p->a[ii*2+1] = y1;
    }
    sqlite3_result_blob(context, p->hdr, 
       4+8*p->nVertex, SQLITE_TRANSIENT);
    sqlite3_free(p);
  }
}






















/*
** 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
................................................................................
static void geopolyAreaFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
  if( p ){
    double rArea = 0.0;
    int ii;
    for(ii=0; ii<p->nVertex-1; ii++){
      rArea += (p->a[ii*2] - p->a[ii*2+2])           /* (x0 - x1) */
                * (p->a[ii*2+1] + p->a[ii*2+3])      /* (y0 + y1) */
                * 0.5;
    }
    rArea += (p->a[ii*2] - p->a[0])                  /* (xN - x0) */
             * (p->a[ii*2+1] + p->a[1])              /* (yN + y0) */
             * 0.5;
    sqlite3_result_double(context, rArea);
    sqlite3_free(p);
  }            
}

/*
** Implementation of the geopoly_reverse(X) function.
**


** Reverse the order of the vertexes in polygon X.  This can be used
** to convert an historical polygon that uses a clockwise rotation into
** a well-formed GeoJSON polygon that uses counter-clockwise rotation.






*/
static void geopolyReverseFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  GeoPoly *p = geopolyFuncParam(context, argv[0], 0);
  if( p ){

    int ii, jj;
    for(ii=2, jj=p->nVertex*2 - 4; ii<jj; ii+=2, jj-=2){
      GeoCoord t = p->a[ii];
      p->a[ii] = p->a[jj];
      p->a[jj] = t;
      t = p->a[ii+1];
      p->a[ii+1] = p->a[jj+1];
      p->a[jj+1] = t;

    }
    sqlite3_result_blob(context, p->hdr, 
       4+8*p->nVertex, SQLITE_TRANSIENT);
    sqlite3_free(p);
  }            
}

................................................................................
     { 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"          },
     { geopolyReverseFunc,       1, 1,    "geopoly_reverse"          },
  };
  static const struct {
    void (*xStep)(sqlite3_context*,int,sqlite3_value**);
    void (*xFinal)(sqlite3_context*);
    const char *zName;
  } aAgg[] = {
     { geopolyBBoxStep, geopolyBBoxFinal, "geopoly_group_bbox"    },

      p->a[ii*2+1] = 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 += (p->a[ii*2] - p->a[ii*2+2])           /* (x0 - x1) */
              * (p->a[ii*2+1] + p->a[ii*2+3])      /* (y0 + y1) */
              * 0.5;
  }
  rArea += (p->a[ii*2] - p->a[0])                  /* (xN - x0) */
           * (p->a[ii*2+1] + p->a[1])              /* (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
................................................................................
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=2, jj=p->nVertex*2 - 4; ii<jj; ii+=2, jj-=2){
        GeoCoord t = p->a[ii];
        p->a[ii] = p->a[jj];
        p->a[jj] = t;
        t = p->a[ii+1];
        p->a[ii+1] = p->a[jj+1];
        p->a[jj+1] = t;
      }
    }
    sqlite3_result_blob(context, p->hdr, 
       4+8*p->nVertex, SQLITE_TRANSIENT);
    sqlite3_free(p);
  }            
}

................................................................................
     { 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"    },