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);
  }            
}



























































/*
** 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
................................................................................
     { 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"            },

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

    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);
  }            
}

#define GEOPOLY_PI 3.1415926535897932385

/* Fast approximation for cosine(X) for X between -0.5*pi and 2*pi
*/
static double geopolyCosine(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 -geopolyCosine(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;
    p->a[i*2] = x - r*geopolyCosine(rAngle-0.5*GEOPOLY_PI);
    p->a[i*2+1] = y + r*geopolyCosine(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
................................................................................
     { 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"          },
  };
  static const struct {
    void (*xStep)(sqlite3_context*,int,sqlite3_value**);
    void (*xFinal)(sqlite3_context*);
    const char *zName;
  } aAgg[] = {
     { geopolyBBoxStep, geopolyBBoxFinal, "geopoly_group_bbox"    },

       )
  FROM geo1
 WHERE geopoly_overlap(_shape,(SELECT poly FROM querypoly));
SELECT geopoly_svg(poly,'style="fill:none;stroke:black;stroke-width:2"')
  FROM querypoly;
ROLLBACK;
.print '</svg>'














.print '</html>'

       )
  FROM geo1
 WHERE geopoly_overlap(_shape,(SELECT poly FROM querypoly));
SELECT geopoly_svg(poly,'style="fill:none;stroke:black;stroke-width:2"')
  FROM querypoly;
ROLLBACK;
.print '</svg>'

.print '<h1>Regular Polygons</h1>'
.print '<svg width="1000" height="200" style="border:1px solid black">'
SELECT geopoly_svg(geopoly_regular(100,100,40,3),'style="fill:none;stroke:red;stroke-width:1"');
SELECT geopoly_svg(geopoly_regular(200,100,40,4),'style="fill:none;stroke:orange;stroke-width:1"');
SELECT geopoly_svg(geopoly_regular(300,100,40,5),'style="fill:none;stroke:green;stroke-width:1"');
SELECT geopoly_svg(geopoly_regular(400,100,40,6),'style="fill:none;stroke:blue;stroke-width:1"');
SELECT geopoly_svg(geopoly_regular(500,100,40,7),'style="fill:none;stroke:purple;stroke-width:1"');
SELECT geopoly_svg(geopoly_regular(600,100,40,8),'style="fill:none;stroke:red;stroke-width:1"');
SELECT geopoly_svg(geopoly_regular(700,100,40,10),'style="fill:none;stroke:orange;stroke-width:1"');
SELECT geopoly_svg(geopoly_regular(800,100,40,20),'style="fill:none;stroke:green;stroke-width:1"');
SELECT geopoly_svg(geopoly_regular(900,100,40,30),'style="fill:none;stroke:blue;stroke-width:1"');
.print '</svg>'

.print '</html>'