/*-------------------------------------------------------------------------
 *
 * geo_ops.c
 *	  2D geometric operations
 *
 * Portions Copyright (c) 1996-2018, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *	  src/backend/utils/adt/geo_ops.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include <math.h>
#include <limits.h>
#include <float.h>
#include <ctype.h>

#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "utils/builtins.h"
#include "utils/geo_decls.h"

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif


/*
 * Internal routines
 */

enum path_delim
{
	PATH_NONE, PATH_OPEN, PATH_CLOSED
};

static int	point_inside(Point *p, int npts, Point *plist);
static int	lseg_crossing(double x, double y, double px, double py);
static BOX *box_construct(double x1, double x2, double y1, double y2);
static BOX *box_fill(BOX *result, double x1, double x2, double y1, double y2);
static bool box_ov(BOX *box1, BOX *box2);
static double box_ht(BOX *box);
static double box_wd(BOX *box);
static double circle_ar(CIRCLE *circle);
static CIRCLE *circle_copy(CIRCLE *circle);
static LINE *line_construct_pm(Point *pt, double m);
static void line_construct_pts(LINE *line, Point *pt1, Point *pt2);
static bool lseg_intersect_internal(LSEG *l1, LSEG *l2);
static double lseg_dt(LSEG *l1, LSEG *l2);
static bool on_ps_internal(Point *pt, LSEG *lseg);
static void make_bound_box(POLYGON *poly);
static bool plist_same(int npts, Point *p1, Point *p2);
static Point *point_construct(double x, double y);
static Point *point_copy(Point *pt);
static double single_decode(char *num, char **endptr_p,
			  const char *type_name, const char *orig_string);
static void single_encode(float8 x, StringInfo str);
static void pair_decode(char *str, double *x, double *y, char **endptr_p,
			const char *type_name, const char *orig_string);
static void pair_encode(float8 x, float8 y, StringInfo str);
static int	pair_count(char *s, char delim);
static void path_decode(char *str, bool opentype, int npts, Point *p,
			bool *isopen, char **endptr_p,
			const char *type_name, const char *orig_string);
static char *path_encode(enum path_delim path_delim, int npts, Point *pt);
static void statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2);
static double box_ar(BOX *box);
static void box_cn(Point *center, BOX *box);
static Point *interpt_sl(LSEG *lseg, LINE *line);
static bool has_interpt_sl(LSEG *lseg, LINE *line);
static double dist_pl_internal(Point *pt, LINE *line);
static double dist_ps_internal(Point *pt, LSEG *lseg);
static Point *line_interpt_internal(LINE *l1, LINE *l2);
static bool lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start);
static Point *lseg_interpt_internal(LSEG *l1, LSEG *l2);
static double dist_ppoly_internal(Point *pt, POLYGON *poly);


/*
 * Delimiters for input and output strings.
 * LDELIM, RDELIM, and DELIM are left, right, and separator delimiters, respectively.
 * LDELIM_EP, RDELIM_EP are left and right delimiters for paths with endpoints.
 */

#define LDELIM			'('
#define RDELIM			')'
#define DELIM			','
#define LDELIM_EP		'['
#define RDELIM_EP		']'
#define LDELIM_C		'<'
#define RDELIM_C		'>'


/*
 * Geometric data types are composed of points.
 * This code tries to support a common format throughout the data types,
 *	to allow for more predictable usage and data type conversion.
 * The fundamental unit is the point. Other units are line segments,
 *	open paths, boxes, closed paths, and polygons (which should be considered
 *	non-intersecting closed paths).
 *
 * Data representation is as follows:
 *	point:				(x,y)
 *	line segment:		[(x1,y1),(x2,y2)]
 *	box:				(x1,y1),(x2,y2)
 *	open path:			[(x1,y1),...,(xn,yn)]
 *	closed path:		((x1,y1),...,(xn,yn))
 *	polygon:			((x1,y1),...,(xn,yn))
 *
 * For boxes, the points are opposite corners with the first point at the top right.
 * For closed paths and polygons, the points should be reordered to allow
 *	fast and correct equality comparisons.
 *
 * XXX perhaps points in complex shapes should be reordered internally
 *	to allow faster internal operations, but should keep track of input order
 *	and restore that order for text output - tgl 97/01/16
 */

static double
single_decode(char *num, char **endptr_p,
			  const char *type_name, const char *orig_string)
{
	return float8in_internal(num, endptr_p, type_name, orig_string);
}								/* single_decode() */

static void
single_encode(float8 x, StringInfo str)
{
	char	   *xstr = float8out_internal(x);

	appendStringInfoString(str, xstr);
	pfree(xstr);
}								/* single_encode() */

static void
pair_decode(char *str, double *x, double *y, char **endptr_p,
			const char *type_name, const char *orig_string)
{
	bool		has_delim;

	while (isspace((unsigned char) *str))
		str++;
	if ((has_delim = (*str == LDELIM)))
		str++;

	*x = float8in_internal(str, &str, type_name, orig_string);

	if (*str++ != DELIM)
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("invalid input syntax for type %s: \"%s\"",
						type_name, orig_string)));

	*y = float8in_internal(str, &str, type_name, orig_string);

	if (has_delim)
	{
		if (*str++ != RDELIM)
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("invalid input syntax for type %s: \"%s\"",
							type_name, orig_string)));
		while (isspace((unsigned char) *str))
			str++;
	}

	/* report stopping point if wanted, else complain if not end of string */
	if (endptr_p)
		*endptr_p = str;
	else if (*str != '\0')
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("invalid input syntax for type %s: \"%s\"",
						type_name, orig_string)));
}

static void
pair_encode(float8 x, float8 y, StringInfo str)
{
	char	   *xstr = float8out_internal(x);
	char	   *ystr = float8out_internal(y);

	appendStringInfo(str, "%s,%s", xstr, ystr);
	pfree(xstr);
	pfree(ystr);
}

static void
path_decode(char *str, bool opentype, int npts, Point *p,
			bool *isopen, char **endptr_p,
			const char *type_name, const char *orig_string)
{
	int			depth = 0;
	char	   *cp;
	int			i;

	while (isspace((unsigned char) *str))
		str++;
	if ((*isopen = (*str == LDELIM_EP)))
	{
		/* no open delimiter allowed? */
		if (!opentype)
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("invalid input syntax for type %s: \"%s\"",
							type_name, orig_string)));
		depth++;
		str++;
	}
	else if (*str == LDELIM)
	{
		cp = (str + 1);
		while (isspace((unsigned char) *cp))
			cp++;
		if (*cp == LDELIM)
		{
			depth++;
			str = cp;
		}
		else if (strrchr(str, LDELIM) == str)
		{
			depth++;
			str = cp;
		}
	}

	for (i = 0; i < npts; i++)
	{
		pair_decode(str, &(p->x), &(p->y), &str, type_name, orig_string);
		if (*str == DELIM)
			str++;
		p++;
	}

	while (isspace((unsigned char) *str))
		str++;
	while (depth > 0)
	{
		if ((*str == RDELIM)
			|| ((*str == RDELIM_EP) && (*isopen) && (depth == 1)))
		{
			depth--;
			str++;
			while (isspace((unsigned char) *str))
				str++;
		}
		else
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("invalid input syntax for type %s: \"%s\"",
							type_name, orig_string)));
	}

	/* report stopping point if wanted, else complain if not end of string */
	if (endptr_p)
		*endptr_p = str;
	else if (*str != '\0')
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("invalid input syntax for type %s: \"%s\"",
						type_name, orig_string)));
}								/* path_decode() */

static char *
path_encode(enum path_delim path_delim, int npts, Point *pt)
{
	StringInfoData str;
	int			i;

	initStringInfo(&str);

	switch (path_delim)
	{
		case PATH_CLOSED:
			appendStringInfoChar(&str, LDELIM);
			break;
		case PATH_OPEN:
			appendStringInfoChar(&str, LDELIM_EP);
			break;
		case PATH_NONE:
			break;
	}

	for (i = 0; i < npts; i++)
	{
		if (i > 0)
			appendStringInfoChar(&str, DELIM);
		appendStringInfoChar(&str, LDELIM);
		pair_encode(pt->x, pt->y, &str);
		appendStringInfoChar(&str, RDELIM);
		pt++;
	}

	switch (path_delim)
	{
		case PATH_CLOSED:
			appendStringInfoChar(&str, RDELIM);
			break;
		case PATH_OPEN:
			appendStringInfoChar(&str, RDELIM_EP);
			break;
		case PATH_NONE:
			break;
	}

	return str.data;
}								/* path_encode() */

/*-------------------------------------------------------------
 * pair_count - count the number of points
 * allow the following notation:
 * '((1,2),(3,4))'
 * '(1,3,2,4)'
 * require an odd number of delim characters in the string
 *-------------------------------------------------------------*/
static int
pair_count(char *s, char delim)
{
	int			ndelim = 0;

	while ((s = strchr(s, delim)) != NULL)
	{
		ndelim++;
		s++;
	}
	return (ndelim % 2) ? ((ndelim + 1) / 2) : -1;
}


/***********************************************************************
 **
 **		Routines for two-dimensional boxes.
 **
 ***********************************************************************/

/*----------------------------------------------------------
 * Formatting and conversion routines.
 *---------------------------------------------------------*/

/*		box_in	-		convert a string to internal form.
 *
 *		External format: (two corners of box)
 *				"(f8, f8), (f8, f8)"
 *				also supports the older style "(f8, f8, f8, f8)"
 */
Datum
box_in(PG_FUNCTION_ARGS)
{
	char	   *str = PG_GETARG_CSTRING(0);
	BOX		   *box = (BOX *) palloc(sizeof(BOX));
	bool		isopen;
	double		x,
				y;

	path_decode(str, false, 2, &(box->high), &isopen, NULL, "box", str);

	/* reorder corners if necessary... */
	if (box->high.x < box->low.x)
	{
		x = box->high.x;
		box->high.x = box->low.x;
		box->low.x = x;
	}
	if (box->high.y < box->low.y)
	{
		y = box->high.y;
		box->high.y = box->low.y;
		box->low.y = y;
	}

	PG_RETURN_BOX_P(box);
}

/*		box_out -		convert a box to external form.
 */
Datum
box_out(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);

	PG_RETURN_CSTRING(path_encode(PATH_NONE, 2, &(box->high)));
}

/*
 *		box_recv			- converts external binary format to box
 */
Datum
box_recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
	BOX		   *box;
	double		x,
				y;

	box = (BOX *) palloc(sizeof(BOX));

	box->high.x = pq_getmsgfloat8(buf);
	box->high.y = pq_getmsgfloat8(buf);
	box->low.x = pq_getmsgfloat8(buf);
	box->low.y = pq_getmsgfloat8(buf);

	/* reorder corners if necessary... */
	if (box->high.x < box->low.x)
	{
		x = box->high.x;
		box->high.x = box->low.x;
		box->low.x = x;
	}
	if (box->high.y < box->low.y)
	{
		y = box->high.y;
		box->high.y = box->low.y;
		box->low.y = y;
	}

	PG_RETURN_BOX_P(box);
}

/*
 *		box_send			- converts box to binary format
 */
Datum
box_send(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);
	StringInfoData buf;

	pq_begintypsend(&buf);
	pq_sendfloat8(&buf, box->high.x);
	pq_sendfloat8(&buf, box->high.y);
	pq_sendfloat8(&buf, box->low.x);
	pq_sendfloat8(&buf, box->low.y);
	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/*		box_construct	-		fill in a new box.
 */
static BOX *
box_construct(double x1, double x2, double y1, double y2)
{
	BOX		   *result = (BOX *) palloc(sizeof(BOX));

	return box_fill(result, x1, x2, y1, y2);
}


/*		box_fill		-		fill in a given box struct
 */
static BOX *
box_fill(BOX *result, double x1, double x2, double y1, double y2)
{
	if (x1 > x2)
	{
		result->high.x = x1;
		result->low.x = x2;
	}
	else
	{
		result->high.x = x2;
		result->low.x = x1;
	}
	if (y1 > y2)
	{
		result->high.y = y1;
		result->low.y = y2;
	}
	else
	{
		result->high.y = y2;
		result->low.y = y1;
	}

	return result;
}


/*		box_copy		-		copy a box
 */
BOX *
box_copy(BOX *box)
{
	BOX		   *result = (BOX *) palloc(sizeof(BOX));

	memcpy((char *) result, (char *) box, sizeof(BOX));

	return result;
}


/*----------------------------------------------------------
 *	Relational operators for BOXes.
 *		<, >, <=, >=, and == are based on box area.
 *---------------------------------------------------------*/

/*		box_same		-		are two boxes identical?
 */
Datum
box_same(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPeq(box1->high.x, box2->high.x) &&
				   FPeq(box1->low.x, box2->low.x) &&
				   FPeq(box1->high.y, box2->high.y) &&
				   FPeq(box1->low.y, box2->low.y));
}

/*		box_overlap		-		does box1 overlap box2?
 */
Datum
box_overlap(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(box_ov(box1, box2));
}

static bool
box_ov(BOX *box1, BOX *box2)
{
	return (FPle(box1->low.x, box2->high.x) &&
			FPle(box2->low.x, box1->high.x) &&
			FPle(box1->low.y, box2->high.y) &&
			FPle(box2->low.y, box1->high.y));
}

/*		box_left		-		is box1 strictly left of box2?
 */
Datum
box_left(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPlt(box1->high.x, box2->low.x));
}

/*		box_overleft	-		is the right edge of box1 at or left of
 *								the right edge of box2?
 *
 *		This is "less than or equal" for the end of a time range,
 *		when time ranges are stored as rectangles.
 */
Datum
box_overleft(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPle(box1->high.x, box2->high.x));
}

/*		box_right		-		is box1 strictly right of box2?
 */
Datum
box_right(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPgt(box1->low.x, box2->high.x));
}

/*		box_overright	-		is the left edge of box1 at or right of
 *								the left edge of box2?
 *
 *		This is "greater than or equal" for time ranges, when time ranges
 *		are stored as rectangles.
 */
Datum
box_overright(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPge(box1->low.x, box2->low.x));
}

/*		box_below		-		is box1 strictly below box2?
 */
Datum
box_below(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPlt(box1->high.y, box2->low.y));
}

/*		box_overbelow	-		is the upper edge of box1 at or below
 *								the upper edge of box2?
 */
Datum
box_overbelow(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPle(box1->high.y, box2->high.y));
}

/*		box_above		-		is box1 strictly above box2?
 */
Datum
box_above(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPgt(box1->low.y, box2->high.y));
}

/*		box_overabove	-		is the lower edge of box1 at or above
 *								the lower edge of box2?
 */
Datum
box_overabove(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPge(box1->low.y, box2->low.y));
}

/*		box_contained	-		is box1 contained by box2?
 */
Datum
box_contained(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPle(box1->high.x, box2->high.x) &&
				   FPge(box1->low.x, box2->low.x) &&
				   FPle(box1->high.y, box2->high.y) &&
				   FPge(box1->low.y, box2->low.y));
}

/*		box_contain		-		does box1 contain box2?
 */
Datum
box_contain(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPge(box1->high.x, box2->high.x) &&
				   FPle(box1->low.x, box2->low.x) &&
				   FPge(box1->high.y, box2->high.y) &&
				   FPle(box1->low.y, box2->low.y));
}


/*		box_positionop	-
 *				is box1 entirely {above,below} box2?
 *
 * box_below_eq and box_above_eq are obsolete versions that (probably
 * erroneously) accept the equal-boundaries case.  Since these are not
 * in sync with the box_left and box_right code, they are deprecated and
 * not supported in the PG 8.1 rtree operator class extension.
 */
Datum
box_below_eq(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPle(box1->high.y, box2->low.y));
}

Datum
box_above_eq(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPge(box1->low.y, box2->high.y));
}


/*		box_relop		-		is area(box1) relop area(box2), within
 *								our accuracy constraint?
 */
Datum
box_lt(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPlt(box_ar(box1), box_ar(box2)));
}

Datum
box_gt(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPgt(box_ar(box1), box_ar(box2)));
}

Datum
box_eq(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPeq(box_ar(box1), box_ar(box2)));
}

Datum
box_le(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPle(box_ar(box1), box_ar(box2)));
}

Datum
box_ge(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(FPge(box_ar(box1), box_ar(box2)));
}


/*----------------------------------------------------------
 *	"Arithmetic" operators on boxes.
 *---------------------------------------------------------*/

/*		box_area		-		returns the area of the box.
 */
Datum
box_area(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);

	PG_RETURN_FLOAT8(box_ar(box));
}


/*		box_width		-		returns the width of the box
 *								  (horizontal magnitude).
 */
Datum
box_width(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);

	PG_RETURN_FLOAT8(box->high.x - box->low.x);
}


/*		box_height		-		returns the height of the box
 *								  (vertical magnitude).
 */
Datum
box_height(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);

	PG_RETURN_FLOAT8(box->high.y - box->low.y);
}


/*		box_distance	-		returns the distance between the
 *								  center points of two boxes.
 */
Datum
box_distance(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);
	Point		a,
				b;

	box_cn(&a, box1);
	box_cn(&b, box2);

	PG_RETURN_FLOAT8(HYPOT(a.x - b.x, a.y - b.y));
}


/*		box_center		-		returns the center point of the box.
 */
Datum
box_center(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);
	Point	   *result = (Point *) palloc(sizeof(Point));

	box_cn(result, box);

	PG_RETURN_POINT_P(result);
}


/*		box_ar	-		returns the area of the box.
 */
static double
box_ar(BOX *box)
{
	return box_wd(box) * box_ht(box);
}


/*		box_cn	-		stores the centerpoint of the box into *center.
 */
static void
box_cn(Point *center, BOX *box)
{
	center->x = (box->high.x + box->low.x) / 2.0;
	center->y = (box->high.y + box->low.y) / 2.0;
}


/*		box_wd	-		returns the width (length) of the box
 *								  (horizontal magnitude).
 */
static double
box_wd(BOX *box)
{
	return box->high.x - box->low.x;
}


/*		box_ht	-		returns the height of the box
 *								  (vertical magnitude).
 */
static double
box_ht(BOX *box)
{
	return box->high.y - box->low.y;
}


/*----------------------------------------------------------
 *	Funky operations.
 *---------------------------------------------------------*/

/*		box_intersect	-
 *				returns the overlapping portion of two boxes,
 *				  or NULL if they do not intersect.
 */
Datum
box_intersect(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0);
	BOX		   *box2 = PG_GETARG_BOX_P(1);
	BOX		   *result;

	if (!box_ov(box1, box2))
		PG_RETURN_NULL();

	result = (BOX *) palloc(sizeof(BOX));

	result->high.x = Min(box1->high.x, box2->high.x);
	result->low.x = Max(box1->low.x, box2->low.x);
	result->high.y = Min(box1->high.y, box2->high.y);
	result->low.y = Max(box1->low.y, box2->low.y);

	PG_RETURN_BOX_P(result);
}


/*		box_diagonal	-
 *				returns a line segment which happens to be the
 *				  positive-slope diagonal of "box".
 */
Datum
box_diagonal(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);
	LSEG	   *result = (LSEG *) palloc(sizeof(LSEG));

	statlseg_construct(result, &box->high, &box->low);

	PG_RETURN_LSEG_P(result);
}

/***********************************************************************
 **
 **		Routines for 2D lines.
 **
 ***********************************************************************/

static bool
line_decode(char *s, const char *str, LINE *line)
{
	/* s was already advanced over leading '{' */
	line->A = single_decode(s, &s, "line", str);
	if (*s++ != DELIM)
		return false;
	line->B = single_decode(s, &s, "line", str);
	if (*s++ != DELIM)
		return false;
	line->C = single_decode(s, &s, "line", str);
	if (*s++ != '}')
		return false;
	while (isspace((unsigned char) *s))
		s++;
	if (*s != '\0')
		return false;
	return true;
}

Datum
line_in(PG_FUNCTION_ARGS)
{
	char	   *str = PG_GETARG_CSTRING(0);
	LINE	   *line = (LINE *) palloc(sizeof(LINE));
	LSEG		lseg;
	bool		isopen;
	char	   *s;

	s = str;
	while (isspace((unsigned char) *s))
		s++;
	if (*s == '{')
	{
		if (!line_decode(s + 1, str, line))
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("invalid input syntax for type %s: \"%s\"",
							"line", str)));
		if (FPzero(line->A) && FPzero(line->B))
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("invalid line specification: A and B cannot both be zero")));
	}
	else
	{
		path_decode(s, true, 2, &(lseg.p[0]), &isopen, NULL, "line", str);
		if (FPeq(lseg.p[0].x, lseg.p[1].x) && FPeq(lseg.p[0].y, lseg.p[1].y))
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("invalid line specification: must be two distinct points")));
		line_construct_pts(line, &lseg.p[0], &lseg.p[1]);
	}

	PG_RETURN_LINE_P(line);
}


Datum
line_out(PG_FUNCTION_ARGS)
{
	LINE	   *line = PG_GETARG_LINE_P(0);
	char	   *astr = float8out_internal(line->A);
	char	   *bstr = float8out_internal(line->B);
	char	   *cstr = float8out_internal(line->C);

	PG_RETURN_CSTRING(psprintf("{%s,%s,%s}", astr, bstr, cstr));
}

/*
 *		line_recv			- converts external binary format to line
 */
Datum
line_recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
	LINE	   *line;

	line = (LINE *) palloc(sizeof(LINE));

	line->A = pq_getmsgfloat8(buf);
	line->B = pq_getmsgfloat8(buf);
	line->C = pq_getmsgfloat8(buf);

	PG_RETURN_LINE_P(line);
}

/*
 *		line_send			- converts line to binary format
 */
Datum
line_send(PG_FUNCTION_ARGS)
{
	LINE	   *line = PG_GETARG_LINE_P(0);
	StringInfoData buf;

	pq_begintypsend(&buf);
	pq_sendfloat8(&buf, line->A);
	pq_sendfloat8(&buf, line->B);
	pq_sendfloat8(&buf, line->C);
	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/*----------------------------------------------------------
 *	Conversion routines from one line formula to internal.
 *		Internal form:	Ax+By+C=0
 *---------------------------------------------------------*/

/* line_construct_pm()
 * point-slope
 */
static LINE *
line_construct_pm(Point *pt, double m)
{
	LINE	   *result = (LINE *) palloc(sizeof(LINE));

	if (m == DBL_MAX)
	{
		/* vertical - use "x = C" */
		result->A = -1;
		result->B = 0;
		result->C = pt->x;
	}
	else
	{
		/* use "mx - y + yinter = 0" */
		result->A = m;
		result->B = -1.0;
		result->C = pt->y - m * pt->x;
	}

	return result;
}

/*
 * Fill already-allocated LINE struct from two points on the line
 */
static void
line_construct_pts(LINE *line, Point *pt1, Point *pt2)
{
	if (FPeq(pt1->x, pt2->x))
	{							/* vertical */
		/* use "x = C" */
		line->A = -1;
		line->B = 0;
		line->C = pt1->x;
#ifdef GEODEBUG
		printf("line_construct_pts- line is vertical\n");
#endif
	}
	else if (FPeq(pt1->y, pt2->y))
	{							/* horizontal */
		/* use "y = C" */
		line->A = 0;
		line->B = -1;
		line->C = pt1->y;
#ifdef GEODEBUG
		printf("line_construct_pts- line is horizontal\n");
#endif
	}
	else
	{
		/* use "mx - y + yinter = 0" */
		line->A = (pt2->y - pt1->y) / (pt2->x - pt1->x);
		line->B = -1.0;
		line->C = pt1->y - line->A * pt1->x;
		/* on some platforms, the preceding expression tends to produce -0 */
		if (line->C == 0.0)
			line->C = 0.0;
#ifdef GEODEBUG
		printf("line_construct_pts- line is neither vertical nor horizontal (diffs x=%.*g, y=%.*g\n",
			   DBL_DIG, (pt2->x - pt1->x), DBL_DIG, (pt2->y - pt1->y));
#endif
	}
}

/* line_construct_pp()
 * two points
 */
Datum
line_construct_pp(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);
	LINE	   *result = (LINE *) palloc(sizeof(LINE));

	line_construct_pts(result, pt1, pt2);
	PG_RETURN_LINE_P(result);
}


/*----------------------------------------------------------
 *	Relative position routines.
 *---------------------------------------------------------*/

Datum
line_intersect(PG_FUNCTION_ARGS)
{
	LINE	   *l1 = PG_GETARG_LINE_P(0);
	LINE	   *l2 = PG_GETARG_LINE_P(1);

	PG_RETURN_BOOL(!DatumGetBool(DirectFunctionCall2(line_parallel,
													 LinePGetDatum(l1),
													 LinePGetDatum(l2))));
}

Datum
line_parallel(PG_FUNCTION_ARGS)
{
	LINE	   *l1 = PG_GETARG_LINE_P(0);
	LINE	   *l2 = PG_GETARG_LINE_P(1);

	if (FPzero(l1->B))
		PG_RETURN_BOOL(FPzero(l2->B));

	PG_RETURN_BOOL(FPeq(l2->A, l1->A * (l2->B / l1->B)));
}

Datum
line_perp(PG_FUNCTION_ARGS)
{
	LINE	   *l1 = PG_GETARG_LINE_P(0);
	LINE	   *l2 = PG_GETARG_LINE_P(1);

	if (FPzero(l1->A))
		PG_RETURN_BOOL(FPzero(l2->B));
	else if (FPzero(l1->B))
		PG_RETURN_BOOL(FPzero(l2->A));

	PG_RETURN_BOOL(FPeq(((l1->A * l2->B) / (l1->B * l2->A)), -1.0));
}

Datum
line_vertical(PG_FUNCTION_ARGS)
{
	LINE	   *line = PG_GETARG_LINE_P(0);

	PG_RETURN_BOOL(FPzero(line->B));
}

Datum
line_horizontal(PG_FUNCTION_ARGS)
{
	LINE	   *line = PG_GETARG_LINE_P(0);

	PG_RETURN_BOOL(FPzero(line->A));
}

Datum
line_eq(PG_FUNCTION_ARGS)
{
	LINE	   *l1 = PG_GETARG_LINE_P(0);
	LINE	   *l2 = PG_GETARG_LINE_P(1);
	double		k;

	if (!FPzero(l2->A))
		k = l1->A / l2->A;
	else if (!FPzero(l2->B))
		k = l1->B / l2->B;
	else if (!FPzero(l2->C))
		k = l1->C / l2->C;
	else
		k = 1.0;

	PG_RETURN_BOOL(FPeq(l1->A, k * l2->A) &&
				   FPeq(l1->B, k * l2->B) &&
				   FPeq(l1->C, k * l2->C));
}


/*----------------------------------------------------------
 *	Line arithmetic routines.
 *---------------------------------------------------------*/

/* line_distance()
 * Distance between two lines.
 */
Datum
line_distance(PG_FUNCTION_ARGS)
{
	LINE	   *l1 = PG_GETARG_LINE_P(0);
	LINE	   *l2 = PG_GETARG_LINE_P(1);
	float8		result;
	Point	   *tmp;

	if (!DatumGetBool(DirectFunctionCall2(line_parallel,
										  LinePGetDatum(l1),
										  LinePGetDatum(l2))))
		PG_RETURN_FLOAT8(0.0);
	if (FPzero(l1->B))			/* vertical? */
		PG_RETURN_FLOAT8(fabs(l1->C - l2->C));
	tmp = point_construct(0.0, l1->C);
	result = dist_pl_internal(tmp, l2);
	PG_RETURN_FLOAT8(result);
}

/* line_interpt()
 * Point where two lines l1, l2 intersect (if any)
 */
Datum
line_interpt(PG_FUNCTION_ARGS)
{
	LINE	   *l1 = PG_GETARG_LINE_P(0);
	LINE	   *l2 = PG_GETARG_LINE_P(1);
	Point	   *result;

	result = line_interpt_internal(l1, l2);

	if (result == NULL)
		PG_RETURN_NULL();
	PG_RETURN_POINT_P(result);
}

/*
 * Internal version of line_interpt
 *
 * returns a NULL pointer if no intersection point
 */
static Point *
line_interpt_internal(LINE *l1, LINE *l2)
{
	Point	   *result;
	double		x,
				y;

	/*
	 * NOTE: if the lines are identical then we will find they are parallel
	 * and report "no intersection".  This is a little weird, but since
	 * there's no *unique* intersection, maybe it's appropriate behavior.
	 */
	if (DatumGetBool(DirectFunctionCall2(line_parallel,
										 LinePGetDatum(l1),
										 LinePGetDatum(l2))))
		return NULL;

	if (FPzero(l1->B))			/* l1 vertical? */
	{
		x = l1->C;
		y = (l2->A * x + l2->C);
	}
	else if (FPzero(l2->B))		/* l2 vertical? */
	{
		x = l2->C;
		y = (l1->A * x + l1->C);
	}
	else
	{
		x = (l1->C - l2->C) / (l2->A - l1->A);
		y = (l1->A * x + l1->C);
	}
	result = point_construct(x, y);

#ifdef GEODEBUG
	printf("line_interpt- lines are A=%.*g, B=%.*g, C=%.*g, A=%.*g, B=%.*g, C=%.*g\n",
		   DBL_DIG, l1->A, DBL_DIG, l1->B, DBL_DIG, l1->C, DBL_DIG, l2->A, DBL_DIG, l2->B, DBL_DIG, l2->C);
	printf("line_interpt- lines intersect at (%.*g,%.*g)\n", DBL_DIG, x, DBL_DIG, y);
#endif

	return result;
}


/***********************************************************************
 **
 **		Routines for 2D paths (sequences of line segments, also
 **				called `polylines').
 **
 **				This is not a general package for geometric paths,
 **				which of course include polygons; the emphasis here
 **				is on (for example) usefulness in wire layout.
 **
 ***********************************************************************/

/*----------------------------------------------------------
 *	String to path / path to string conversion.
 *		External format:
 *				"((xcoord, ycoord),... )"
 *				"[(xcoord, ycoord),... ]"
 *				"(xcoord, ycoord),... "
 *				"[xcoord, ycoord,... ]"
 *		Also support older format:
 *				"(closed, npts, xcoord, ycoord,... )"
 *---------------------------------------------------------*/

Datum
path_area(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P(0);
	double		area = 0.0;
	int			i,
				j;

	if (!path->closed)
		PG_RETURN_NULL();

	for (i = 0; i < path->npts; i++)
	{
		j = (i + 1) % path->npts;
		area += path->p[i].x * path->p[j].y;
		area -= path->p[i].y * path->p[j].x;
	}

	area *= 0.5;
	PG_RETURN_FLOAT8(area < 0.0 ? -area : area);
}


Datum
path_in(PG_FUNCTION_ARGS)
{
	char	   *str = PG_GETARG_CSTRING(0);
	PATH	   *path;
	bool		isopen;
	char	   *s;
	int			npts;
	int			size;
	int			base_size;
	int			depth = 0;

	if ((npts = pair_count(str, ',')) <= 0)
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("invalid input syntax for type %s: \"%s\"",
						"path", str)));

	s = str;
	while (isspace((unsigned char) *s))
		s++;

	/* skip single leading paren */
	if ((*s == LDELIM) && (strrchr(s, LDELIM) == s))
	{
		s++;
		depth++;
	}

	base_size = sizeof(path->p[0]) * npts;
	size = offsetof(PATH, p) + base_size;

	/* Check for integer overflow */
	if (base_size / npts != sizeof(path->p[0]) || size <= base_size)
		ereport(ERROR,
				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
				 errmsg("too many points requested")));

	path = (PATH *) palloc(size);

	SET_VARSIZE(path, size);
	path->npts = npts;

	path_decode(s, true, npts, &(path->p[0]), &isopen, &s, "path", str);

	if (depth >= 1)
	{
		if (*s++ != RDELIM)
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("invalid input syntax for type %s: \"%s\"",
							"path", str)));
		while (isspace((unsigned char) *s))
			s++;
	}
	if (*s != '\0')
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("invalid input syntax for type %s: \"%s\"",
						"path", str)));

	path->closed = (!isopen);
	/* prevent instability in unused pad bytes */
	path->dummy = 0;

	PG_RETURN_PATH_P(path);
}


Datum
path_out(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P(0);

	PG_RETURN_CSTRING(path_encode(path->closed ? PATH_CLOSED : PATH_OPEN, path->npts, path->p));
}

/*
 *		path_recv			- converts external binary format to path
 *
 * External representation is closed flag (a boolean byte), int32 number
 * of points, and the points.
 */
Datum
path_recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
	PATH	   *path;
	int			closed;
	int32		npts;
	int32		i;
	int			size;

	closed = pq_getmsgbyte(buf);
	npts = pq_getmsgint(buf, sizeof(int32));
	if (npts <= 0 || npts >= (int32) ((INT_MAX - offsetof(PATH, p)) / sizeof(Point)))
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
				 errmsg("invalid number of points in external \"path\" value")));

	size = offsetof(PATH, p) + sizeof(path->p[0]) * npts;
	path = (PATH *) palloc(size);

	SET_VARSIZE(path, size);
	path->npts = npts;
	path->closed = (closed ? 1 : 0);
	/* prevent instability in unused pad bytes */
	path->dummy = 0;

	for (i = 0; i < npts; i++)
	{
		path->p[i].x = pq_getmsgfloat8(buf);
		path->p[i].y = pq_getmsgfloat8(buf);
	}

	PG_RETURN_PATH_P(path);
}

/*
 *		path_send			- converts path to binary format
 */
Datum
path_send(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P(0);
	StringInfoData buf;
	int32		i;

	pq_begintypsend(&buf);
	pq_sendbyte(&buf, path->closed ? 1 : 0);
	pq_sendint32(&buf, path->npts);
	for (i = 0; i < path->npts; i++)
	{
		pq_sendfloat8(&buf, path->p[i].x);
		pq_sendfloat8(&buf, path->p[i].y);
	}
	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/*----------------------------------------------------------
 *	Relational operators.
 *		These are based on the path cardinality,
 *		as stupid as that sounds.
 *
 *		Better relops and access methods coming soon.
 *---------------------------------------------------------*/

Datum
path_n_lt(PG_FUNCTION_ARGS)
{
	PATH	   *p1 = PG_GETARG_PATH_P(0);
	PATH	   *p2 = PG_GETARG_PATH_P(1);

	PG_RETURN_BOOL(p1->npts < p2->npts);
}

Datum
path_n_gt(PG_FUNCTION_ARGS)
{
	PATH	   *p1 = PG_GETARG_PATH_P(0);
	PATH	   *p2 = PG_GETARG_PATH_P(1);

	PG_RETURN_BOOL(p1->npts > p2->npts);
}

Datum
path_n_eq(PG_FUNCTION_ARGS)
{
	PATH	   *p1 = PG_GETARG_PATH_P(0);
	PATH	   *p2 = PG_GETARG_PATH_P(1);

	PG_RETURN_BOOL(p1->npts == p2->npts);
}

Datum
path_n_le(PG_FUNCTION_ARGS)
{
	PATH	   *p1 = PG_GETARG_PATH_P(0);
	PATH	   *p2 = PG_GETARG_PATH_P(1);

	PG_RETURN_BOOL(p1->npts <= p2->npts);
}

Datum
path_n_ge(PG_FUNCTION_ARGS)
{
	PATH	   *p1 = PG_GETARG_PATH_P(0);
	PATH	   *p2 = PG_GETARG_PATH_P(1);

	PG_RETURN_BOOL(p1->npts >= p2->npts);
}

/*----------------------------------------------------------
 * Conversion operators.
 *---------------------------------------------------------*/

Datum
path_isclosed(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P(0);

	PG_RETURN_BOOL(path->closed);
}

Datum
path_isopen(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P(0);

	PG_RETURN_BOOL(!path->closed);
}

Datum
path_npoints(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P(0);

	PG_RETURN_INT32(path->npts);
}


Datum
path_close(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P_COPY(0);

	path->closed = true;

	PG_RETURN_PATH_P(path);
}

Datum
path_open(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P_COPY(0);

	path->closed = false;

	PG_RETURN_PATH_P(path);
}


/* path_inter -
 *		Does p1 intersect p2 at any point?
 *		Use bounding boxes for a quick (O(n)) check, then do a
 *		O(n^2) iterative edge check.
 */
Datum
path_inter(PG_FUNCTION_ARGS)
{
	PATH	   *p1 = PG_GETARG_PATH_P(0);
	PATH	   *p2 = PG_GETARG_PATH_P(1);
	BOX			b1,
				b2;
	int			i,
				j;
	LSEG		seg1,
				seg2;

	if (p1->npts <= 0 || p2->npts <= 0)
		PG_RETURN_BOOL(false);

	b1.high.x = b1.low.x = p1->p[0].x;
	b1.high.y = b1.low.y = p1->p[0].y;
	for (i = 1; i < p1->npts; i++)
	{
		b1.high.x = Max(p1->p[i].x, b1.high.x);
		b1.high.y = Max(p1->p[i].y, b1.high.y);
		b1.low.x = Min(p1->p[i].x, b1.low.x);
		b1.low.y = Min(p1->p[i].y, b1.low.y);
	}
	b2.high.x = b2.low.x = p2->p[0].x;
	b2.high.y = b2.low.y = p2->p[0].y;
	for (i = 1; i < p2->npts; i++)
	{
		b2.high.x = Max(p2->p[i].x, b2.high.x);
		b2.high.y = Max(p2->p[i].y, b2.high.y);
		b2.low.x = Min(p2->p[i].x, b2.low.x);
		b2.low.y = Min(p2->p[i].y, b2.low.y);
	}
	if (!box_ov(&b1, &b2))
		PG_RETURN_BOOL(false);

	/* pairwise check lseg intersections */
	for (i = 0; i < p1->npts; i++)
	{
		int			iprev;

		if (i > 0)
			iprev = i - 1;
		else
		{
			if (!p1->closed)
				continue;
			iprev = p1->npts - 1;	/* include the closure segment */
		}

		for (j = 0; j < p2->npts; j++)
		{
			int			jprev;

			if (j > 0)
				jprev = j - 1;
			else
			{
				if (!p2->closed)
					continue;
				jprev = p2->npts - 1;	/* include the closure segment */
			}

			statlseg_construct(&seg1, &p1->p[iprev], &p1->p[i]);
			statlseg_construct(&seg2, &p2->p[jprev], &p2->p[j]);
			if (lseg_intersect_internal(&seg1, &seg2))
				PG_RETURN_BOOL(true);
		}
	}

	/* if we dropped through, no two segs intersected */
	PG_RETURN_BOOL(false);
}

/* path_distance()
 * This essentially does a cartesian product of the lsegs in the
 *	two paths, and finds the min distance between any two lsegs
 */
Datum
path_distance(PG_FUNCTION_ARGS)
{
	PATH	   *p1 = PG_GETARG_PATH_P(0);
	PATH	   *p2 = PG_GETARG_PATH_P(1);
	float8		min = 0.0;		/* initialize to keep compiler quiet */
	bool		have_min = false;
	float8		tmp;
	int			i,
				j;
	LSEG		seg1,
				seg2;

	for (i = 0; i < p1->npts; i++)
	{
		int			iprev;

		if (i > 0)
			iprev = i - 1;
		else
		{
			if (!p1->closed)
				continue;
			iprev = p1->npts - 1;	/* include the closure segment */
		}

		for (j = 0; j < p2->npts; j++)
		{
			int			jprev;

			if (j > 0)
				jprev = j - 1;
			else
			{
				if (!p2->closed)
					continue;
				jprev = p2->npts - 1;	/* include the closure segment */
			}

			statlseg_construct(&seg1, &p1->p[iprev], &p1->p[i]);
			statlseg_construct(&seg2, &p2->p[jprev], &p2->p[j]);

			tmp = DatumGetFloat8(DirectFunctionCall2(lseg_distance,
													 LsegPGetDatum(&seg1),
													 LsegPGetDatum(&seg2)));
			if (!have_min || tmp < min)
			{
				min = tmp;
				have_min = true;
			}
		}
	}

	if (!have_min)
		PG_RETURN_NULL();

	PG_RETURN_FLOAT8(min);
}


/*----------------------------------------------------------
 *	"Arithmetic" operations.
 *---------------------------------------------------------*/

Datum
path_length(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P(0);
	float8		result = 0.0;
	int			i;

	for (i = 0; i < path->npts; i++)
	{
		int			iprev;

		if (i > 0)
			iprev = i - 1;
		else
		{
			if (!path->closed)
				continue;
			iprev = path->npts - 1; /* include the closure segment */
		}

		result += point_dt(&path->p[iprev], &path->p[i]);
	}

	PG_RETURN_FLOAT8(result);
}

/***********************************************************************
 **
 **		Routines for 2D points.
 **
 ***********************************************************************/

/*----------------------------------------------------------
 *	String to point, point to string conversion.
 *		External format:
 *				"(x,y)"
 *				"x,y"
 *---------------------------------------------------------*/

Datum
point_in(PG_FUNCTION_ARGS)
{
	char	   *str = PG_GETARG_CSTRING(0);
	Point	   *point = (Point *) palloc(sizeof(Point));

	pair_decode(str, &point->x, &point->y, NULL, "point", str);
	PG_RETURN_POINT_P(point);
}

Datum
point_out(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);

	PG_RETURN_CSTRING(path_encode(PATH_NONE, 1, pt));
}

/*
 *		point_recv			- converts external binary format to point
 */
Datum
point_recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
	Point	   *point;

	point = (Point *) palloc(sizeof(Point));
	point->x = pq_getmsgfloat8(buf);
	point->y = pq_getmsgfloat8(buf);
	PG_RETURN_POINT_P(point);
}

/*
 *		point_send			- converts point to binary format
 */
Datum
point_send(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	StringInfoData buf;

	pq_begintypsend(&buf);
	pq_sendfloat8(&buf, pt->x);
	pq_sendfloat8(&buf, pt->y);
	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


static Point *
point_construct(double x, double y)
{
	Point	   *result = (Point *) palloc(sizeof(Point));

	result->x = x;
	result->y = y;
	return result;
}


static Point *
point_copy(Point *pt)
{
	Point	   *result;

	if (!PointerIsValid(pt))
		return NULL;

	result = (Point *) palloc(sizeof(Point));

	result->x = pt->x;
	result->y = pt->y;
	return result;
}


/*----------------------------------------------------------
 *	Relational operators for Points.
 *		Since we do have a sense of coordinates being
 *		"equal" to a given accuracy (point_vert, point_horiz),
 *		the other ops must preserve that sense.  This means
 *		that results may, strictly speaking, be a lie (unless
 *		EPSILON = 0.0).
 *---------------------------------------------------------*/

Datum
point_left(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);

	PG_RETURN_BOOL(FPlt(pt1->x, pt2->x));
}

Datum
point_right(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);

	PG_RETURN_BOOL(FPgt(pt1->x, pt2->x));
}

Datum
point_above(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);

	PG_RETURN_BOOL(FPgt(pt1->y, pt2->y));
}

Datum
point_below(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);

	PG_RETURN_BOOL(FPlt(pt1->y, pt2->y));
}

Datum
point_vert(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);

	PG_RETURN_BOOL(FPeq(pt1->x, pt2->x));
}

Datum
point_horiz(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);

	PG_RETURN_BOOL(FPeq(pt1->y, pt2->y));
}

Datum
point_eq(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);

	PG_RETURN_BOOL(FPeq(pt1->x, pt2->x) && FPeq(pt1->y, pt2->y));
}

Datum
point_ne(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);

	PG_RETURN_BOOL(FPne(pt1->x, pt2->x) || FPne(pt1->y, pt2->y));
}

/*----------------------------------------------------------
 *	"Arithmetic" operators on points.
 *---------------------------------------------------------*/

Datum
point_distance(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);

	PG_RETURN_FLOAT8(HYPOT(pt1->x - pt2->x, pt1->y - pt2->y));
}

double
point_dt(Point *pt1, Point *pt2)
{
#ifdef GEODEBUG
	printf("point_dt- segment (%f,%f),(%f,%f) length is %f\n",
		   pt1->x, pt1->y, pt2->x, pt2->y, HYPOT(pt1->x - pt2->x, pt1->y - pt2->y));
#endif
	return HYPOT(pt1->x - pt2->x, pt1->y - pt2->y);
}

Datum
point_slope(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);

	PG_RETURN_FLOAT8(point_sl(pt1, pt2));
}


double
point_sl(Point *pt1, Point *pt2)
{
	return (FPeq(pt1->x, pt2->x)
			? (double) DBL_MAX
			: (pt1->y - pt2->y) / (pt1->x - pt2->x));
}


/***********************************************************************
 **
 **		Routines for 2D line segments.
 **
 ***********************************************************************/

/*----------------------------------------------------------
 *	String to lseg, lseg to string conversion.
 *		External forms: "[(x1, y1), (x2, y2)]"
 *						"(x1, y1), (x2, y2)"
 *						"x1, y1, x2, y2"
 *		closed form ok	"((x1, y1), (x2, y2))"
 *		(old form)		"(x1, y1, x2, y2)"
 *---------------------------------------------------------*/

Datum
lseg_in(PG_FUNCTION_ARGS)
{
	char	   *str = PG_GETARG_CSTRING(0);
	LSEG	   *lseg = (LSEG *) palloc(sizeof(LSEG));
	bool		isopen;

	path_decode(str, true, 2, &(lseg->p[0]), &isopen, NULL, "lseg", str);
	PG_RETURN_LSEG_P(lseg);
}


Datum
lseg_out(PG_FUNCTION_ARGS)
{
	LSEG	   *ls = PG_GETARG_LSEG_P(0);

	PG_RETURN_CSTRING(path_encode(PATH_OPEN, 2, (Point *) &(ls->p[0])));
}

/*
 *		lseg_recv			- converts external binary format to lseg
 */
Datum
lseg_recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
	LSEG	   *lseg;

	lseg = (LSEG *) palloc(sizeof(LSEG));

	lseg->p[0].x = pq_getmsgfloat8(buf);
	lseg->p[0].y = pq_getmsgfloat8(buf);
	lseg->p[1].x = pq_getmsgfloat8(buf);
	lseg->p[1].y = pq_getmsgfloat8(buf);

	PG_RETURN_LSEG_P(lseg);
}

/*
 *		lseg_send			- converts lseg to binary format
 */
Datum
lseg_send(PG_FUNCTION_ARGS)
{
	LSEG	   *ls = PG_GETARG_LSEG_P(0);
	StringInfoData buf;

	pq_begintypsend(&buf);
	pq_sendfloat8(&buf, ls->p[0].x);
	pq_sendfloat8(&buf, ls->p[0].y);
	pq_sendfloat8(&buf, ls->p[1].x);
	pq_sendfloat8(&buf, ls->p[1].y);
	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/* lseg_construct -
 *		form a LSEG from two Points.
 */
Datum
lseg_construct(PG_FUNCTION_ARGS)
{
	Point	   *pt1 = PG_GETARG_POINT_P(0);
	Point	   *pt2 = PG_GETARG_POINT_P(1);
	LSEG	   *result = (LSEG *) palloc(sizeof(LSEG));

	result->p[0].x = pt1->x;
	result->p[0].y = pt1->y;
	result->p[1].x = pt2->x;
	result->p[1].y = pt2->y;

	PG_RETURN_LSEG_P(result);
}

/* like lseg_construct, but assume space already allocated */
static void
statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2)
{
	lseg->p[0].x = pt1->x;
	lseg->p[0].y = pt1->y;
	lseg->p[1].x = pt2->x;
	lseg->p[1].y = pt2->y;
}

Datum
lseg_length(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);

	PG_RETURN_FLOAT8(point_dt(&lseg->p[0], &lseg->p[1]));
}

/*----------------------------------------------------------
 *	Relative position routines.
 *---------------------------------------------------------*/

/*
 **  find intersection of the two lines, and see if it falls on
 **  both segments.
 */
Datum
lseg_intersect(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);

	PG_RETURN_BOOL(lseg_intersect_internal(l1, l2));
}

static bool
lseg_intersect_internal(LSEG *l1, LSEG *l2)
{
	LINE		ln;
	Point	   *interpt;
	bool		retval;

	line_construct_pts(&ln, &l2->p[0], &l2->p[1]);
	interpt = interpt_sl(l1, &ln);

	if (interpt != NULL && on_ps_internal(interpt, l2))
		retval = true;			/* interpt on l1 and l2 */
	else
		retval = false;
	return retval;
}

Datum
lseg_parallel(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);

	PG_RETURN_BOOL(FPeq(point_sl(&l1->p[0], &l1->p[1]),
						point_sl(&l2->p[0], &l2->p[1])));
}

/* lseg_perp()
 * Determine if two line segments are perpendicular.
 *
 * This code did not get the correct answer for
 *	'((0,0),(0,1))'::lseg ?-| '((0,0),(1,0))'::lseg
 * So, modified it to check explicitly for slope of vertical line
 *	returned by point_sl() and the results seem better.
 * - thomas 1998-01-31
 */
Datum
lseg_perp(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
	double		m1,
				m2;

	m1 = point_sl(&(l1->p[0]), &(l1->p[1]));
	m2 = point_sl(&(l2->p[0]), &(l2->p[1]));

#ifdef GEODEBUG
	printf("lseg_perp- slopes are %g and %g\n", m1, m2);
#endif
	if (FPzero(m1))
		PG_RETURN_BOOL(FPeq(m2, DBL_MAX));
	else if (FPzero(m2))
		PG_RETURN_BOOL(FPeq(m1, DBL_MAX));

	PG_RETURN_BOOL(FPeq(m1 / m2, -1.0));
}

Datum
lseg_vertical(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);

	PG_RETURN_BOOL(FPeq(lseg->p[0].x, lseg->p[1].x));
}

Datum
lseg_horizontal(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);

	PG_RETURN_BOOL(FPeq(lseg->p[0].y, lseg->p[1].y));
}


Datum
lseg_eq(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);

	PG_RETURN_BOOL(FPeq(l1->p[0].x, l2->p[0].x) &&
				   FPeq(l1->p[0].y, l2->p[0].y) &&
				   FPeq(l1->p[1].x, l2->p[1].x) &&
				   FPeq(l1->p[1].y, l2->p[1].y));
}

Datum
lseg_ne(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);

	PG_RETURN_BOOL(!FPeq(l1->p[0].x, l2->p[0].x) ||
				   !FPeq(l1->p[0].y, l2->p[0].y) ||
				   !FPeq(l1->p[1].x, l2->p[1].x) ||
				   !FPeq(l1->p[1].y, l2->p[1].y));
}

Datum
lseg_lt(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);

	PG_RETURN_BOOL(FPlt(point_dt(&l1->p[0], &l1->p[1]),
						point_dt(&l2->p[0], &l2->p[1])));
}

Datum
lseg_le(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);

	PG_RETURN_BOOL(FPle(point_dt(&l1->p[0], &l1->p[1]),
						point_dt(&l2->p[0], &l2->p[1])));
}

Datum
lseg_gt(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);

	PG_RETURN_BOOL(FPgt(point_dt(&l1->p[0], &l1->p[1]),
						point_dt(&l2->p[0], &l2->p[1])));
}

Datum
lseg_ge(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);

	PG_RETURN_BOOL(FPge(point_dt(&l1->p[0], &l1->p[1]),
						point_dt(&l2->p[0], &l2->p[1])));
}


/*----------------------------------------------------------
 *	Line arithmetic routines.
 *---------------------------------------------------------*/

/* lseg_distance -
 *		If two segments don't intersect, then the closest
 *		point will be from one of the endpoints to the other
 *		segment.
 */
Datum
lseg_distance(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);

	PG_RETURN_FLOAT8(lseg_dt(l1, l2));
}

/* lseg_dt()
 * Distance between two line segments.
 * Must check both sets of endpoints to ensure minimum distance is found.
 * - thomas 1998-02-01
 */
static double
lseg_dt(LSEG *l1, LSEG *l2)
{
	double		result,
				d;

	if (lseg_intersect_internal(l1, l2))
		return 0.0;

	d = dist_ps_internal(&l1->p[0], l2);
	result = d;
	d = dist_ps_internal(&l1->p[1], l2);
	result = Min(result, d);
	d = dist_ps_internal(&l2->p[0], l1);
	result = Min(result, d);
	d = dist_ps_internal(&l2->p[1], l1);
	result = Min(result, d);

	return result;
}


Datum
lseg_center(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
	Point	   *result;

	result = (Point *) palloc(sizeof(Point));

	result->x = (lseg->p[0].x + lseg->p[1].x) / 2.0;
	result->y = (lseg->p[0].y + lseg->p[1].y) / 2.0;

	PG_RETURN_POINT_P(result);
}

static Point *
lseg_interpt_internal(LSEG *l1, LSEG *l2)
{
	Point	   *result;
	LINE		tmp1,
				tmp2;

	/*
	 * Find the intersection of the appropriate lines, if any.
	 */
	line_construct_pts(&tmp1, &l1->p[0], &l1->p[1]);
	line_construct_pts(&tmp2, &l2->p[0], &l2->p[1]);
	result = line_interpt_internal(&tmp1, &tmp2);
	if (!PointerIsValid(result))
		return NULL;

	/*
	 * If the line intersection point isn't within l1 (or equivalently l2),
	 * there is no valid segment intersection point at all.
	 */
	if (!on_ps_internal(result, l1) ||
		!on_ps_internal(result, l2))
	{
		pfree(result);
		return NULL;
	}

	/*
	 * If there is an intersection, then check explicitly for matching
	 * endpoints since there may be rounding effects with annoying lsb
	 * residue. - tgl 1997-07-09
	 */
	if ((FPeq(l1->p[0].x, l2->p[0].x) && FPeq(l1->p[0].y, l2->p[0].y)) ||
		(FPeq(l1->p[0].x, l2->p[1].x) && FPeq(l1->p[0].y, l2->p[1].y)))
	{
		result->x = l1->p[0].x;
		result->y = l1->p[0].y;
	}
	else if ((FPeq(l1->p[1].x, l2->p[0].x) && FPeq(l1->p[1].y, l2->p[0].y)) ||
			 (FPeq(l1->p[1].x, l2->p[1].x) && FPeq(l1->p[1].y, l2->p[1].y)))
	{
		result->x = l1->p[1].x;
		result->y = l1->p[1].y;
	}

	return result;
}

/* lseg_interpt -
 *		Find the intersection point of two segments (if any).
 */
Datum
lseg_interpt(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
	Point	   *result;

	result = lseg_interpt_internal(l1, l2);
	if (!PointerIsValid(result))
		PG_RETURN_NULL();

	PG_RETURN_POINT_P(result);
}

/***********************************************************************
 **
 **		Routines for position comparisons of differently-typed
 **				2D objects.
 **
 ***********************************************************************/

/*---------------------------------------------------------------------
 *		dist_
 *				Minimum distance from one object to another.
 *-------------------------------------------------------------------*/

/*
 * Distance from a point to a line
 */
Datum
dist_pl(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	LINE	   *line = PG_GETARG_LINE_P(1);

	PG_RETURN_FLOAT8(dist_pl_internal(pt, line));
}

static double
dist_pl_internal(Point *pt, LINE *line)
{
	return fabs((line->A * pt->x + line->B * pt->y + line->C) /
				HYPOT(line->A, line->B));
}

/*
 * Distance from a point to a lseg
 */
Datum
dist_ps(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	LSEG	   *lseg = PG_GETARG_LSEG_P(1);

	PG_RETURN_FLOAT8(dist_ps_internal(pt, lseg));
}

static double
dist_ps_internal(Point *pt, LSEG *lseg)
{
	double		m;				/* slope of perp. */
	LINE	   *ln;
	double		result,
				tmpdist;
	Point	   *ip;

	/*
	 * Construct a line perpendicular to the input segment and through the
	 * input point
	 */
	if (lseg->p[1].x == lseg->p[0].x)
		m = 0;
	else if (lseg->p[1].y == lseg->p[0].y)
		m = (double) DBL_MAX;	/* slope is infinite */
	else
		m = (lseg->p[0].x - lseg->p[1].x) / (lseg->p[1].y - lseg->p[0].y);
	ln = line_construct_pm(pt, m);

#ifdef GEODEBUG
	printf("dist_ps- line is A=%g B=%g C=%g from (point) slope (%f,%f) %g\n",
		   ln->A, ln->B, ln->C, pt->x, pt->y, m);
#endif

	/*
	 * Calculate distance to the line segment or to the nearest endpoint of
	 * the segment.
	 */

	/* intersection is on the line segment? */
	if ((ip = interpt_sl(lseg, ln)) != NULL)
	{
		/* yes, so use distance to the intersection point */
		result = point_dt(pt, ip);
#ifdef GEODEBUG
		printf("dist_ps- distance is %f to intersection point is (%f,%f)\n",
			   result, ip->x, ip->y);
#endif
	}
	else
	{
		/* no, so use distance to the nearer endpoint */
		result = point_dt(pt, &lseg->p[0]);
		tmpdist = point_dt(pt, &lseg->p[1]);
		if (tmpdist < result)
			result = tmpdist;
	}

	return result;
}

/*
 * Distance from a point to a path
 */
Datum
dist_ppath(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	PATH	   *path = PG_GETARG_PATH_P(1);
	float8		result = 0.0;	/* keep compiler quiet */
	bool		have_min = false;
	float8		tmp;
	int			i;
	LSEG		lseg;

	switch (path->npts)
	{
		case 0:
			/* no points in path? then result is undefined... */
			PG_RETURN_NULL();
		case 1:
			/* one point in path? then get distance between two points... */
			result = point_dt(pt, &path->p[0]);
			break;
		default:
			/* make sure the path makes sense... */
			Assert(path->npts > 1);

			/*
			 * the distance from a point to a path is the smallest distance
			 * from the point to any of its constituent segments.
			 */
			for (i = 0; i < path->npts; i++)
			{
				int			iprev;

				if (i > 0)
					iprev = i - 1;
				else
				{
					if (!path->closed)
						continue;
					iprev = path->npts - 1; /* include the closure segment */
				}

				statlseg_construct(&lseg, &path->p[iprev], &path->p[i]);
				tmp = dist_ps_internal(pt, &lseg);
				if (!have_min || tmp < result)
				{
					result = tmp;
					have_min = true;
				}
			}
			break;
	}
	PG_RETURN_FLOAT8(result);
}

/*
 * Distance from a point to a box
 */
Datum
dist_pb(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	BOX		   *box = PG_GETARG_BOX_P(1);
	float8		result;
	Point	   *near;

	near = DatumGetPointP(DirectFunctionCall2(close_pb,
											  PointPGetDatum(pt),
											  BoxPGetDatum(box)));
	result = point_dt(near, pt);

	PG_RETURN_FLOAT8(result);
}

/*
 * Distance from a lseg to a line
 */
Datum
dist_sl(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
	LINE	   *line = PG_GETARG_LINE_P(1);
	float8		result,
				d2;

	if (has_interpt_sl(lseg, line))
		result = 0.0;
	else
	{
		result = dist_pl_internal(&lseg->p[0], line);
		d2 = dist_pl_internal(&lseg->p[1], line);
		/* XXX shouldn't we take the min not max? */
		if (d2 > result)
			result = d2;
	}

	PG_RETURN_FLOAT8(result);
}

/*
 * Distance from a lseg to a box
 */
Datum
dist_sb(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
	BOX		   *box = PG_GETARG_BOX_P(1);
	Point	   *tmp;
	Datum		result;

	tmp = DatumGetPointP(DirectFunctionCall2(close_sb,
											 LsegPGetDatum(lseg),
											 BoxPGetDatum(box)));
	result = DirectFunctionCall2(dist_pb,
								 PointPGetDatum(tmp),
								 BoxPGetDatum(box));

	PG_RETURN_DATUM(result);
}

/*
 * Distance from a line to a box
 */
Datum
dist_lb(PG_FUNCTION_ARGS)
{
#ifdef NOT_USED
	LINE	   *line = PG_GETARG_LINE_P(0);
	BOX		   *box = PG_GETARG_BOX_P(1);
#endif

	/* need to think about this one for a while */
	ereport(ERROR,
			(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
			 errmsg("function \"dist_lb\" not implemented")));

	PG_RETURN_NULL();
}

/*
 * Distance from a circle to a polygon
 */
Datum
dist_cpoly(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	POLYGON    *poly = PG_GETARG_POLYGON_P(1);
	float8		result;

	/* calculate distance to center, and subtract radius */
	result = dist_ppoly_internal(&circle->center, poly);

	result -= circle->radius;
	if (result < 0)
		result = 0;

	PG_RETURN_FLOAT8(result);
}

/*
 * Distance from a point to a polygon
 */
Datum
dist_ppoly(PG_FUNCTION_ARGS)
{
	Point	   *point = PG_GETARG_POINT_P(0);
	POLYGON    *poly = PG_GETARG_POLYGON_P(1);
	float8		result;

	result = dist_ppoly_internal(point, poly);

	PG_RETURN_FLOAT8(result);
}

Datum
dist_polyp(PG_FUNCTION_ARGS)
{
	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	float8		result;

	result = dist_ppoly_internal(point, poly);

	PG_RETURN_FLOAT8(result);
}

static double
dist_ppoly_internal(Point *pt, POLYGON *poly)
{
	float8		result;
	float8		d;
	int			i;
	LSEG		seg;

	if (point_inside(pt, poly->npts, poly->p) != 0)
	{
#ifdef GEODEBUG
		printf("dist_ppoly_internal- point inside of polygon\n");
#endif
		return 0.0;
	}

	/* initialize distance with segment between first and last points */
	seg.p[0].x = poly->p[0].x;
	seg.p[0].y = poly->p[0].y;
	seg.p[1].x = poly->p[poly->npts - 1].x;
	seg.p[1].y = poly->p[poly->npts - 1].y;
	result = dist_ps_internal(pt, &seg);
#ifdef GEODEBUG
	printf("dist_ppoly_internal- segment 0/n distance is %f\n", result);
#endif

	/* check distances for other segments */
	for (i = 0; (i < poly->npts - 1); i++)
	{
		seg.p[0].x = poly->p[i].x;
		seg.p[0].y = poly->p[i].y;
		seg.p[1].x = poly->p[i + 1].x;
		seg.p[1].y = poly->p[i + 1].y;
		d = dist_ps_internal(pt, &seg);
#ifdef GEODEBUG
		printf("dist_ppoly_internal- segment %d distance is %f\n", (i + 1), d);
#endif
		if (d < result)
			result = d;
	}

	return result;
}


/*---------------------------------------------------------------------
 *		interpt_
 *				Intersection point of objects.
 *				We choose to ignore the "point" of intersection between
 *				  lines and boxes, since there are typically two.
 *-------------------------------------------------------------------*/

/* Get intersection point of lseg and line; returns NULL if no intersection */
static Point *
interpt_sl(LSEG *lseg, LINE *line)
{
	LINE		tmp;
	Point	   *p;

	line_construct_pts(&tmp, &lseg->p[0], &lseg->p[1]);
	p = line_interpt_internal(&tmp, line);
#ifdef GEODEBUG
	printf("interpt_sl- segment is (%.*g %.*g) (%.*g %.*g)\n",
		   DBL_DIG, lseg->p[0].x, DBL_DIG, lseg->p[0].y, DBL_DIG, lseg->p[1].x, DBL_DIG, lseg->p[1].y);
	printf("interpt_sl- segment becomes line A=%.*g B=%.*g C=%.*g\n",
		   DBL_DIG, tmp.A, DBL_DIG, tmp.B, DBL_DIG, tmp.C);
#endif
	if (PointerIsValid(p))
	{
#ifdef GEODEBUG
		printf("interpt_sl- intersection point is (%.*g %.*g)\n", DBL_DIG, p->x, DBL_DIG, p->y);
#endif
		if (on_ps_internal(p, lseg))
		{
#ifdef GEODEBUG
			printf("interpt_sl- intersection point is on segment\n");
#endif
		}
		else
			p = NULL;
	}

	return p;
}

/* variant: just indicate if intersection point exists */
static bool
has_interpt_sl(LSEG *lseg, LINE *line)
{
	Point	   *tmp;

	tmp = interpt_sl(lseg, line);
	if (tmp)
		return true;
	return false;
}

/*---------------------------------------------------------------------
 *		close_
 *				Point of closest proximity between objects.
 *-------------------------------------------------------------------*/

/* close_pl -
 *		The intersection point of a perpendicular of the line
 *		through the point.
 */
Datum
close_pl(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	LINE	   *line = PG_GETARG_LINE_P(1);
	Point	   *result;
	LINE	   *tmp;
	double		invm;

	result = (Point *) palloc(sizeof(Point));

	if (FPzero(line->B))		/* vertical? */
	{
		result->x = line->C;
		result->y = pt->y;
		PG_RETURN_POINT_P(result);
	}
	if (FPzero(line->A))		/* horizontal? */
	{
		result->x = pt->x;
		result->y = line->C;
		PG_RETURN_POINT_P(result);
	}
	/* drop a perpendicular and find the intersection point */

	/* invert and flip the sign on the slope to get a perpendicular */
	invm = line->B / line->A;
	tmp = line_construct_pm(pt, invm);
	result = line_interpt_internal(tmp, line);
	Assert(result != NULL);
	PG_RETURN_POINT_P(result);
}


/* close_ps()
 * Closest point on line segment to specified point.
 * Take the closest endpoint if the point is left, right,
 *	above, or below the segment, otherwise find the intersection
 *	point of the segment and its perpendicular through the point.
 *
 * Some tricky code here, relying on boolean expressions
 *	evaluating to only zero or one to use as an array index.
 *		bug fixes by gthaker@atl.lmco.com; May 1, 1998
 */
Datum
close_ps(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	LSEG	   *lseg = PG_GETARG_LSEG_P(1);
	Point	   *result = NULL;
	LINE	   *tmp;
	double		invm;
	int			xh,
				yh;

#ifdef GEODEBUG
	printf("close_sp:pt->x %f pt->y %f\nlseg(0).x %f lseg(0).y %f  lseg(1).x %f lseg(1).y %f\n",
		   pt->x, pt->y, lseg->p[0].x, lseg->p[0].y,
		   lseg->p[1].x, lseg->p[1].y);
#endif

	/* xh (or yh) is the index of upper x( or y) end point of lseg */
	/* !xh (or !yh) is the index of lower x( or y) end point of lseg */
	xh = lseg->p[0].x < lseg->p[1].x;
	yh = lseg->p[0].y < lseg->p[1].y;

	if (FPeq(lseg->p[0].x, lseg->p[1].x))	/* vertical? */
	{
#ifdef GEODEBUG
		printf("close_ps- segment is vertical\n");
#endif
		/* first check if point is below or above the entire lseg. */
		if (pt->y < lseg->p[!yh].y)
			result = point_copy(&lseg->p[!yh]); /* below the lseg */
		else if (pt->y > lseg->p[yh].y)
			result = point_copy(&lseg->p[yh]);	/* above the lseg */
		if (result != NULL)
			PG_RETURN_POINT_P(result);

		/* point lines along (to left or right) of the vertical lseg. */

		result = (Point *) palloc(sizeof(Point));
		result->x = lseg->p[0].x;
		result->y = pt->y;
		PG_RETURN_POINT_P(result);
	}
	else if (FPeq(lseg->p[0].y, lseg->p[1].y))	/* horizontal? */
	{
#ifdef GEODEBUG
		printf("close_ps- segment is horizontal\n");
#endif
		/* first check if point is left or right of the entire lseg. */
		if (pt->x < lseg->p[!xh].x)
			result = point_copy(&lseg->p[!xh]); /* left of the lseg */
		else if (pt->x > lseg->p[xh].x)
			result = point_copy(&lseg->p[xh]);	/* right of the lseg */
		if (result != NULL)
			PG_RETURN_POINT_P(result);

		/* point lines along (at top or below) the horiz. lseg. */
		result = (Point *) palloc(sizeof(Point));
		result->x = pt->x;
		result->y = lseg->p[0].y;
		PG_RETURN_POINT_P(result);
	}

	/*
	 * vert. and horiz. cases are down, now check if the closest point is one
	 * of the end points or someplace on the lseg.
	 */

	invm = -1.0 / point_sl(&(lseg->p[0]), &(lseg->p[1]));
	tmp = line_construct_pm(&lseg->p[!yh], invm);	/* lower edge of the
													 * "band" */
	if (pt->y < (tmp->A * pt->x + tmp->C))
	{							/* we are below the lower edge */
		result = point_copy(&lseg->p[!yh]); /* below the lseg, take lower end
											 * pt */
#ifdef GEODEBUG
		printf("close_ps below: tmp A %f  B %f   C %f\n",
			   tmp->A, tmp->B, tmp->C);
#endif
		PG_RETURN_POINT_P(result);
	}
	tmp = line_construct_pm(&lseg->p[yh], invm);	/* upper edge of the
													 * "band" */
	if (pt->y > (tmp->A * pt->x + tmp->C))
	{							/* we are below the lower edge */
		result = point_copy(&lseg->p[yh]);	/* above the lseg, take higher end
											 * pt */
#ifdef GEODEBUG
		printf("close_ps above: tmp A %f  B %f   C %f\n",
			   tmp->A, tmp->B, tmp->C);
#endif
		PG_RETURN_POINT_P(result);
	}

	/*
	 * at this point the "normal" from point will hit lseg. The closest point
	 * will be somewhere on the lseg
	 */
	tmp = line_construct_pm(pt, invm);
#ifdef GEODEBUG
	printf("close_ps- tmp A %f  B %f   C %f\n",
		   tmp->A, tmp->B, tmp->C);
#endif
	result = interpt_sl(lseg, tmp);

	/*
	 * ordinarily we should always find an intersection point, but that could
	 * fail in the presence of NaN coordinates, and perhaps even from simple
	 * roundoff issues.  Return a SQL NULL if so.
	 */
	if (result == NULL)
		PG_RETURN_NULL();

#ifdef GEODEBUG
	printf("close_ps- result.x %f  result.y %f\n", result->x, result->y);
#endif
	PG_RETURN_POINT_P(result);
}


/* close_lseg()
 * Closest point to l1 on l2.
 */
Datum
close_lseg(PG_FUNCTION_ARGS)
{
	LSEG	   *l1 = PG_GETARG_LSEG_P(0);
	LSEG	   *l2 = PG_GETARG_LSEG_P(1);
	Point	   *result = NULL;
	Point		point;
	double		dist;
	double		d;

	d = dist_ps_internal(&l1->p[0], l2);
	dist = d;
	memcpy(&point, &l1->p[0], sizeof(Point));

	if ((d = dist_ps_internal(&l1->p[1], l2)) < dist)
	{
		dist = d;
		memcpy(&point, &l1->p[1], sizeof(Point));
	}

	if (dist_ps_internal(&l2->p[0], l1) < dist)
	{
		result = DatumGetPointP(DirectFunctionCall2(close_ps,
													PointPGetDatum(&l2->p[0]),
													LsegPGetDatum(l1)));
		memcpy(&point, result, sizeof(Point));
		result = DatumGetPointP(DirectFunctionCall2(close_ps,
													PointPGetDatum(&point),
													LsegPGetDatum(l2)));
	}

	if (dist_ps_internal(&l2->p[1], l1) < dist)
	{
		result = DatumGetPointP(DirectFunctionCall2(close_ps,
													PointPGetDatum(&l2->p[1]),
													LsegPGetDatum(l1)));
		memcpy(&point, result, sizeof(Point));
		result = DatumGetPointP(DirectFunctionCall2(close_ps,
													PointPGetDatum(&point),
													LsegPGetDatum(l2)));
	}

	if (result == NULL)
		result = point_copy(&point);

	PG_RETURN_POINT_P(result);
}

/* close_pb()
 * Closest point on or in box to specified point.
 */
Datum
close_pb(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	BOX		   *box = PG_GETARG_BOX_P(1);
	LSEG		lseg,
				seg;
	Point		point;
	double		dist,
				d;

	if (DatumGetBool(DirectFunctionCall2(on_pb,
										 PointPGetDatum(pt),
										 BoxPGetDatum(box))))
		PG_RETURN_POINT_P(pt);

	/* pairwise check lseg distances */
	point.x = box->low.x;
	point.y = box->high.y;
	statlseg_construct(&lseg, &box->low, &point);
	dist = dist_ps_internal(pt, &lseg);

	statlseg_construct(&seg, &box->high, &point);
	if ((d = dist_ps_internal(pt, &seg)) < dist)
	{
		dist = d;
		memcpy(&lseg, &seg, sizeof(lseg));
	}

	point.x = box->high.x;
	point.y = box->low.y;
	statlseg_construct(&seg, &box->low, &point);
	if ((d = dist_ps_internal(pt, &seg)) < dist)
	{
		dist = d;
		memcpy(&lseg, &seg, sizeof(lseg));
	}

	statlseg_construct(&seg, &box->high, &point);
	if ((d = dist_ps_internal(pt, &seg)) < dist)
	{
		dist = d;
		memcpy(&lseg, &seg, sizeof(lseg));
	}

	PG_RETURN_DATUM(DirectFunctionCall2(close_ps,
										PointPGetDatum(pt),
										LsegPGetDatum(&lseg)));
}

/* close_sl()
 * Closest point on line to line segment.
 *
 * XXX THIS CODE IS WRONG
 * The code is actually calculating the point on the line segment
 *	which is backwards from the routine naming convention.
 * Copied code to new routine close_ls() but haven't fixed this one yet.
 * - thomas 1998-01-31
 */
Datum
close_sl(PG_FUNCTION_ARGS)
{
#ifdef NOT_USED
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
	LINE	   *line = PG_GETARG_LINE_P(1);
	Point	   *result;
	float8		d1,
				d2;

	result = interpt_sl(lseg, line);
	if (result)
		PG_RETURN_POINT_P(result);

	d1 = dist_pl_internal(&lseg->p[0], line);
	d2 = dist_pl_internal(&lseg->p[1], line);
	if (d1 < d2)
		result = point_copy(&lseg->p[0]);
	else
		result = point_copy(&lseg->p[1]);

	PG_RETURN_POINT_P(result);
#endif

	ereport(ERROR,
			(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
			 errmsg("function \"close_sl\" not implemented")));

	PG_RETURN_NULL();
}

/* close_ls()
 * Closest point on line segment to line.
 */
Datum
close_ls(PG_FUNCTION_ARGS)
{
	LINE	   *line = PG_GETARG_LINE_P(0);
	LSEG	   *lseg = PG_GETARG_LSEG_P(1);
	Point	   *result;
	float8		d1,
				d2;

	result = interpt_sl(lseg, line);
	if (result)
		PG_RETURN_POINT_P(result);

	d1 = dist_pl_internal(&lseg->p[0], line);
	d2 = dist_pl_internal(&lseg->p[1], line);
	if (d1 < d2)
		result = point_copy(&lseg->p[0]);
	else
		result = point_copy(&lseg->p[1]);

	PG_RETURN_POINT_P(result);
}

/* close_sb()
 * Closest point on or in box to line segment.
 */
Datum
close_sb(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
	BOX		   *box = PG_GETARG_BOX_P(1);
	Point		point;
	LSEG		bseg,
				seg;
	double		dist,
				d;

	/* segment intersects box? then just return closest point to center */
	if (DatumGetBool(DirectFunctionCall2(inter_sb,
										 LsegPGetDatum(lseg),
										 BoxPGetDatum(box))))
	{
		box_cn(&point, box);
		PG_RETURN_DATUM(DirectFunctionCall2(close_ps,
											PointPGetDatum(&point),
											LsegPGetDatum(lseg)));
	}

	/* pairwise check lseg distances */
	point.x = box->low.x;
	point.y = box->high.y;
	statlseg_construct(&bseg, &box->low, &point);
	dist = lseg_dt(lseg, &bseg);

	statlseg_construct(&seg, &box->high, &point);
	if ((d = lseg_dt(lseg, &seg)) < dist)
	{
		dist = d;
		memcpy(&bseg, &seg, sizeof(bseg));
	}

	point.x = box->high.x;
	point.y = box->low.y;
	statlseg_construct(&seg, &box->low, &point);
	if ((d = lseg_dt(lseg, &seg)) < dist)
	{
		dist = d;
		memcpy(&bseg, &seg, sizeof(bseg));
	}

	statlseg_construct(&seg, &box->high, &point);
	if ((d = lseg_dt(lseg, &seg)) < dist)
	{
		dist = d;
		memcpy(&bseg, &seg, sizeof(bseg));
	}

	/* OK, we now have the closest line segment on the box boundary */
	PG_RETURN_DATUM(DirectFunctionCall2(close_lseg,
										LsegPGetDatum(lseg),
										LsegPGetDatum(&bseg)));
}

Datum
close_lb(PG_FUNCTION_ARGS)
{
#ifdef NOT_USED
	LINE	   *line = PG_GETARG_LINE_P(0);
	BOX		   *box = PG_GETARG_BOX_P(1);
#endif

	/* think about this one for a while */
	ereport(ERROR,
			(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
			 errmsg("function \"close_lb\" not implemented")));

	PG_RETURN_NULL();
}

/*---------------------------------------------------------------------
 *		on_
 *				Whether one object lies completely within another.
 *-------------------------------------------------------------------*/

/* on_pl -
 *		Does the point satisfy the equation?
 */
Datum
on_pl(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	LINE	   *line = PG_GETARG_LINE_P(1);

	PG_RETURN_BOOL(FPzero(line->A * pt->x + line->B * pt->y + line->C));
}


/* on_ps -
 *		Determine colinearity by detecting a triangle inequality.
 * This algorithm seems to behave nicely even with lsb residues - tgl 1997-07-09
 */
Datum
on_ps(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	LSEG	   *lseg = PG_GETARG_LSEG_P(1);

	PG_RETURN_BOOL(on_ps_internal(pt, lseg));
}

static bool
on_ps_internal(Point *pt, LSEG *lseg)
{
	return FPeq(point_dt(pt, &lseg->p[0]) + point_dt(pt, &lseg->p[1]),
				point_dt(&lseg->p[0], &lseg->p[1]));
}

Datum
on_pb(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	BOX		   *box = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(pt->x <= box->high.x && pt->x >= box->low.x &&
				   pt->y <= box->high.y && pt->y >= box->low.y);
}

Datum
box_contain_pt(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);
	Point	   *pt = PG_GETARG_POINT_P(1);

	PG_RETURN_BOOL(pt->x <= box->high.x && pt->x >= box->low.x &&
				   pt->y <= box->high.y && pt->y >= box->low.y);
}

/* on_ppath -
 *		Whether a point lies within (on) a polyline.
 *		If open, we have to (groan) check each segment.
 * (uses same algorithm as for point intersecting segment - tgl 1997-07-09)
 *		If closed, we use the old O(n) ray method for point-in-polygon.
 *				The ray is horizontal, from pt out to the right.
 *				Each segment that crosses the ray counts as an
 *				intersection; note that an endpoint or edge may touch
 *				but not cross.
 *				(we can do p-in-p in lg(n), but it takes preprocessing)
 */
Datum
on_ppath(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	PATH	   *path = PG_GETARG_PATH_P(1);
	int			i,
				n;
	double		a,
				b;

	/*-- OPEN --*/
	if (!path->closed)
	{
		n = path->npts - 1;
		a = point_dt(pt, &path->p[0]);
		for (i = 0; i < n; i++)
		{
			b = point_dt(pt, &path->p[i + 1]);
			if (FPeq(a + b,
					 point_dt(&path->p[i], &path->p[i + 1])))
				PG_RETURN_BOOL(true);
			a = b;
		}
		PG_RETURN_BOOL(false);
	}

	/*-- CLOSED --*/
	PG_RETURN_BOOL(point_inside(pt, path->npts, path->p) != 0);
}

Datum
on_sl(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
	LINE	   *line = PG_GETARG_LINE_P(1);

	PG_RETURN_BOOL(DatumGetBool(DirectFunctionCall2(on_pl,
													PointPGetDatum(&lseg->p[0]),
													LinePGetDatum(line))) &&
				   DatumGetBool(DirectFunctionCall2(on_pl,
													PointPGetDatum(&lseg->p[1]),
													LinePGetDatum(line))));
}

Datum
on_sb(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
	BOX		   *box = PG_GETARG_BOX_P(1);

	PG_RETURN_BOOL(DatumGetBool(DirectFunctionCall2(on_pb,
													PointPGetDatum(&lseg->p[0]),
													BoxPGetDatum(box))) &&
				   DatumGetBool(DirectFunctionCall2(on_pb,
													PointPGetDatum(&lseg->p[1]),
													BoxPGetDatum(box))));
}

/*---------------------------------------------------------------------
 *		inter_
 *				Whether one object intersects another.
 *-------------------------------------------------------------------*/

Datum
inter_sl(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
	LINE	   *line = PG_GETARG_LINE_P(1);

	PG_RETURN_BOOL(has_interpt_sl(lseg, line));
}

/* inter_sb()
 * Do line segment and box intersect?
 *
 * Segment completely inside box counts as intersection.
 * If you want only segments crossing box boundaries,
 *	try converting box to path first.
 *
 * Optimize for non-intersection by checking for box intersection first.
 * - thomas 1998-01-30
 */
Datum
inter_sb(PG_FUNCTION_ARGS)
{
	LSEG	   *lseg = PG_GETARG_LSEG_P(0);
	BOX		   *box = PG_GETARG_BOX_P(1);
	BOX			lbox;
	LSEG		bseg;
	Point		point;

	lbox.low.x = Min(lseg->p[0].x, lseg->p[1].x);
	lbox.low.y = Min(lseg->p[0].y, lseg->p[1].y);
	lbox.high.x = Max(lseg->p[0].x, lseg->p[1].x);
	lbox.high.y = Max(lseg->p[0].y, lseg->p[1].y);

	/* nothing close to overlap? then not going to intersect */
	if (!box_ov(&lbox, box))
		PG_RETURN_BOOL(false);

	/* an endpoint of segment is inside box? then clearly intersects */
	if (DatumGetBool(DirectFunctionCall2(on_pb,
										 PointPGetDatum(&lseg->p[0]),
										 BoxPGetDatum(box))) ||
		DatumGetBool(DirectFunctionCall2(on_pb,
										 PointPGetDatum(&lseg->p[1]),
										 BoxPGetDatum(box))))
		PG_RETURN_BOOL(true);

	/* pairwise check lseg intersections */
	point.x = box->low.x;
	point.y = box->high.y;
	statlseg_construct(&bseg, &box->low, &point);
	if (lseg_intersect_internal(&bseg, lseg))
		PG_RETURN_BOOL(true);

	statlseg_construct(&bseg, &box->high, &point);
	if (lseg_intersect_internal(&bseg, lseg))
		PG_RETURN_BOOL(true);

	point.x = box->high.x;
	point.y = box->low.y;
	statlseg_construct(&bseg, &box->low, &point);
	if (lseg_intersect_internal(&bseg, lseg))
		PG_RETURN_BOOL(true);

	statlseg_construct(&bseg, &box->high, &point);
	if (lseg_intersect_internal(&bseg, lseg))
		PG_RETURN_BOOL(true);

	/* if we dropped through, no two segs intersected */
	PG_RETURN_BOOL(false);
}

/* inter_lb()
 * Do line and box intersect?
 */
Datum
inter_lb(PG_FUNCTION_ARGS)
{
	LINE	   *line = PG_GETARG_LINE_P(0);
	BOX		   *box = PG_GETARG_BOX_P(1);
	LSEG		bseg;
	Point		p1,
				p2;

	/* pairwise check lseg intersections */
	p1.x = box->low.x;
	p1.y = box->low.y;
	p2.x = box->low.x;
	p2.y = box->high.y;
	statlseg_construct(&bseg, &p1, &p2);
	if (has_interpt_sl(&bseg, line))
		PG_RETURN_BOOL(true);
	p1.x = box->high.x;
	p1.y = box->high.y;
	statlseg_construct(&bseg, &p1, &p2);
	if (has_interpt_sl(&bseg, line))
		PG_RETURN_BOOL(true);
	p2.x = box->high.x;
	p2.y = box->low.y;
	statlseg_construct(&bseg, &p1, &p2);
	if (has_interpt_sl(&bseg, line))
		PG_RETURN_BOOL(true);
	p1.x = box->low.x;
	p1.y = box->low.y;
	statlseg_construct(&bseg, &p1, &p2);
	if (has_interpt_sl(&bseg, line))
		PG_RETURN_BOOL(true);

	/* if we dropped through, no intersection */
	PG_RETURN_BOOL(false);
}

/*------------------------------------------------------------------
 * The following routines define a data type and operator class for
 * POLYGONS .... Part of which (the polygon's bounding box) is built on
 * top of the BOX data type.
 *
 * make_bound_box - create the bounding box for the input polygon
 *------------------------------------------------------------------*/

/*---------------------------------------------------------------------
 * Make the smallest bounding box for the given polygon.
 *---------------------------------------------------------------------*/
static void
make_bound_box(POLYGON *poly)
{
	int			i;
	double		x1,
				y1,
				x2,
				y2;

	if (poly->npts > 0)
	{
		x2 = x1 = poly->p[0].x;
		y2 = y1 = poly->p[0].y;
		for (i = 1; i < poly->npts; i++)
		{
			if (poly->p[i].x < x1)
				x1 = poly->p[i].x;
			if (poly->p[i].x > x2)
				x2 = poly->p[i].x;
			if (poly->p[i].y < y1)
				y1 = poly->p[i].y;
			if (poly->p[i].y > y2)
				y2 = poly->p[i].y;
		}

		box_fill(&(poly->boundbox), x1, x2, y1, y2);
	}
	else
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
				 errmsg("cannot create bounding box for empty polygon")));
}

/*------------------------------------------------------------------
 * poly_in - read in the polygon from a string specification
 *
 *		External format:
 *				"((x0,y0),...,(xn,yn))"
 *				"x0,y0,...,xn,yn"
 *				also supports the older style "(x1,...,xn,y1,...yn)"
 *------------------------------------------------------------------*/
Datum
poly_in(PG_FUNCTION_ARGS)
{
	char	   *str = PG_GETARG_CSTRING(0);
	POLYGON    *poly;
	int			npts;
	int			size;
	int			base_size;
	bool		isopen;

	if ((npts = pair_count(str, ',')) <= 0)
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("invalid input syntax for type %s: \"%s\"",
						"polygon", str)));

	base_size = sizeof(poly->p[0]) * npts;
	size = offsetof(POLYGON, p) + base_size;

	/* Check for integer overflow */
	if (base_size / npts != sizeof(poly->p[0]) || size <= base_size)
		ereport(ERROR,
				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
				 errmsg("too many points requested")));

	poly = (POLYGON *) palloc0(size);	/* zero any holes */

	SET_VARSIZE(poly, size);
	poly->npts = npts;

	path_decode(str, false, npts, &(poly->p[0]), &isopen, NULL, "polygon", str);

	make_bound_box(poly);

	PG_RETURN_POLYGON_P(poly);
}

/*---------------------------------------------------------------
 * poly_out - convert internal POLYGON representation to the
 *			  character string format "((f8,f8),...,(f8,f8))"
 *---------------------------------------------------------------*/
Datum
poly_out(PG_FUNCTION_ARGS)
{
	POLYGON    *poly = PG_GETARG_POLYGON_P(0);

	PG_RETURN_CSTRING(path_encode(PATH_CLOSED, poly->npts, poly->p));
}

/*
 *		poly_recv			- converts external binary format to polygon
 *
 * External representation is int32 number of points, and the points.
 * We recompute the bounding box on read, instead of trusting it to
 * be valid.  (Checking it would take just as long, so may as well
 * omit it from external representation.)
 */
Datum
poly_recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
	POLYGON    *poly;
	int32		npts;
	int32		i;
	int			size;

	npts = pq_getmsgint(buf, sizeof(int32));
	if (npts <= 0 || npts >= (int32) ((INT_MAX - offsetof(POLYGON, p)) / sizeof(Point)))
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
				 errmsg("invalid number of points in external \"polygon\" value")));

	size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * npts;
	poly = (POLYGON *) palloc0(size);	/* zero any holes */

	SET_VARSIZE(poly, size);
	poly->npts = npts;

	for (i = 0; i < npts; i++)
	{
		poly->p[i].x = pq_getmsgfloat8(buf);
		poly->p[i].y = pq_getmsgfloat8(buf);
	}

	make_bound_box(poly);

	PG_RETURN_POLYGON_P(poly);
}

/*
 *		poly_send			- converts polygon to binary format
 */
Datum
poly_send(PG_FUNCTION_ARGS)
{
	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
	StringInfoData buf;
	int32		i;

	pq_begintypsend(&buf);
	pq_sendint32(&buf, poly->npts);
	for (i = 0; i < poly->npts; i++)
	{
		pq_sendfloat8(&buf, poly->p[i].x);
		pq_sendfloat8(&buf, poly->p[i].y);
	}
	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/*-------------------------------------------------------
 * Is polygon A strictly left of polygon B? i.e. is
 * the right most point of A left of the left most point
 * of B?
 *-------------------------------------------------------*/
Datum
poly_left(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	result = polya->boundbox.high.x < polyb->boundbox.low.x;

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}

/*-------------------------------------------------------
 * Is polygon A overlapping or left of polygon B? i.e. is
 * the right most point of A at or left of the right most point
 * of B?
 *-------------------------------------------------------*/
Datum
poly_overleft(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	result = polya->boundbox.high.x <= polyb->boundbox.high.x;

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}

/*-------------------------------------------------------
 * Is polygon A strictly right of polygon B? i.e. is
 * the left most point of A right of the right most point
 * of B?
 *-------------------------------------------------------*/
Datum
poly_right(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	result = polya->boundbox.low.x > polyb->boundbox.high.x;

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}

/*-------------------------------------------------------
 * Is polygon A overlapping or right of polygon B? i.e. is
 * the left most point of A at or right of the left most point
 * of B?
 *-------------------------------------------------------*/
Datum
poly_overright(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	result = polya->boundbox.low.x >= polyb->boundbox.low.x;

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}

/*-------------------------------------------------------
 * Is polygon A strictly below polygon B? i.e. is
 * the upper most point of A below the lower most point
 * of B?
 *-------------------------------------------------------*/
Datum
poly_below(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	result = polya->boundbox.high.y < polyb->boundbox.low.y;

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}

/*-------------------------------------------------------
 * Is polygon A overlapping or below polygon B? i.e. is
 * the upper most point of A at or below the upper most point
 * of B?
 *-------------------------------------------------------*/
Datum
poly_overbelow(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	result = polya->boundbox.high.y <= polyb->boundbox.high.y;

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}

/*-------------------------------------------------------
 * Is polygon A strictly above polygon B? i.e. is
 * the lower most point of A above the upper most point
 * of B?
 *-------------------------------------------------------*/
Datum
poly_above(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	result = polya->boundbox.low.y > polyb->boundbox.high.y;

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}

/*-------------------------------------------------------
 * Is polygon A overlapping or above polygon B? i.e. is
 * the lower most point of A at or above the lower most point
 * of B?
 *-------------------------------------------------------*/
Datum
poly_overabove(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	result = polya->boundbox.low.y >= polyb->boundbox.low.y;

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}


/*-------------------------------------------------------
 * Is polygon A the same as polygon B? i.e. are all the
 * points the same?
 * Check all points for matches in both forward and reverse
 *	direction since polygons are non-directional and are
 *	closed shapes.
 *-------------------------------------------------------*/
Datum
poly_same(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	if (polya->npts != polyb->npts)
		result = false;
	else
		result = plist_same(polya->npts, polya->p, polyb->p);

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}

/*-----------------------------------------------------------------
 * Determine if polygon A overlaps polygon B
 *-----------------------------------------------------------------*/
Datum
poly_overlap(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	/* Quick check by bounding box */
	result = (polya->npts > 0 && polyb->npts > 0 &&
			  box_ov(&polya->boundbox, &polyb->boundbox)) ? true : false;

	/*
	 * Brute-force algorithm - try to find intersected edges, if so then
	 * polygons are overlapped else check is one polygon inside other or not
	 * by testing single point of them.
	 */
	if (result)
	{
		int			ia,
					ib;
		LSEG		sa,
					sb;

		/* Init first of polya's edge with last point */
		sa.p[0] = polya->p[polya->npts - 1];
		result = false;

		for (ia = 0; ia < polya->npts && result == false; ia++)
		{
			/* Second point of polya's edge is a current one */
			sa.p[1] = polya->p[ia];

			/* Init first of polyb's edge with last point */
			sb.p[0] = polyb->p[polyb->npts - 1];

			for (ib = 0; ib < polyb->npts && result == false; ib++)
			{
				sb.p[1] = polyb->p[ib];
				result = lseg_intersect_internal(&sa, &sb);
				sb.p[0] = sb.p[1];
			}

			/*
			 * move current endpoint to the first point of next edge
			 */
			sa.p[0] = sa.p[1];
		}

		if (result == false)
		{
			result = (point_inside(polya->p, polyb->npts, polyb->p)
					  ||
					  point_inside(polyb->p, polya->npts, polya->p));
		}
	}

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}

/*
 * Tests special kind of segment for in/out of polygon.
 * Special kind means:
 *	- point a should be on segment s
 *	- segment (a,b) should not be contained by s
 * Returns true if:
 *	- segment (a,b) is collinear to s and (a,b) is in polygon
 *	- segment (a,b) s not collinear to s. Note: that doesn't
 *	  mean that segment is in polygon!
 */

static bool
touched_lseg_inside_poly(Point *a, Point *b, LSEG *s, POLYGON *poly, int start)
{
	/* point a is on s, b is not */
	LSEG		t;

	t.p[0] = *a;
	t.p[1] = *b;

#define POINTEQ(pt1, pt2)	(FPeq((pt1)->x, (pt2)->x) && FPeq((pt1)->y, (pt2)->y))
	if (POINTEQ(a, s->p))
	{
		if (on_ps_internal(s->p + 1, &t))
			return lseg_inside_poly(b, s->p + 1, poly, start);
	}
	else if (POINTEQ(a, s->p + 1))
	{
		if (on_ps_internal(s->p, &t))
			return lseg_inside_poly(b, s->p, poly, start);
	}
	else if (on_ps_internal(s->p, &t))
	{
		return lseg_inside_poly(b, s->p, poly, start);
	}
	else if (on_ps_internal(s->p + 1, &t))
	{
		return lseg_inside_poly(b, s->p + 1, poly, start);
	}

	return true;				/* may be not true, but that will check later */
}

/*
 * Returns true if segment (a,b) is in polygon, option
 * start is used for optimization - function checks
 * polygon's edges started from start
 */
static bool
lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start)
{
	LSEG		s,
				t;
	int			i;
	bool		res = true,
				intersection = false;

	/* since this function recurses, it could be driven to stack overflow */
	check_stack_depth();

	t.p[0] = *a;
	t.p[1] = *b;
	s.p[0] = poly->p[(start == 0) ? (poly->npts - 1) : (start - 1)];

	for (i = start; i < poly->npts && res; i++)
	{
		Point	   *interpt;

		CHECK_FOR_INTERRUPTS();

		s.p[1] = poly->p[i];

		if (on_ps_internal(t.p, &s))
		{
			if (on_ps_internal(t.p + 1, &s))
				return true;	/* t is contained by s */

			/* Y-cross */
			res = touched_lseg_inside_poly(t.p, t.p + 1, &s, poly, i + 1);
		}
		else if (on_ps_internal(t.p + 1, &s))
		{
			/* Y-cross */
			res = touched_lseg_inside_poly(t.p + 1, t.p, &s, poly, i + 1);
		}
		else if ((interpt = lseg_interpt_internal(&t, &s)) != NULL)
		{
			/*
			 * segments are X-crossing, go to check each subsegment
			 */

			intersection = true;
			res = lseg_inside_poly(t.p, interpt, poly, i + 1);
			if (res)
				res = lseg_inside_poly(t.p + 1, interpt, poly, i + 1);
			pfree(interpt);
		}

		s.p[0] = s.p[1];
	}

	if (res && !intersection)
	{
		Point		p;

		/*
		 * if X-intersection wasn't found  then check central point of tested
		 * segment. In opposite case we already check all subsegments
		 */
		p.x = (t.p[0].x + t.p[1].x) / 2.0;
		p.y = (t.p[0].y + t.p[1].y) / 2.0;

		res = point_inside(&p, poly->npts, poly->p);
	}

	return res;
}

/*-----------------------------------------------------------------
 * Determine if polygon A contains polygon B.
 *-----------------------------------------------------------------*/
Datum
poly_contain(PG_FUNCTION_ARGS)
{
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
	bool		result;

	/*
	 * Quick check to see if bounding box is contained.
	 */
	if (polya->npts > 0 && polyb->npts > 0 &&
		DatumGetBool(DirectFunctionCall2(box_contain,
										 BoxPGetDatum(&polya->boundbox),
										 BoxPGetDatum(&polyb->boundbox))))
	{
		int			i;
		LSEG		s;

		s.p[0] = polyb->p[polyb->npts - 1];
		result = true;

		for (i = 0; i < polyb->npts && result; i++)
		{
			s.p[1] = polyb->p[i];
			result = lseg_inside_poly(s.p, s.p + 1, polya, 0);
			s.p[0] = s.p[1];
		}
	}
	else
	{
		result = false;
	}

	/*
	 * Avoid leaking memory for toasted inputs ... needed for rtree indexes
	 */
	PG_FREE_IF_COPY(polya, 0);
	PG_FREE_IF_COPY(polyb, 1);

	PG_RETURN_BOOL(result);
}


/*-----------------------------------------------------------------
 * Determine if polygon A is contained by polygon B
 *-----------------------------------------------------------------*/
Datum
poly_contained(PG_FUNCTION_ARGS)
{
	Datum		polya = PG_GETARG_DATUM(0);
	Datum		polyb = PG_GETARG_DATUM(1);

	/* Just switch the arguments and pass it off to poly_contain */
	PG_RETURN_DATUM(DirectFunctionCall2(poly_contain, polyb, polya));
}


Datum
poly_contain_pt(PG_FUNCTION_ARGS)
{
	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
	Point	   *p = PG_GETARG_POINT_P(1);

	PG_RETURN_BOOL(point_inside(p, poly->npts, poly->p) != 0);
}

Datum
pt_contained_poly(PG_FUNCTION_ARGS)
{
	Point	   *p = PG_GETARG_POINT_P(0);
	POLYGON    *poly = PG_GETARG_POLYGON_P(1);

	PG_RETURN_BOOL(point_inside(p, poly->npts, poly->p) != 0);
}


Datum
poly_distance(PG_FUNCTION_ARGS)
{
#ifdef NOT_USED
	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
#endif

	ereport(ERROR,
			(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
			 errmsg("function \"poly_distance\" not implemented")));

	PG_RETURN_NULL();
}


/***********************************************************************
 **
 **		Routines for 2D points.
 **
 ***********************************************************************/

Datum
construct_point(PG_FUNCTION_ARGS)
{
	float8		x = PG_GETARG_FLOAT8(0);
	float8		y = PG_GETARG_FLOAT8(1);

	PG_RETURN_POINT_P(point_construct(x, y));
}

Datum
point_add(PG_FUNCTION_ARGS)
{
	Point	   *p1 = PG_GETARG_POINT_P(0);
	Point	   *p2 = PG_GETARG_POINT_P(1);
	Point	   *result;

	result = (Point *) palloc(sizeof(Point));

	result->x = (p1->x + p2->x);
	result->y = (p1->y + p2->y);

	PG_RETURN_POINT_P(result);
}

Datum
point_sub(PG_FUNCTION_ARGS)
{
	Point	   *p1 = PG_GETARG_POINT_P(0);
	Point	   *p2 = PG_GETARG_POINT_P(1);
	Point	   *result;

	result = (Point *) palloc(sizeof(Point));

	result->x = (p1->x - p2->x);
	result->y = (p1->y - p2->y);

	PG_RETURN_POINT_P(result);
}

Datum
point_mul(PG_FUNCTION_ARGS)
{
	Point	   *p1 = PG_GETARG_POINT_P(0);
	Point	   *p2 = PG_GETARG_POINT_P(1);
	Point	   *result;

	result = (Point *) palloc(sizeof(Point));

	result->x = (p1->x * p2->x) - (p1->y * p2->y);
	result->y = (p1->x * p2->y) + (p1->y * p2->x);

	PG_RETURN_POINT_P(result);
}

Datum
point_div(PG_FUNCTION_ARGS)
{
	Point	   *p1 = PG_GETARG_POINT_P(0);
	Point	   *p2 = PG_GETARG_POINT_P(1);
	Point	   *result;
	double		div;

	result = (Point *) palloc(sizeof(Point));

	div = (p2->x * p2->x) + (p2->y * p2->y);

	if (div == 0.0)
		ereport(ERROR,
				(errcode(ERRCODE_DIVISION_BY_ZERO),
				 errmsg("division by zero")));

	result->x = ((p1->x * p2->x) + (p1->y * p2->y)) / div;
	result->y = ((p2->x * p1->y) - (p2->y * p1->x)) / div;

	PG_RETURN_POINT_P(result);
}


/***********************************************************************
 **
 **		Routines for 2D boxes.
 **
 ***********************************************************************/

Datum
points_box(PG_FUNCTION_ARGS)
{
	Point	   *p1 = PG_GETARG_POINT_P(0);
	Point	   *p2 = PG_GETARG_POINT_P(1);

	PG_RETURN_BOX_P(box_construct(p1->x, p2->x, p1->y, p2->y));
}

Datum
box_add(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);
	Point	   *p = PG_GETARG_POINT_P(1);

	PG_RETURN_BOX_P(box_construct((box->high.x + p->x),
								  (box->low.x + p->x),
								  (box->high.y + p->y),
								  (box->low.y + p->y)));
}

Datum
box_sub(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);
	Point	   *p = PG_GETARG_POINT_P(1);

	PG_RETURN_BOX_P(box_construct((box->high.x - p->x),
								  (box->low.x - p->x),
								  (box->high.y - p->y),
								  (box->low.y - p->y)));
}

Datum
box_mul(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);
	Point	   *p = PG_GETARG_POINT_P(1);
	BOX		   *result;
	Point	   *high,
			   *low;

	high = DatumGetPointP(DirectFunctionCall2(point_mul,
											  PointPGetDatum(&box->high),
											  PointPGetDatum(p)));
	low = DatumGetPointP(DirectFunctionCall2(point_mul,
											 PointPGetDatum(&box->low),
											 PointPGetDatum(p)));

	result = box_construct(high->x, low->x, high->y, low->y);

	PG_RETURN_BOX_P(result);
}

Datum
box_div(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);
	Point	   *p = PG_GETARG_POINT_P(1);
	BOX		   *result;
	Point	   *high,
			   *low;

	high = DatumGetPointP(DirectFunctionCall2(point_div,
											  PointPGetDatum(&box->high),
											  PointPGetDatum(p)));
	low = DatumGetPointP(DirectFunctionCall2(point_div,
											 PointPGetDatum(&box->low),
											 PointPGetDatum(p)));

	result = box_construct(high->x, low->x, high->y, low->y);

	PG_RETURN_BOX_P(result);
}

/*
 * Convert point to empty box
 */
Datum
point_box(PG_FUNCTION_ARGS)
{
	Point	   *pt = PG_GETARG_POINT_P(0);
	BOX		   *box;

	box = (BOX *) palloc(sizeof(BOX));

	box->high.x = pt->x;
	box->low.x = pt->x;
	box->high.y = pt->y;
	box->low.y = pt->y;

	PG_RETURN_BOX_P(box);
}

/*
 * Smallest bounding box that includes both of the given boxes
 */
Datum
boxes_bound_box(PG_FUNCTION_ARGS)
{
	BOX		   *box1 = PG_GETARG_BOX_P(0),
			   *box2 = PG_GETARG_BOX_P(1),
			   *container;

	container = (BOX *) palloc(sizeof(BOX));

	container->high.x = Max(box1->high.x, box2->high.x);
	container->low.x = Min(box1->low.x, box2->low.x);
	container->high.y = Max(box1->high.y, box2->high.y);
	container->low.y = Min(box1->low.y, box2->low.y);

	PG_RETURN_BOX_P(container);
}


/***********************************************************************
 **
 **		Routines for 2D paths.
 **
 ***********************************************************************/

/* path_add()
 * Concatenate two paths (only if they are both open).
 */
Datum
path_add(PG_FUNCTION_ARGS)
{
	PATH	   *p1 = PG_GETARG_PATH_P(0);
	PATH	   *p2 = PG_GETARG_PATH_P(1);
	PATH	   *result;
	int			size,
				base_size;
	int			i;

	if (p1->closed || p2->closed)
		PG_RETURN_NULL();

	base_size = sizeof(p1->p[0]) * (p1->npts + p2->npts);
	size = offsetof(PATH, p) + base_size;

	/* Check for integer overflow */
	if (base_size / sizeof(p1->p[0]) != (p1->npts + p2->npts) ||
		size <= base_size)
		ereport(ERROR,
				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
				 errmsg("too many points requested")));

	result = (PATH *) palloc(size);

	SET_VARSIZE(result, size);
	result->npts = (p1->npts + p2->npts);
	result->closed = p1->closed;
	/* prevent instability in unused pad bytes */
	result->dummy = 0;

	for (i = 0; i < p1->npts; i++)
	{
		result->p[i].x = p1->p[i].x;
		result->p[i].y = p1->p[i].y;
	}
	for (i = 0; i < p2->npts; i++)
	{
		result->p[i + p1->npts].x = p2->p[i].x;
		result->p[i + p1->npts].y = p2->p[i].y;
	}

	PG_RETURN_PATH_P(result);
}

/* path_add_pt()
 * Translation operators.
 */
Datum
path_add_pt(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P_COPY(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	int			i;

	for (i = 0; i < path->npts; i++)
	{
		path->p[i].x += point->x;
		path->p[i].y += point->y;
	}

	PG_RETURN_PATH_P(path);
}

Datum
path_sub_pt(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P_COPY(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	int			i;

	for (i = 0; i < path->npts; i++)
	{
		path->p[i].x -= point->x;
		path->p[i].y -= point->y;
	}

	PG_RETURN_PATH_P(path);
}

/* path_mul_pt()
 * Rotation and scaling operators.
 */
Datum
path_mul_pt(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P_COPY(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	Point	   *p;
	int			i;

	for (i = 0; i < path->npts; i++)
	{
		p = DatumGetPointP(DirectFunctionCall2(point_mul,
											   PointPGetDatum(&path->p[i]),
											   PointPGetDatum(point)));
		path->p[i].x = p->x;
		path->p[i].y = p->y;
	}

	PG_RETURN_PATH_P(path);
}

Datum
path_div_pt(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P_COPY(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	Point	   *p;
	int			i;

	for (i = 0; i < path->npts; i++)
	{
		p = DatumGetPointP(DirectFunctionCall2(point_div,
											   PointPGetDatum(&path->p[i]),
											   PointPGetDatum(point)));
		path->p[i].x = p->x;
		path->p[i].y = p->y;
	}

	PG_RETURN_PATH_P(path);
}


Datum
path_center(PG_FUNCTION_ARGS)
{
#ifdef NOT_USED
	PATH	   *path = PG_GETARG_PATH_P(0);
#endif

	ereport(ERROR,
			(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
			 errmsg("function \"path_center\" not implemented")));

	PG_RETURN_NULL();
}

Datum
path_poly(PG_FUNCTION_ARGS)
{
	PATH	   *path = PG_GETARG_PATH_P(0);
	POLYGON    *poly;
	int			size;
	int			i;

	/* This is not very consistent --- other similar cases return NULL ... */
	if (!path->closed)
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
				 errmsg("open path cannot be converted to polygon")));

	/*
	 * Never overflows: the old size fit in MaxAllocSize, and the new size is
	 * just a small constant larger.
	 */
	size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * path->npts;
	poly = (POLYGON *) palloc(size);

	SET_VARSIZE(poly, size);
	poly->npts = path->npts;

	for (i = 0; i < path->npts; i++)
	{
		poly->p[i].x = path->p[i].x;
		poly->p[i].y = path->p[i].y;
	}

	make_bound_box(poly);

	PG_RETURN_POLYGON_P(poly);
}


/***********************************************************************
 **
 **		Routines for 2D polygons.
 **
 ***********************************************************************/

Datum
poly_npoints(PG_FUNCTION_ARGS)
{
	POLYGON    *poly = PG_GETARG_POLYGON_P(0);

	PG_RETURN_INT32(poly->npts);
}


Datum
poly_center(PG_FUNCTION_ARGS)
{
	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
	Datum		result;
	CIRCLE	   *circle;

	circle = DatumGetCircleP(DirectFunctionCall1(poly_circle,
												 PolygonPGetDatum(poly)));
	result = DirectFunctionCall1(circle_center,
								 CirclePGetDatum(circle));

	PG_RETURN_DATUM(result);
}


Datum
poly_box(PG_FUNCTION_ARGS)
{
	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
	BOX		   *box;

	if (poly->npts < 1)
		PG_RETURN_NULL();

	box = box_copy(&poly->boundbox);

	PG_RETURN_BOX_P(box);
}


/* box_poly()
 * Convert a box to a polygon.
 */
Datum
box_poly(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);
	POLYGON    *poly;
	int			size;

	/* map four corners of the box to a polygon */
	size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * 4;
	poly = (POLYGON *) palloc(size);

	SET_VARSIZE(poly, size);
	poly->npts = 4;

	poly->p[0].x = box->low.x;
	poly->p[0].y = box->low.y;
	poly->p[1].x = box->low.x;
	poly->p[1].y = box->high.y;
	poly->p[2].x = box->high.x;
	poly->p[2].y = box->high.y;
	poly->p[3].x = box->high.x;
	poly->p[3].y = box->low.y;

	box_fill(&poly->boundbox, box->high.x, box->low.x,
			 box->high.y, box->low.y);

	PG_RETURN_POLYGON_P(poly);
}


Datum
poly_path(PG_FUNCTION_ARGS)
{
	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
	PATH	   *path;
	int			size;
	int			i;

	/*
	 * Never overflows: the old size fit in MaxAllocSize, and the new size is
	 * smaller by a small constant.
	 */
	size = offsetof(PATH, p) + sizeof(path->p[0]) * poly->npts;
	path = (PATH *) palloc(size);

	SET_VARSIZE(path, size);
	path->npts = poly->npts;
	path->closed = true;
	/* prevent instability in unused pad bytes */
	path->dummy = 0;

	for (i = 0; i < poly->npts; i++)
	{
		path->p[i].x = poly->p[i].x;
		path->p[i].y = poly->p[i].y;
	}

	PG_RETURN_PATH_P(path);
}


/***********************************************************************
 **
 **		Routines for circles.
 **
 ***********************************************************************/

/*----------------------------------------------------------
 * Formatting and conversion routines.
 *---------------------------------------------------------*/

/*		circle_in		-		convert a string to internal form.
 *
 *		External format: (center and radius of circle)
 *				"<(f8,f8),f8>"
 *				also supports quick entry style "f8,f8,f8"
 */
Datum
circle_in(PG_FUNCTION_ARGS)
{
	char	   *str = PG_GETARG_CSTRING(0);
	CIRCLE	   *circle = (CIRCLE *) palloc(sizeof(CIRCLE));
	char	   *s,
			   *cp;
	int			depth = 0;

	s = str;
	while (isspace((unsigned char) *s))
		s++;
	if (*s == LDELIM_C)
		depth++, s++;
	else if (*s == LDELIM)
	{
		/* If there are two left parens, consume the first one */
		cp = (s + 1);
		while (isspace((unsigned char) *cp))
			cp++;
		if (*cp == LDELIM)
			depth++, s = cp;
	}

	/* pair_decode will consume parens around the pair, if any */
	pair_decode(s, &circle->center.x, &circle->center.y, &s, "circle", str);

	if (*s == DELIM)
		s++;

	circle->radius = single_decode(s, &s, "circle", str);
	if (circle->radius < 0)
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("invalid input syntax for type %s: \"%s\"",
						"circle", str)));

	while (depth > 0)
	{
		if ((*s == RDELIM)
			|| ((*s == RDELIM_C) && (depth == 1)))
		{
			depth--;
			s++;
			while (isspace((unsigned char) *s))
				s++;
		}
		else
			ereport(ERROR,
					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
					 errmsg("invalid input syntax for type %s: \"%s\"",
							"circle", str)));
	}

	if (*s != '\0')
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
				 errmsg("invalid input syntax for type %s: \"%s\"",
						"circle", str)));

	PG_RETURN_CIRCLE_P(circle);
}

/*		circle_out		-		convert a circle to external form.
 */
Datum
circle_out(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	StringInfoData str;

	initStringInfo(&str);

	appendStringInfoChar(&str, LDELIM_C);
	appendStringInfoChar(&str, LDELIM);
	pair_encode(circle->center.x, circle->center.y, &str);
	appendStringInfoChar(&str, RDELIM);
	appendStringInfoChar(&str, DELIM);
	single_encode(circle->radius, &str);
	appendStringInfoChar(&str, RDELIM_C);

	PG_RETURN_CSTRING(str.data);
}

/*
 *		circle_recv			- converts external binary format to circle
 */
Datum
circle_recv(PG_FUNCTION_ARGS)
{
	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
	CIRCLE	   *circle;

	circle = (CIRCLE *) palloc(sizeof(CIRCLE));

	circle->center.x = pq_getmsgfloat8(buf);
	circle->center.y = pq_getmsgfloat8(buf);
	circle->radius = pq_getmsgfloat8(buf);

	if (circle->radius < 0)
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
				 errmsg("invalid radius in external \"circle\" value")));

	PG_RETURN_CIRCLE_P(circle);
}

/*
 *		circle_send			- converts circle to binary format
 */
Datum
circle_send(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	StringInfoData buf;

	pq_begintypsend(&buf);
	pq_sendfloat8(&buf, circle->center.x);
	pq_sendfloat8(&buf, circle->center.y);
	pq_sendfloat8(&buf, circle->radius);
	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


/*----------------------------------------------------------
 *	Relational operators for CIRCLEs.
 *		<, >, <=, >=, and == are based on circle area.
 *---------------------------------------------------------*/

/*		circles identical?
 */
Datum
circle_same(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPeq(circle1->radius, circle2->radius) &&
				   FPeq(circle1->center.x, circle2->center.x) &&
				   FPeq(circle1->center.y, circle2->center.y));
}

/*		circle_overlap	-		does circle1 overlap circle2?
 */
Datum
circle_overlap(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPle(point_dt(&circle1->center, &circle2->center),
						circle1->radius + circle2->radius));
}

/*		circle_overleft -		is the right edge of circle1 at or left of
 *								the right edge of circle2?
 */
Datum
circle_overleft(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPle((circle1->center.x + circle1->radius),
						(circle2->center.x + circle2->radius)));
}

/*		circle_left		-		is circle1 strictly left of circle2?
 */
Datum
circle_left(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPlt((circle1->center.x + circle1->radius),
						(circle2->center.x - circle2->radius)));
}

/*		circle_right	-		is circle1 strictly right of circle2?
 */
Datum
circle_right(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPgt((circle1->center.x - circle1->radius),
						(circle2->center.x + circle2->radius)));
}

/*		circle_overright	-	is the left edge of circle1 at or right of
 *								the left edge of circle2?
 */
Datum
circle_overright(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPge((circle1->center.x - circle1->radius),
						(circle2->center.x - circle2->radius)));
}

/*		circle_contained		-		is circle1 contained by circle2?
 */
Datum
circle_contained(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPle((point_dt(&circle1->center, &circle2->center) + circle1->radius), circle2->radius));
}

/*		circle_contain	-		does circle1 contain circle2?
 */
Datum
circle_contain(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPle((point_dt(&circle1->center, &circle2->center) + circle2->radius), circle1->radius));
}


/*		circle_below		-		is circle1 strictly below circle2?
 */
Datum
circle_below(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPlt((circle1->center.y + circle1->radius),
						(circle2->center.y - circle2->radius)));
}

/*		circle_above	-		is circle1 strictly above circle2?
 */
Datum
circle_above(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPgt((circle1->center.y - circle1->radius),
						(circle2->center.y + circle2->radius)));
}

/*		circle_overbelow -		is the upper edge of circle1 at or below
 *								the upper edge of circle2?
 */
Datum
circle_overbelow(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPle((circle1->center.y + circle1->radius),
						(circle2->center.y + circle2->radius)));
}

/*		circle_overabove	-	is the lower edge of circle1 at or above
 *								the lower edge of circle2?
 */
Datum
circle_overabove(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPge((circle1->center.y - circle1->radius),
						(circle2->center.y - circle2->radius)));
}


/*		circle_relop	-		is area(circle1) relop area(circle2), within
 *								our accuracy constraint?
 */
Datum
circle_eq(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPeq(circle_ar(circle1), circle_ar(circle2)));
}

Datum
circle_ne(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPne(circle_ar(circle1), circle_ar(circle2)));
}

Datum
circle_lt(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPlt(circle_ar(circle1), circle_ar(circle2)));
}

Datum
circle_gt(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPgt(circle_ar(circle1), circle_ar(circle2)));
}

Datum
circle_le(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPle(circle_ar(circle1), circle_ar(circle2)));
}

Datum
circle_ge(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);

	PG_RETURN_BOOL(FPge(circle_ar(circle1), circle_ar(circle2)));
}


/*----------------------------------------------------------
 *	"Arithmetic" operators on circles.
 *---------------------------------------------------------*/

static CIRCLE *
circle_copy(CIRCLE *circle)
{
	CIRCLE	   *result;

	if (!PointerIsValid(circle))
		return NULL;

	result = (CIRCLE *) palloc(sizeof(CIRCLE));
	memcpy((char *) result, (char *) circle, sizeof(CIRCLE));
	return result;
}


/* circle_add_pt()
 * Translation operator.
 */
Datum
circle_add_pt(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	CIRCLE	   *result;

	result = circle_copy(circle);

	result->center.x += point->x;
	result->center.y += point->y;

	PG_RETURN_CIRCLE_P(result);
}

Datum
circle_sub_pt(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	CIRCLE	   *result;

	result = circle_copy(circle);

	result->center.x -= point->x;
	result->center.y -= point->y;

	PG_RETURN_CIRCLE_P(result);
}


/* circle_mul_pt()
 * Rotation and scaling operators.
 */
Datum
circle_mul_pt(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	CIRCLE	   *result;
	Point	   *p;

	result = circle_copy(circle);

	p = DatumGetPointP(DirectFunctionCall2(point_mul,
										   PointPGetDatum(&circle->center),
										   PointPGetDatum(point)));
	result->center.x = p->x;
	result->center.y = p->y;
	result->radius *= HYPOT(point->x, point->y);

	PG_RETURN_CIRCLE_P(result);
}

Datum
circle_div_pt(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	CIRCLE	   *result;
	Point	   *p;

	result = circle_copy(circle);

	p = DatumGetPointP(DirectFunctionCall2(point_div,
										   PointPGetDatum(&circle->center),
										   PointPGetDatum(point)));
	result->center.x = p->x;
	result->center.y = p->y;
	result->radius /= HYPOT(point->x, point->y);

	PG_RETURN_CIRCLE_P(result);
}


/*		circle_area		-		returns the area of the circle.
 */
Datum
circle_area(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);

	PG_RETURN_FLOAT8(circle_ar(circle));
}


/*		circle_diameter -		returns the diameter of the circle.
 */
Datum
circle_diameter(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);

	PG_RETURN_FLOAT8(2 * circle->radius);
}


/*		circle_radius	-		returns the radius of the circle.
 */
Datum
circle_radius(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);

	PG_RETURN_FLOAT8(circle->radius);
}


/*		circle_distance -		returns the distance between
 *								  two circles.
 */
Datum
circle_distance(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle1 = PG_GETARG_CIRCLE_P(0);
	CIRCLE	   *circle2 = PG_GETARG_CIRCLE_P(1);
	float8		result;

	result = point_dt(&circle1->center, &circle2->center)
		- (circle1->radius + circle2->radius);
	if (result < 0)
		result = 0;
	PG_RETURN_FLOAT8(result);
}


Datum
circle_contain_pt(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	double		d;

	d = point_dt(&circle->center, point);
	PG_RETURN_BOOL(d <= circle->radius);
}


Datum
pt_contained_circle(PG_FUNCTION_ARGS)
{
	Point	   *point = PG_GETARG_POINT_P(0);
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(1);
	double		d;

	d = point_dt(&circle->center, point);
	PG_RETURN_BOOL(d <= circle->radius);
}


/*		dist_pc -		returns the distance between
 *						  a point and a circle.
 */
Datum
dist_pc(PG_FUNCTION_ARGS)
{
	Point	   *point = PG_GETARG_POINT_P(0);
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(1);
	float8		result;

	result = point_dt(point, &circle->center) - circle->radius;
	if (result < 0)
		result = 0;
	PG_RETURN_FLOAT8(result);
}

/*
 * Distance from a circle to a point
 */
Datum
dist_cpoint(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	Point	   *point = PG_GETARG_POINT_P(1);
	float8		result;

	result = point_dt(point, &circle->center) - circle->radius;
	if (result < 0)
		result = 0;
	PG_RETURN_FLOAT8(result);
}

/*		circle_center	-		returns the center point of the circle.
 */
Datum
circle_center(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	Point	   *result;

	result = (Point *) palloc(sizeof(Point));
	result->x = circle->center.x;
	result->y = circle->center.y;

	PG_RETURN_POINT_P(result);
}


/*		circle_ar		-		returns the area of the circle.
 */
static double
circle_ar(CIRCLE *circle)
{
	return M_PI * (circle->radius * circle->radius);
}


/*----------------------------------------------------------
 *	Conversion operators.
 *---------------------------------------------------------*/

Datum
cr_circle(PG_FUNCTION_ARGS)
{
	Point	   *center = PG_GETARG_POINT_P(0);
	float8		radius = PG_GETARG_FLOAT8(1);
	CIRCLE	   *result;

	result = (CIRCLE *) palloc(sizeof(CIRCLE));

	result->center.x = center->x;
	result->center.y = center->y;
	result->radius = radius;

	PG_RETURN_CIRCLE_P(result);
}

Datum
circle_box(PG_FUNCTION_ARGS)
{
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
	BOX		   *box;
	double		delta;

	box = (BOX *) palloc(sizeof(BOX));

	delta = circle->radius / sqrt(2.0);

	box->high.x = circle->center.x + delta;
	box->low.x = circle->center.x - delta;
	box->high.y = circle->center.y + delta;
	box->low.y = circle->center.y - delta;

	PG_RETURN_BOX_P(box);
}

/* box_circle()
 * Convert a box to a circle.
 */
Datum
box_circle(PG_FUNCTION_ARGS)
{
	BOX		   *box = PG_GETARG_BOX_P(0);
	CIRCLE	   *circle;

	circle = (CIRCLE *) palloc(sizeof(CIRCLE));

	circle->center.x = (box->high.x + box->low.x) / 2;
	circle->center.y = (box->high.y + box->low.y) / 2;

	circle->radius = point_dt(&circle->center, &box->high);

	PG_RETURN_CIRCLE_P(circle);
}


Datum
circle_poly(PG_FUNCTION_ARGS)
{
	int32		npts = PG_GETARG_INT32(0);
	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(1);
	POLYGON    *poly;
	int			base_size,
				size;
	int			i;
	double		angle;
	double		anglestep;

	if (FPzero(circle->radius))
		ereport(ERROR,
				(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
				 errmsg("cannot convert circle with radius zero to polygon")));

	if (npts < 2)
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
				 errmsg("must request at least 2 points")));

	base_size = sizeof(poly->p[0]) * npts;
	size = offsetof(POLYGON, p) + base_size;

	/* Check for integer overflow */
	if (base_size / npts != sizeof(poly->p[0]) || size <= base_size)
		ereport(ERROR,
				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
				 errmsg("too many points requested")));

	poly = (POLYGON *) palloc0(size);	/* zero any holes */
	SET_VARSIZE(poly, size);
	poly->npts = npts;

	anglestep = (2.0 * M_PI) / npts;

	for (i = 0; i < npts; i++)
	{
		angle = i * anglestep;
		poly->p[i].x = circle->center.x - (circle->radius * cos(angle));
		poly->p[i].y = circle->center.y + (circle->radius * sin(angle));
	}

	make_bound_box(poly);

	PG_RETURN_POLYGON_P(poly);
}

/*		poly_circle		- convert polygon to circle
 *
 * XXX This algorithm should use weighted means of line segments
 *	rather than straight average values of points - tgl 97/01/21.
 */
Datum
poly_circle(PG_FUNCTION_ARGS)
{
	POLYGON    *poly = PG_GETARG_POLYGON_P(0);
	CIRCLE	   *circle;
	int			i;

	if (poly->npts < 1)
		ereport(ERROR,
				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
				 errmsg("cannot convert empty polygon to circle")));

	circle = (CIRCLE *) palloc(sizeof(CIRCLE));

	circle->center.x = 0;
	circle->center.y = 0;
	circle->radius = 0;

	for (i = 0; i < poly->npts; i++)
	{
		circle->center.x += poly->p[i].x;
		circle->center.y += poly->p[i].y;
	}
	circle->center.x /= poly->npts;
	circle->center.y /= poly->npts;

	for (i = 0; i < poly->npts; i++)
		circle->radius += point_dt(&poly->p[i], &circle->center);
	circle->radius /= poly->npts;

	PG_RETURN_CIRCLE_P(circle);
}


/***********************************************************************
 **
 **		Private routines for multiple types.
 **
 ***********************************************************************/

/*
 *	Test to see if the point is inside the polygon, returns 1/0, or 2 if
 *	the point is on the polygon.
 *	Code adapted but not copied from integer-based routines in WN: A
 *	Server for the HTTP
 *	version 1.15.1, file wn/image.c
 *	http://hopf.math.northwestern.edu/index.html
 *	Description of algorithm:  http://www.linuxjournal.com/article/2197
 *							   http://www.linuxjournal.com/article/2029
 */

#define POINT_ON_POLYGON INT_MAX

static int
point_inside(Point *p, int npts, Point *plist)
{
	double		x0,
				y0;
	double		prev_x,
				prev_y;
	int			i = 0;
	double		x,
				y;
	int			cross,
				total_cross = 0;

	if (npts <= 0)
		return 0;

	/* compute first polygon point relative to single point */
	x0 = plist[0].x - p->x;
	y0 = plist[0].y - p->y;

	prev_x = x0;
	prev_y = y0;
	/* loop over polygon points and aggregate total_cross */
	for (i = 1; i < npts; i++)
	{
		/* compute next polygon point relative to single point */
		x = plist[i].x - p->x;
		y = plist[i].y - p->y;

		/* compute previous to current point crossing */
		if ((cross = lseg_crossing(x, y, prev_x, prev_y)) == POINT_ON_POLYGON)
			return 2;
		total_cross += cross;

		prev_x = x;
		prev_y = y;
	}

	/* now do the first point */
	if ((cross = lseg_crossing(x0, y0, prev_x, prev_y)) == POINT_ON_POLYGON)
		return 2;
	total_cross += cross;

	if (total_cross != 0)
		return 1;
	return 0;
}


/* lseg_crossing()
 * Returns +/-2 if line segment crosses the positive X-axis in a +/- direction.
 * Returns +/-1 if one point is on the positive X-axis.
 * Returns 0 if both points are on the positive X-axis, or there is no crossing.
 * Returns POINT_ON_POLYGON if the segment contains (0,0).
 * Wow, that is one confusing API, but it is used above, and when summed,
 * can tell is if a point is in a polygon.
 */

static int
lseg_crossing(double x, double y, double prev_x, double prev_y)
{
	double		z;
	int			y_sign;

	if (FPzero(y))
	{							/* y == 0, on X axis */
		if (FPzero(x))			/* (x,y) is (0,0)? */
			return POINT_ON_POLYGON;
		else if (FPgt(x, 0))
		{						/* x > 0 */
			if (FPzero(prev_y)) /* y and prev_y are zero */
				/* prev_x > 0? */
				return FPgt(prev_x, 0) ? 0 : POINT_ON_POLYGON;
			return FPlt(prev_y, 0) ? 1 : -1;
		}
		else
		{						/* x < 0, x not on positive X axis */
			if (FPzero(prev_y))
				/* prev_x < 0? */
				return FPlt(prev_x, 0) ? 0 : POINT_ON_POLYGON;
			return 0;
		}
	}
	else
	{							/* y != 0 */
		/* compute y crossing direction from previous point */
		y_sign = FPgt(y, 0) ? 1 : -1;

		if (FPzero(prev_y))
			/* previous point was on X axis, so new point is either off or on */
			return FPlt(prev_x, 0) ? 0 : y_sign;
		else if (FPgt(y_sign * prev_y, 0))
			/* both above or below X axis */
			return 0;			/* same sign */
		else
		{						/* y and prev_y cross X-axis */
			if (FPge(x, 0) && FPgt(prev_x, 0))
				/* both non-negative so cross positive X-axis */
				return 2 * y_sign;
			if (FPlt(x, 0) && FPle(prev_x, 0))
				/* both non-positive so do not cross positive X-axis */
				return 0;

			/* x and y cross axises, see URL above point_inside() */
			z = (x - prev_x) * y - (y - prev_y) * x;
			if (FPzero(z))
				return POINT_ON_POLYGON;
			return FPgt((y_sign * z), 0) ? 0 : 2 * y_sign;
		}
	}
}


static bool
plist_same(int npts, Point *p1, Point *p2)
{
	int			i,
				ii,
				j;

	/* find match for first point */
	for (i = 0; i < npts; i++)
	{
		if ((FPeq(p2[i].x, p1[0].x))
			&& (FPeq(p2[i].y, p1[0].y)))
		{

			/* match found? then look forward through remaining points */
			for (ii = 1, j = i + 1; ii < npts; ii++, j++)
			{
				if (j >= npts)
					j = 0;
				if ((!FPeq(p2[j].x, p1[ii].x))
					|| (!FPeq(p2[j].y, p1[ii].y)))
				{
#ifdef GEODEBUG
					printf("plist_same- %d failed forward match with %d\n", j, ii);
#endif
					break;
				}
			}
#ifdef GEODEBUG
			printf("plist_same- ii = %d/%d after forward match\n", ii, npts);
#endif
			if (ii == npts)
				return true;

			/* match not found forwards? then look backwards */
			for (ii = 1, j = i - 1; ii < npts; ii++, j--)
			{
				if (j < 0)
					j = (npts - 1);
				if ((!FPeq(p2[j].x, p1[ii].x))
					|| (!FPeq(p2[j].y, p1[ii].y)))
				{
#ifdef GEODEBUG
					printf("plist_same- %d failed reverse match with %d\n", j, ii);
#endif
					break;
				}
			}
#ifdef GEODEBUG
			printf("plist_same- ii = %d/%d after reverse match\n", ii, npts);
#endif
			if (ii == npts)
				return true;
		}
	}

	return false;
}


/*-------------------------------------------------------------------------
 * Determine the hypotenuse.
 *
 * If required, x and y are swapped to make x the larger number. The
 * traditional formula of x^2+y^2 is rearranged to factor x outside the
 * sqrt. This allows computation of the hypotenuse for significantly
 * larger values, and with a higher precision than when using the naive
 * formula.  In particular, this cannot overflow unless the final result
 * would be out-of-range.
 *
 * sqrt( x^2 + y^2 ) = sqrt( x^2( 1 + y^2/x^2) )
 *					 = x * sqrt( 1 + y^2/x^2 )
 *					 = x * sqrt( 1 + y/x * y/x )
 *
 * It is expected that this routine will eventually be replaced with the
 * C99 hypot() function.
 *
 * This implementation conforms to IEEE Std 1003.1 and GLIBC, in that the
 * case of hypot(inf,nan) results in INF, and not NAN.
 *-----------------------------------------------------------------------
 */
double
pg_hypot(double x, double y)
{
	double		yx;

	/* Handle INF and NaN properly */
	if (isinf(x) || isinf(y))
		return get_float8_infinity();

	if (isnan(x) || isnan(y))
		return get_float8_nan();

	/* Else, drop any minus signs */
	x = fabs(x);
	y = fabs(y);

	/* Swap x and y if needed to make x the larger one */
	if (x < y)
	{
		double		temp = x;

		x = y;
		y = temp;
	}

	/*
	 * If y is zero, the hypotenuse is x.  This test saves a few cycles in
	 * such cases, but more importantly it also protects against
	 * divide-by-zero errors, since now x >= y.
	 */
	if (y == 0.0)
		return x;

	/* Determine the hypotenuse */
	yx = y / x;
	return x * sqrt(1.0 + (yx * yx));
}
