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))









/*
** State of a parse of a GeoJSON input.
*/
typedef struct GeoParse GeoParse;
struct GeoParse {
  const unsigned char *z;   /* Unparsed input */
................................................................................
        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*2; ii++){
            geopolySwab32((unsigned char*)&p->a[ii]);

          }
          p->hdr[0] ^= 1;
        }
      }
    }
    if( pRc ) *pRc = SQLITE_OK;
    return p;
................................................................................
  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],", p->a[i*2], p->a[i*2+1]);
    }
    sqlite3_str_appendf(x, "[%!g,%!g]]", p->a[0], p->a[1]);
    sqlite3_result_text(context, sqlite3_str_finish(x), -1, sqlite3_free);
    sqlite3_free(p);
  }
}

/*
** SQL function:     geopoly_svg(X, ....)
................................................................................
  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, p->a[i*2], p->a[i*2+1]);
      cSep = ' ';
    }
    sqlite3_str_appendf(x, " %g,%g'", p->a[0], p->a[1]);
    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>");
................................................................................
  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 = p->a[ii*2];
      y0 = p->a[ii*2+1];
      x1 = (GeoCoord)(A*x0 + B*y0 + E);
      y1 = (GeoCoord)(C*x0 + D*y0 + F);
      p->a[ii*2] = x1;
      p->a[ii*2+1] = y1;
    }
    sqlite3_result_blob(context, p->hdr, 
       4+8*p->nVertex, SQLITE_TRANSIENT);
    sqlite3_free(p);
  }
}

................................................................................
** 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.
**
................................................................................
  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 - 2; 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);
  }            
}
................................................................................
  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;
    p->a[i*2] = x - r*geopolySine(rAngle-0.5*GEOPOLY_PI);
    p->a[i*2+1] = 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:
................................................................................
    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 = (float)r;
      else if( r>mxX ) mxX = (float)r;
      r = p->a[ii*2+1];
      if( r<mnY ) mnY = (float)r;
      else if( r>mxY ) mxY = (float)r;
    }
    if( pRc ) *pRc = SQLITE_OK;
    if( aCoord==0 ){
      geopolyBboxFill:
      pOut = sqlite3_realloc(p, GEOPOLY_SZ(4));
................................................................................
      }
      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;
      pOut->a[4] = mxX;
      pOut->a[5] = mxY;
      pOut->a[6] = mnX;
      pOut->a[7] = mxY;
    }else{
      sqlite3_free(p);
      aCoord[0].f = mnX;
      aCoord[1].f = mxX;
      aCoord[2].f = mnY;
      aCoord[3].f = mxY;
    }
................................................................................
  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,p1->a[ii*2],p1->a[ii*2+1],
                               p1->a[ii*2+2],p1->a[ii*2+3]);
    if( v==2 ) break;
    cnt += v;
  }
  if( v!=2 ){
    v = pointBeneathLine(x0,y0,p1->a[ii*2],p1->a[ii*2+1],
                               p1->a[0],p1->a[1]);
  }
  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);
................................................................................
  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 = pPoly->a + (i*2);
    geopolyAddOneSegment(p, x[0], x[1], x[2], x[3], side, i);
  }
  x = pPoly->a + (i*2);
  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){

  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 */
................................................................................
        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;
................................................................................
  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, ....)
................................................................................
  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>");
................................................................................
  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);
  }
}

................................................................................
** 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.
**
................................................................................
  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);
  }            
}
................................................................................
  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:
................................................................................
    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_realloc(p, GEOPOLY_SZ(4));
................................................................................
      }
      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;
    }
................................................................................
  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);
................................................................................
  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){