
+          p->op = 'B';
+          p->iCoord = 0;
+          p->u.rValue = bbox[1].f;
+          p++;
+          p->op = 'D';
+          p->iCoord = 1;
+          p->u.rValue = bbox[0].f;
+          p++;
+          p->op = 'B';
+          p->iCoord = 2;
+          p->u.rValue = bbox[3].f;
+          p++;
+          p->op = 'D';
+          p->iCoord = 3;
+          p->u.rValue = bbox[2].f;
+        }else{
+          /* Within query */
+          p->op = 'D';
+          p->iCoord = 0;
+          p->u.rValue = bbox[0].f;
+          p++;
+          p->op = 'B';
+          p->iCoord = 1;
+          p->u.rValue = bbox[1].f;
+          p++;
+          p->op = 'D';
+          p->iCoord = 2;
+          p->u.rValue = bbox[2].f;
+          p++;
+          p->op = 'B';
+          p->iCoord = 3;
+          p->u.rValue = bbox[3].f;
+        }
+      }
+    }
+    if( rc==SQLITE_OK ){
+      RtreeSearchPoint *pNew;
+      pNew = rtreeSearchPointNew(pCsr, RTREE_ZERO, (u8)(pRtree->iDepth+1));
+      if( pNew==0 ){
+        rc = SQLITE_NOMEM;
+        goto geopoly_filter_end;
+      }
+      pNew->id = 1;
+      pNew->iCell = 0;
+      pNew->eWithin = PARTLY_WITHIN;
+      assert( pCsr->bPoint==1 );
+      pCsr->aNode[0] = pRoot;
+      pRoot = 0;
+      RTREE_QUEUE_TRACE(pCsr, "PUSH-Fm:");
+      rc = rtreeStepToLeaf(pCsr);
+    }
+  }
+
+geopoly_filter_end:
+  nodeRelease(pRtree, pRoot);
+  rtreeRelease(pRtree);
+  return rc;
+}
+
+/*
+** 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        "rowid"       Direct lookup by rowid.
+**     2        "rtree"       R-tree overlap query using geopoly_overlap()
+**     3        "rtree"       R-tree within query using geopoly_within()
+**     4        "fullscan"    full-table scan.
+**   ------------------------------------------------
+*/
+static int geopolyBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){
+  int ii;
+  int iRowidTerm = -1;
+  int iFuncTerm = -1;
+  int idxNum = 0;
+
+  for(ii=0; ii<pIdxInfo->nConstraint; ii++){
+    struct sqlite3_index_constraint *p = &pIdxInfo->aConstraint[ii];
+    if( !p->usable ) continue;
+    if( p->iColumn<0 && p->op==SQLITE_INDEX_CONSTRAINT_EQ  ){
+      iRowidTerm = ii;
+      break;
+    }
+    if( p->iColumn==0 && p->op>=SQLITE_INDEX_CONSTRAINT_FUNCTION ){
+      /* p->op==SQLITE_INDEX_CONSTRAINT_FUNCTION for geopoly_overlap()
+      ** p->op==(SQLITE_INDEX_CONTRAINT_FUNCTION+1) for geopoly_within().
+      ** See geopolyFindFunction() */
+      iFuncTerm = ii;
+      idxNum = p->op - SQLITE_INDEX_CONSTRAINT_FUNCTION + 2;
+    }
+  }
+
+  if( iRowidTerm>=0 ){
+    pIdxInfo->idxNum = 1;
+    pIdxInfo->idxStr = "rowid";
+    pIdxInfo->aConstraintUsage[iRowidTerm].argvIndex = 1;
+    pIdxInfo->aConstraintUsage[iRowidTerm].omit = 1;
+    pIdxInfo->estimatedCost = 30.0;
+    pIdxInfo->estimatedRows = 1;
+    pIdxInfo->idxFlags = SQLITE_INDEX_SCAN_UNIQUE;
+    return SQLITE_OK;
+  }
+  if( iFuncTerm>=0 ){
+    pIdxInfo->idxNum = idxNum;
+    pIdxInfo->idxStr = "rtree";
+    pIdxInfo->aConstraintUsage[iFuncTerm].argvIndex = 1;
+    pIdxInfo->aConstraintUsage[iFuncTerm].omit = 0;
+    pIdxInfo->estimatedCost = 300.0;
+    pIdxInfo->estimatedRows = 10;
+    return SQLITE_OK;
+  }
+  pIdxInfo->idxNum = 4;
+  pIdxInfo->idxStr = "fullscan";
+  pIdxInfo->estimatedCost = 3000000.0;
+  pIdxInfo->estimatedRows = 100000;
+  return SQLITE_OK;
+}
+
+
+/* 
+** GEOPOLY virtual table module xColumn method.
+*/
+static int geopolyColumn(sqlite3_vtab_cursor *cur, sqlite3_context *ctx, int i){
+  Rtree *pRtree = (Rtree *)cur->pVtab;
+  RtreeCursor *pCsr = (RtreeCursor *)cur;
+  RtreeSearchPoint *p = rtreeSearchPointFirst(pCsr);
+  int rc = SQLITE_OK;
+  RtreeNode *pNode = rtreeNodeOfFirstSearchPoint(pCsr, &rc);
+
+  if( rc ) return rc;
+  if( p==0 ) return SQLITE_OK;
+  if( i==0 && sqlite3_vtab_nochange(ctx) ) return SQLITE_OK;
+  if( i<=pRtree->nAux ){
+    if( !pCsr->bAuxValid ){
+      if( pCsr->pReadAux==0 ){
+        rc = sqlite3_prepare_v3(pRtree->db, pRtree->zReadAuxSql, -1, 0,
+                                &pCsr->pReadAux, 0);
+        if( rc ) return rc;
+      }
+      sqlite3_bind_int64(pCsr->pReadAux, 1, 
+          nodeGetRowid(pRtree, pNode, p->iCell));
+      rc = sqlite3_step(pCsr->pReadAux);
+      if( rc==SQLITE_ROW ){
+        pCsr->bAuxValid = 1;
+      }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.
+**
+** For DELETE:
+**
+**     argv[0] = the rowid to be deleted
+**
+** For INSERT:
+**
+**     argv[0] = SQL NULL
+**     argv[1] = rowid to insert, or an SQL NULL to select automatically
+**     argv[2] = _shape column
+**     argv[3] = first application-defined column....
+**
+** For UPDATE:
+**
+**     argv[0] = rowid to modify.  Never NULL
+**     argv[1] = rowid after the change.  Never NULL
+**     argv[2] = new value for _shape
+**     argv[3] = new value for first application-defined column....
+*/
+static int geopolyUpdate(
+  sqlite3_vtab *pVtab, 
+  int nData, 
+  sqlite3_value **aData, 
+  sqlite_int64 *pRowid
+){
+  Rtree *pRtree = (Rtree *)pVtab;
+  int rc = SQLITE_OK;
+  RtreeCell cell;                 /* New cell to insert if nData>1 */
+  i64 oldRowid;                   /* The old rowid */
+  int oldRowidValid;              /* True if oldRowid is valid */
+  i64 newRowid;                   /* The new rowid */
+  int newRowidValid;              /* True if newRowid is valid */
+  int coordChange = 0;            /* Change in coordinates */
+
+  if( pRtree->nNodeRef ){
+    /* Unable to write to the btree while another cursor is reading from it,
+    ** since the write might do a rebalance which would disrupt the read
+    ** cursor. */
+    return SQLITE_LOCKED_VTAB;
+  }
+  rtreeReference(pRtree);
+  assert(nData>=1);
+
+  oldRowidValid = sqlite3_value_type(aData[0])!=SQLITE_NULL;;
+  oldRowid = oldRowidValid ? sqlite3_value_int64(aData[0]) : 0;
+  newRowidValid = nData>1 && sqlite3_value_type(aData[1])!=SQLITE_NULL;
+  newRowid = newRowidValid ? sqlite3_value_int64(aData[1]) : 0;
+  cell.iRowid = newRowid;
+
+  if( nData>1                                 /* not a DELETE */
+   && (!oldRowidValid                         /* INSERT */
+        || !sqlite3_value_nochange(aData[2])  /* UPDATE _shape */
+        || oldRowid!=newRowid)                /* Rowid change */
+  ){
+    assert( aData[2]!=0 );
+    geopolyBBox(0, aData[2], cell.aCoord, &rc);
+    if( rc ){
+      if( rc==SQLITE_ERROR ){
+        pVtab->zErrMsg =
+          sqlite3_mprintf("_shape does not contain a valid polygon");
+      }
+      goto geopoly_update_end;
+    }
+    coordChange = 1;
+
+    /* If a rowid value was supplied, check if it is already present in 
+    ** the table. If so, the constraint has failed. */
+    if( newRowidValid && (!oldRowidValid || oldRowid!=newRowid) ){
+      int steprc;
+      sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);
+      steprc = sqlite3_step(pRtree->pReadRowid);
+      rc = sqlite3_reset(pRtree->pReadRowid);
+      if( SQLITE_ROW==steprc ){
+        if( sqlite3_vtab_on_conflict(pRtree->db)==SQLITE_REPLACE ){
+          rc = rtreeDeleteRowid(pRtree, cell.iRowid);
+        }else{
+          rc = rtreeConstraintError(pRtree, 0);
+        }
+      }
+    }
+  }
+
+  /* If aData[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( rc==SQLITE_OK && (nData==1 || (coordChange && oldRowidValid)) ){
+    rc = rtreeDeleteRowid(pRtree, oldRowid);
+  }
+
+  /* If the aData[] array contains more than one element, elements
+  ** (aData[2]..aData[argc-1]) contain a new record to insert into
+  ** the r-tree structure.
+  */
+  if( rc==SQLITE_OK && nData>1 && coordChange ){
+    /* Insert the new record into the r-tree */
+    RtreeNode *pLeaf = 0;
+    if( !newRowidValid ){
+      rc = rtreeNewRowid(pRtree, &cell.iRowid);
+    }
+    *pRowid = cell.iRowid;
+    if( rc==SQLITE_OK ){
+      rc = ChooseLeaf(pRtree, &cell, 0, &pLeaf);
+    }
+    if( rc==SQLITE_OK ){
+      int rc2;
+      pRtree->iReinsertHeight = -1;
+      rc = rtreeInsertCell(pRtree, pLeaf, &cell, 0);
+      rc2 = nodeRelease(pRtree, pLeaf);
+      if( rc==SQLITE_OK ){
+        rc = rc2;
+      }
+    }
+  }
+
+  /* Change the data */
+  if( rc==SQLITE_OK && nData>1 ){
+    sqlite3_stmt *pUp = pRtree->pWriteAux;
+    int jj;
+    int nChange = 0;
+    sqlite3_bind_int64(pUp, 1, cell.iRowid);
+    assert( pRtree->nAux>=1 );
+    if( sqlite3_value_nochange(aData[2]) ){
+      sqlite3_bind_null(pUp, 2);
+    }else{
+      GeoPoly *p = 0;
+      if( sqlite3_value_type(aData[2])==SQLITE_TEXT
+       && (p = geopolyFuncParam(0, aData[2], &rc))!=0
+       && rc==SQLITE_OK
+      ){
+        sqlite3_bind_blob(pUp, 2, p->hdr, 4+8*p->nVertex, SQLITE_TRANSIENT);
+      }else{
+        sqlite3_bind_value(pUp, 2, aData[2]);
+      }
+      sqlite3_free(p);
+      nChange = 1;
+    }
+    for(jj=1; jj<nData-2; jj++){
+      nChange++;
+      sqlite3_bind_value(pUp, jj+2, aData[jj+2]);
+    }
+    if( nChange ){
+      sqlite3_step(pUp);
+      rc = sqlite3_reset(pUp);
+    }
+  }
+
+geopoly_update_end:
+  rtreeRelease(pRtree);
+  return rc;
+}
+
+/*
+** Report that geopoly_overlap() is an overloaded function suitable
+** for use in xBestIndex.
+*/
+static int geopolyFindFunction(
+  sqlite3_vtab *pVtab,
+  int nArg,
+  const char *zName,
+  void (**pxFunc)(sqlite3_context*,int,sqlite3_value**),
+  void **ppArg
+){
+  if( sqlite3_stricmp(zName, "geopoly_overlap")==0 ){
+    *pxFunc = geopolyOverlapFunc;
+    *ppArg = 0;
+    return SQLITE_INDEX_CONSTRAINT_FUNCTION;
+  }
+  if( sqlite3_stricmp(zName, "geopoly_within")==0 ){
+    *pxFunc = geopolyWithinFunc;
+    *ppArg = 0;
+    return SQLITE_INDEX_CONSTRAINT_FUNCTION+1;
+  }
+  return 0;
+}
+
+
+static sqlite3_module geopolyModule = {
+  3,                          /* iVersion */
+  geopolyCreate,              /* xCreate - create a table */
+  geopolyConnect,             /* xConnect - connect to an existing table */
+  geopolyBestIndex,           /* xBestIndex - Determine search strategy */
+  rtreeDisconnect,            /* xDisconnect - Disconnect from a table */
+  rtreeDestroy,               /* xDestroy - Drop a table */
+  rtreeOpen,                  /* xOpen - open a cursor */
+  rtreeClose,                 /* xClose - close a cursor */
+  geopolyFilter,              /* xFilter - configure scan constraints */
+  rtreeNext,                  /* xNext - advance a cursor */
+  rtreeEof,                   /* xEof */
+  geopolyColumn,              /* xColumn - read data */
+  rtreeRowid,                 /* xRowid - read data */
+  geopolyUpdate,              /* xUpdate - write data */
+  rtreeBeginTransaction,      /* xBegin - begin transaction */
+  rtreeEndTransaction,        /* xSync - sync transaction */
+  rtreeEndTransaction,        /* xCommit - commit transaction */
+  rtreeEndTransaction,        /* xRollback - rollback transaction */
+  geopolyFindFunction,        /* xFindFunction - function overloading */
+  rtreeRename,                /* xRename - rename the table */
+  rtreeSavepoint,             /* xSavepoint */
+  0,                          /* xRelease */
+  0,                          /* xRollbackTo */
+  rtreeShadowName             /* xShadowName */
+};
+
+static int sqlite3_geopoly_init(sqlite3 *db){
+  int rc = SQLITE_OK;
+  static const struct {
+    void (*xFunc)(sqlite3_context*,int,sqlite3_value**);
+    signed char nArg;
+    unsigned char bPure;
+    const char *zName;
+  } aFunc[] = {
+     { geopolyAreaFunc,          1, 1,    "geopoly_area"             },
+     { geopolyBlobFunc,          1, 1,    "geopoly_blob"             },
+     { geopolyJsonFunc,          1, 1,    "geopoly_json"             },
+     { geopolySvgFunc,          -1, 1,    "geopoly_svg"              },
+     { geopolyWithinFunc,        2, 1,    "geopoly_within"           },
+     { geopolyContainsPointFunc, 3, 1,    "geopoly_contains_point"   },
+     { geopolyOverlapFunc,       2, 1,    "geopoly_overlap"          },
+     { geopolyDebugFunc,         1, 0,    "geopoly_debug"            },
+     { geopolyBBoxFunc,          1, 1,    "geopoly_bbox"             },
+     { geopolyXformFunc,         7, 1,    "geopoly_xform"            },
+     { geopolyRegularFunc,       4, 1,    "geopoly_regular"          },
+     { geopolyCcwFunc,           1, 1,    "geopoly_ccw"              },
+  };
+  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++){
+    int enc;
+    if( aFunc[i].bPure ){
+      enc = SQLITE_UTF8|SQLITE_DETERMINISTIC|SQLITE_INNOCUOUS;
+    }else{
+      enc = SQLITE_UTF8|SQLITE_DIRECTONLY;
+    }
+    rc = sqlite3_create_function(db, aFunc[i].zName, aFunc[i].nArg,
+                                 enc, 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|SQLITE_DETERMINISTIC|SQLITE_INNOCUOUS, 0,
+              0, aAgg[i].xStep, aAgg[i].xFinal);
+  }
+  if( rc==SQLITE_OK ){
+    rc = sqlite3_create_module_v2(db, "geopoly", &geopolyModule, 0, 0);
+  }
+  return rc;
+}