This commit was manufactured by cvs2git to create branch 'ecpg_big_bison'.

Sprout from master 2002-06-20 20:29:54 UTC Bruce Momjian <bruce@momjian.us> 'Update copyright to 2002.'
Delete:
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diff --git a/src/backend/utils/adt/geo_ops.c b/src/backend/utils/adt/geo_ops.c
deleted file mode 100644
index 2b2df7ba0db..00000000000
--- a/src/backend/utils/adt/geo_ops.c
+++ /dev/null
@@ -1,4661 +0,0 @@
-/*-------------------------------------------------------------------------
- *
- * geo_ops.c
- *	  2D geometric operations
- *
- * Portions Copyright (c) 1996-2002, PostgreSQL Global Development Group
- * Portions Copyright (c) 1994, Regents of the University of California
- *
- *
- * IDENTIFICATION
- *	  $Header: /cvsroot/pgsql/src/backend/utils/adt/geo_ops.c,v 1.62 2002/06/20 20:29:37 momjian Exp $
- *
- *-------------------------------------------------------------------------
- */
-#include <math.h>
-#include <limits.h>
-#include <float.h>
-#include <ctype.h>
-
-#include "postgres.h"
-
-#include "utils/geo_decls.h"
-
-#ifndef PI
-#define PI 3.1415926536
-#endif
-
-/*
- * Internal routines
- */
-
-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_copy(BOX *box);
-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 int	single_decode(char *str, float8 *x, char **ss);
-static int	single_encode(float8 x, char *str);
-static int	pair_decode(char *str, float8 *x, float8 *y, char **s);
-static int	pair_encode(float8 x, float8 y, char *str);
-static int	pair_count(char *s, char delim);
-static int	path_decode(int opentype, int npts, char *str, int *isopen, char **ss, Point *p);
-static char *path_encode(bool closed, 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);
-
-
-/*
- * 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		'>'
-
-/* Maximum number of output digits printed */
-#define P_MAXDIG DBL_DIG
-#define P_MAXLEN (2*(P_MAXDIG+7)+1)
-
-static int	digits8 = P_MAXDIG;
-
-
-/*
- * 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 int
-single_decode(char *str, float8 *x, char **s)
-{
-	char	   *cp;
-
-	if (!PointerIsValid(str))
-		return FALSE;
-
-	while (isspace((unsigned char) *str))
-		str++;
-	*x = strtod(str, &cp);
-#ifdef GEODEBUG
-	printf("single_decode- (%x) try decoding %s to %g\n", (cp - str), str, *x);
-#endif
-	if (cp <= str)
-		return FALSE;
-	while (isspace((unsigned char) *cp))
-		cp++;
-
-	if (s != NULL)
-		*s = cp;
-
-	return TRUE;
-}	/* single_decode() */
-
-static int
-single_encode(float8 x, char *str)
-{
-	sprintf(str, "%.*g", digits8, x);
-	return TRUE;
-}	/* single_encode() */
-
-static int
-pair_decode(char *str, float8 *x, float8 *y, char **s)
-{
-	int			has_delim;
-	char	   *cp;
-
-	if (!PointerIsValid(str))
-		return FALSE;
-
-	while (isspace((unsigned char) *str))
-		str++;
-	if ((has_delim = (*str == LDELIM)))
-		str++;
-
-	while (isspace((unsigned char) *str))
-		str++;
-	*x = strtod(str, &cp);
-	if (cp <= str)
-		return FALSE;
-	while (isspace((unsigned char) *cp))
-		cp++;
-	if (*cp++ != DELIM)
-		return FALSE;
-	while (isspace((unsigned char) *cp))
-		cp++;
-	*y = strtod(cp, &str);
-	if (str <= cp)
-		return FALSE;
-	while (isspace((unsigned char) *str))
-		str++;
-	if (has_delim)
-	{
-		if (*str != RDELIM)
-			return FALSE;
-		str++;
-		while (isspace((unsigned char) *str))
-			str++;
-	}
-	if (s != NULL)
-		*s = str;
-
-	return TRUE;
-}
-
-static int
-pair_encode(float8 x, float8 y, char *str)
-{
-	sprintf(str, "%.*g,%.*g", digits8, x, digits8, y);
-	return TRUE;
-}
-
-static int
-path_decode(int opentype, int npts, char *str, int *isopen, char **ss, Point *p)
-{
-	int			depth = 0;
-	char	   *s,
-			   *cp;
-	int			i;
-
-	s = str;
-	while (isspace((unsigned char) *s))
-		s++;
-	if ((*isopen = (*s == LDELIM_EP)))
-	{
-		/* no open delimiter allowed? */
-		if (!opentype)
-			return FALSE;
-		depth++;
-		s++;
-		while (isspace((unsigned char) *s))
-			s++;
-
-	}
-	else if (*s == LDELIM)
-	{
-		cp = (s + 1);
-		while (isspace((unsigned char) *cp))
-			cp++;
-		if (*cp == LDELIM)
-		{
-#ifdef NOT_USED
-			/* nested delimiters with only one point? */
-			if (npts <= 1)
-				return FALSE;
-#endif
-			depth++;
-			s = cp;
-		}
-		else if (strrchr(s, LDELIM) == s)
-		{
-			depth++;
-			s = cp;
-		}
-	}
-
-	for (i = 0; i < npts; i++)
-	{
-		if (!pair_decode(s, &(p->x), &(p->y), &s))
-			return FALSE;
-
-		if (*s == DELIM)
-			s++;
-		p++;
-	}
-
-	while (depth > 0)
-	{
-		if ((*s == RDELIM)
-			|| ((*s == RDELIM_EP) && (*isopen) && (depth == 1)))
-		{
-			depth--;
-			s++;
-			while (isspace((unsigned char) *s))
-				s++;
-		}
-		else
-			return FALSE;
-	}
-	*ss = s;
-
-	return TRUE;
-}	/* path_decode() */
-
-static char *
-path_encode(bool closed, int npts, Point *pt)
-{
-	char	   *result = palloc(npts * (P_MAXLEN + 3) + 2);
-
-	char	   *cp;
-	int			i;
-
-	cp = result;
-	switch (closed)
-	{
-		case TRUE:
-			*cp++ = LDELIM;
-			break;
-		case FALSE:
-			*cp++ = LDELIM_EP;
-			break;
-		default:
-			break;
-	}
-
-	for (i = 0; i < npts; i++)
-	{
-		*cp++ = LDELIM;
-		if (!pair_encode(pt->x, pt->y, cp))
-			elog(ERROR, "Unable to format path");
-		cp += strlen(cp);
-		*cp++ = RDELIM;
-		*cp++ = DELIM;
-		pt++;
-	}
-	cp--;
-	switch (closed)
-	{
-		case TRUE:
-			*cp++ = RDELIM;
-			break;
-		case FALSE:
-			*cp++ = RDELIM_EP;
-			break;
-		default:
-			break;
-	}
-	*cp = '\0';
-
-	return result;
-}	/* 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));
-	int			isopen;
-	char	   *s;
-	double		x,
-				y;
-
-	if ((!path_decode(FALSE, 2, str, &isopen, &s, &(box->high)))
-		|| (*s != '\0'))
-		elog(ERROR, "Bad box external representation '%s'", 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(-1, 2, &(box->high)));
-}
-
-
-/*		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
- */
-static 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 ((FPge(box1->high.x, box2->high.x) &&
-			 FPle(box1->low.x, box2->high.x)) ||
-			(FPge(box2->high.x, box1->high.x) &&
-			 FPle(box2->low.x, box1->high.x)))
-		&&
-		((FPge(box1->high.y, box2->high.y) &&
-		  FPle(box1->low.y, box2->high.y)) ||
-		 (FPge(box2->high.y, box1->high.y) &&
-		  FPle(box2->low.y, box1->high.y)));
-}
-
-/*		box_overleft	-		is the right edge of box1 to the 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_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_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 to the 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_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?
- */
-Datum
-box_below(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(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.
- **				Lines are not intended to be used as ADTs per se,
- **				but their ops are useful tools for other ADT ops.  Thus,
- **				there are few relops.
- **
- ***********************************************************************/
-
-Datum
-line_in(PG_FUNCTION_ARGS)
-{
-#ifdef ENABLE_LINE_TYPE
-	char	   *str = PG_GETARG_CSTRING(0);
-#endif
-	LINE	   *line;
-
-#ifdef ENABLE_LINE_TYPE
-	LSEG		lseg;
-	int			isopen;
-	char	   *s;
-
-	if ((!path_decode(TRUE, 2, str, &isopen, &s, &(lseg.p[0])))
-		|| (*s != '\0'))
-		elog(ERROR, "Bad line external representation '%s'", str);
-
-	line = (LINE *) palloc(sizeof(LINE));
-	line_construct_pts(line, &lseg.p[0], &lseg.p[1]);
-#else
-	elog(ERROR, "line not yet implemented");
-	line = NULL;
-#endif
-
-	PG_RETURN_LINE_P(line);
-}
-
-
-Datum
-line_out(PG_FUNCTION_ARGS)
-{
-#ifdef ENABLE_LINE_TYPE
-	LINE	   *line = PG_GETARG_LINE_P(0);
-#endif
-	char	   *result;
-
-#ifdef ENABLE_LINE_TYPE
-	LSEG		lseg;
-
-	if (FPzero(line->B))
-	{							/* vertical */
-		/* use "x = C" */
-		result->A = -1;
-		result->B = 0;
-		result->C = pt1->x;
-#ifdef GEODEBUG
-		printf("line_out- line is vertical\n");
-#endif
-#ifdef NOT_USED
-		result->m = DBL_MAX;
-#endif
-
-	}
-	else if (FPzero(line->A))
-	{							/* horizontal */
-		/* use "x = C" */
-		result->A = 0;
-		result->B = -1;
-		result->C = pt1->y;
-#ifdef GEODEBUG
-		printf("line_out- line is horizontal\n");
-#endif
-#ifdef NOT_USED
-		result->m = 0.0;
-#endif
-
-	}
-	else
-	{
-	}
-
-	if (FPzero(line->A))		/* horizontal? */
-	{
-	}
-	else if (FPzero(line->B))	/* vertical? */
-	{
-	}
-	else
-	{
-	}
-
-	return path_encode(TRUE, 2, (Point *) &(ls->p[0]));
-#else
-	elog(ERROR, "line not yet implemented");
-	result = NULL;
-#endif
-
-	PG_RETURN_CSTRING(result);
-}
-
-
-/*----------------------------------------------------------
- *	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));
-
-	/* use "mx - y + yinter = 0" */
-	result->A = m;
-	result->B = -1.0;
-	if (m == DBL_MAX)
-		result->C = pt->y;
-	else
-		result->C = pt->y - m * pt->x;
-
-#ifdef NOT_USED
-	result->m = m;
-#endif
-
-	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 NOT_USED
-		line->m = DBL_MAX;
-#endif
-#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 NOT_USED
-		line->m = 0.0;
-#endif
-#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;
-#ifdef NOT_USED
-		line->m = line->A;
-#endif
-#ifdef GEODEBUG
-		printf("line_construct_pts- line is neither vertical nor horizontal (diffs x=%.*g, y=%.*g\n",
-			   digits8, (pt2->x - pt1->x), digits8, (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);
-
-#ifdef NOT_USED
-	PG_RETURN_BOOL(FPeq(l1->m, l2->m));
-#endif
-	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);
-
-#ifdef NOT_USED
-	if (l1->m)
-		PG_RETURN_BOOL(FPeq(l2->m / l1->m, -1.0));
-	else if (l2->m)
-		PG_RETURN_BOOL(FPeq(l1->m / l2->m, -1.0));
-#endif
-	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;
-
-#ifdef NOT_USED
-	if (FPzero(l1->B))			/* l1 vertical? */
-		result = point_construct(l2->m * l1->C + l2->C, l1->C);
-	else if (FPzero(l2->B))		/* l2 vertical? */
-		result = point_construct(l1->m * l2->C + l1->C, l2->C);
-	else
-	{
-		x = (l1->C - l2->C) / (l2->A - l1->A);
-		result = point_construct(x, l1->m * x + l1->C);
-	}
-#endif
-
-	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",
-		   digits8, l1->A, digits8, l1->B, digits8, l1->C, digits8, l2->A, digits8, l2->B, digits8, l2->C);
-	printf("line_interpt- lines intersect at (%.*g,%.*g)\n", digits8, x, digits8, 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_in(PG_FUNCTION_ARGS)
-{
-	char	   *str = PG_GETARG_CSTRING(0);
-	PATH	   *path;
-	int			isopen;
-	char	   *s;
-	int			npts;
-	int			size;
-	int			depth = 0;
-
-	if ((npts = pair_count(str, ',')) <= 0)
-		elog(ERROR, "Bad path external representation '%s'", str);
-
-	s = str;
-	while (isspace((unsigned char) *s))
-		s++;
-
-	/* skip single leading paren */
-	if ((*s == LDELIM) && (strrchr(s, LDELIM) == s))
-	{
-		s++;
-		depth++;
-	}
-
-	size = offsetof(PATH, p[0]) +sizeof(path->p[0]) * npts;
-	path = (PATH *) palloc(size);
-
-	path->size = size;
-	path->npts = npts;
-
-	if ((!path_decode(TRUE, npts, s, &isopen, &s, &(path->p[0])))
-		&& (!((depth == 0) && (*s == '\0'))) && !((depth >= 1) && (*s == RDELIM)))
-		elog(ERROR, "Bad path external representation '%s'", str);
-
-	path->closed = (!isopen);
-
-	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->npts, path->p));
-}
-
-
-/*----------------------------------------------------------
- *	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;
-	double		x,
-				y;
-	char	   *s;
-
-	if (!pair_decode(str, &x, &y, &s) || (*s != '\0'))
-		elog(ERROR, "Bad point external representation '%s'", str);
-
-	point = (Point *) palloc(sizeof(Point));
-
-	point->x = x;
-	point->y = y;
-
-	PG_RETURN_POINT_P(point);
-}
-
-Datum
-point_out(PG_FUNCTION_ARGS)
-{
-	Point	   *pt = PG_GETARG_POINT_P(0);
-
-	PG_RETURN_CSTRING(path_encode(-1, 1, pt));
-}
-
-
-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;
-	int			isopen;
-	char	   *s;
-
-	lseg = (LSEG *) palloc(sizeof(LSEG));
-
-	if ((!path_decode(TRUE, 2, str, &isopen, &s, &(lseg->p[0])))
-		|| (*s != '\0'))
-		elog(ERROR, "Bad lseg external representation '%s'", str);
-
-#ifdef NOT_USED
-	lseg->m = point_sl(&lseg->p[0], &lseg->p[1]);
-#endif
-
-	PG_RETURN_LSEG_P(lseg);
-}
-
-
-Datum
-lseg_out(PG_FUNCTION_ARGS)
-{
-	LSEG	   *ls = PG_GETARG_LSEG_P(0);
-
-	PG_RETURN_CSTRING(path_encode(FALSE, 2, (Point *) &(ls->p[0])));
-}
-
-
-/* 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;
-
-#ifdef NOT_USED
-	result->m = point_sl(pt1, pt2);
-#endif
-
-	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;
-
-#ifdef NOT_USED
-	lseg->m = point_sl(pt1, pt2);
-#endif
-}
-
-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);
-
-#ifdef NOT_USED
-	PG_RETURN_BOOL(FPeq(l1->m, l2->m));
-#endif
-	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[1].y, l2->p[1].y) &&
-				   FPeq(l1->p[0].x, l2->p[0].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[1].y, l2->p[1].y) ||
-				   !FPeq(l1->p[0].x, l2->p[0].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);
-}
-
-
-/* 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;
-	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))
-		PG_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))
-		PG_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;
-	}
-
-	PG_RETURN_POINT_P(result);
-}
-
-/***********************************************************************
- **
- **		Routines for position comparisons of differently-typed
- **				2D objects.
- **
- ***********************************************************************/
-
-/*---------------------------------------------------------------------
- *		dist_
- *				Minimum distance from one object to another.
- *-------------------------------------------------------------------*/
-
-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 (line->A * pt->x + line->B * pt->y + line->C) /
-		HYPOT(line->A, line->B);
-}
-
-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)
-	{							/* slope is infinite */
-		m = (double) DBL_MAX;
-	}
-	else
-		m = ((lseg->p[0].y - lseg->p[1].y) / (lseg->p[1].x - lseg->p[0].x));
-	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 endpoints of the segment.
-	 */
-
-	/* intersection is on the line segment? */
-	if ((ip = interpt_sl(lseg, ln)) != NULL)
-	{
-		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
-	{
-		/* intersection is not on line segment */
-		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);
-}
-
-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);
-}
-
-
-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);
-}
-
-
-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);
-}
-
-
-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 */
-	elog(ERROR, "dist_lb not implemented");
-
-	PG_RETURN_NULL();
-}
-
-
-Datum
-dist_cpoly(PG_FUNCTION_ARGS)
-{
-	CIRCLE	   *circle = PG_GETARG_CIRCLE_P(0);
-	POLYGON    *poly = PG_GETARG_POLYGON_P(1);
-	float8		result;
-	float8		d;
-	int			i;
-	LSEG		seg;
-
-	if (point_inside(&(circle->center), poly->npts, poly->p) != 0)
-	{
-#ifdef GEODEBUG
-		printf("dist_cpoly- center inside of polygon\n");
-#endif
-		PG_RETURN_FLOAT8(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(&circle->center, &seg);
-#ifdef GEODEBUG
-	printf("dist_cpoly- 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(&circle->center, &seg);
-#ifdef GEODEBUG
-		printf("dist_cpoly- segment %d distance is %f\n", (i + 1), d);
-#endif
-		if (d < result)
-			result = d;
-	}
-
-	result -= circle->radius;
-	if (result < 0)
-		result = 0;
-
-	PG_RETURN_FLOAT8(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",
-		   digits8, lseg->p[0].x, digits8, lseg->p[0].y, digits8, lseg->p[1].x, digits8, lseg->p[1].y);
-	printf("interpt_sl- segment becomes line A=%.*g B=%.*g C=%.*g\n",
-		   digits8, tmp.A, digits8, tmp.B, digits8, tmp.C);
-#endif
-	if (PointerIsValid(p))
-	{
-#ifdef GEODEBUG
-		printf("interpt_sl- intersection point is (%.*g %.*g)\n", digits8, p->x, digits8, 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));
-
-#ifdef NOT_USED
-	if (FPeq(line->A, -1.0) && FPzero(line->B))
-	{							/* vertical */
-	}
-#endif
-	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 */
-#ifdef NOT_USED
-	invm = -1.0 / line->m;
-#endif
-	/* 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    m %f\n",
-			   tmp->A, tmp->B, tmp->C, tmp->m);
-#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    m %f\n",
-			   tmp->A, tmp->B, tmp->C, tmp->m);
-#endif
-		PG_RETURN_POINT_P(result);
-	}
-
-	/*
-	 * at this point the "normal" from point will hit lseg. The closet
-	 * 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    m %f\n",
-		   tmp->A, tmp->B, tmp->C, tmp->m);
-#endif
-	result = interpt_sl(lseg, tmp);
-	Assert(result != 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 ((d = 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 ((d = 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 = d = 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)
-{
-	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);
-}
-
-/* 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 */
-	elog(ERROR, "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);
-}
-
-/* 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
-		elog(ERROR, "Unable to 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			isopen;
-	char	   *s;
-
-	if ((npts = pair_count(str, ',')) <= 0)
-		elog(ERROR, "Bad polygon external representation '%s'", str);
-
-	size = offsetof(POLYGON, p[0]) +sizeof(poly->p[0]) * npts;
-	poly = (POLYGON *) palloc(size);
-
-	MemSet((char *) poly, 0, size);		/* zero any holes */
-	poly->size = size;
-	poly->npts = npts;
-
-	if ((!path_decode(FALSE, npts, str, &isopen, &s, &(poly->p[0])))
-		|| (*s != '\0'))
-		elog(ERROR, "Bad polygon external representation '%s'", 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(TRUE, poly->npts, poly->p));
-}
-
-
-/*-------------------------------------------------------
- * 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 left most point of A 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.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 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 right most point of A 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.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 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 by determining if
- * their bounding boxes overlap.
- *
- * XXX ought to do a more correct check?
- *-----------------------------------------------------------------*/
-Datum
-poly_overlap(PG_FUNCTION_ARGS)
-{
-	POLYGON    *polya = PG_GETARG_POLYGON_P(0);
-	POLYGON    *polyb = PG_GETARG_POLYGON_P(1);
-	bool		result;
-
-	result = box_ov(&polya->boundbox, &polyb->boundbox);
-
-	/*
-	 * 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 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;
-	int			i;
-
-	/*
-	 * Quick check to see if bounding box is contained.
-	 */
-	if (DatumGetBool(DirectFunctionCall2(box_contain,
-										 BoxPGetDatum(&polya->boundbox),
-										 BoxPGetDatum(&polyb->boundbox))))
-	{
-		result = true;			/* assume true for now */
-		for (i = 0; i < polyb->npts; i++)
-		{
-			if (point_inside(&(polyb->p[i]), polya->npts, &(polya->p[0])) == 0)
-			{
-#if GEODEBUG
-				printf("poly_contain- point (%f,%f) not in polygon\n", polyb->p[i].x, polyb->p[i].y);
-#endif
-				result = false;
-				break;
-			}
-		}
-		if (result)
-		{
-			for (i = 0; i < polya->npts; i++)
-			{
-				if (point_inside(&(polya->p[i]), polyb->npts, &(polyb->p[0])) == 1)
-				{
-#if GEODEBUG
-					printf("poly_contain- point (%f,%f) in polygon\n", polya->p[i].x, polya->p[i].y);
-#endif
-					result = false;
-					break;
-				}
-			}
-		}
-	}
-	else
-	{
-#if GEODEBUG
-		printf("poly_contain- bound box ((%f,%f),(%f,%f)) not inside ((%f,%f),(%f,%f))\n",
-			   polyb->boundbox.low.x, polyb->boundbox.low.y, polyb->boundbox.high.x, polyb->boundbox.high.y,
-			   polya->boundbox.low.x, polya->boundbox.low.y, polya->boundbox.high.x, polya->boundbox.high.y);
-#endif
-		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 by determining
- * if A's bounding box is contained by B's bounding box.
- *-----------------------------------------------------------------*/
-Datum
-poly_contained(PG_FUNCTION_ARGS)
-{
-	Datum		polya = PG_GETARG_DATUM(0);
-	Datum		polyb = PG_GETARG_DATUM(1);
-
-	PG_RETURN_DATUM(DirectFunctionCall2(poly_contain, polyb, polya));
-}
-
-
-/* poly_contain_pt()
- * Test to see if the point is inside the polygon.
- * Code adapted from integer-based routines in
- *	Wn: A Server for the HTTP
- *	File: wn/image.c
- *	Version 1.15.1
- *	Copyright (C) 1995	<by John Franks>
- * (code offered for use by J. Franks in Linux Journal letter.)
- */
-
-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
-
-	elog(ERROR, "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)
-		elog(ERROR, "point_div:  divide by 0.0 error");
-
-	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);
-}
-
-
-/***********************************************************************
- **
- **		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;
-	int			i;
-
-	if (p1->closed || p2->closed)
-		PG_RETURN_NULL();
-
-	size = offsetof(PATH, p[0]) +sizeof(p1->p[0]) * (p1->npts + p2->npts);
-	result = (PATH *) palloc(size);
-
-	result->size = size;
-	result->npts = (p1->npts + p2->npts);
-	result->closed = p1->closed;
-
-	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
-
-	elog(ERROR, "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)
-		elog(ERROR, "Open path cannot be converted to polygon");
-
-	size = offsetof(POLYGON, p[0]) +sizeof(poly->p[0]) * path->npts;
-	poly = (POLYGON *) palloc(size);
-
-	poly->size = 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[0]) +sizeof(poly->p[0]) * 4;
-	poly = (POLYGON *) palloc(size);
-
-	poly->size = 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;
-
-	size = offsetof(PATH, p[0]) +sizeof(path->p[0]) * poly->npts;
-	path = (PATH *) palloc(size);
-
-	path->size = size;
-	path->npts = poly->npts;
-	path->closed = TRUE;
-
-	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;
-	char	   *s,
-			   *cp;
-	int			depth = 0;
-
-	circle = (CIRCLE *) palloc(sizeof(CIRCLE));
-
-	s = str;
-	while (isspace((unsigned char) *s))
-		s++;
-	if ((*s == LDELIM_C) || (*s == LDELIM))
-	{
-		depth++;
-		cp = (s + 1);
-		while (isspace((unsigned char) *cp))
-			cp++;
-		if (*cp == LDELIM)
-			s = cp;
-	}
-
-	if (!pair_decode(s, &circle->center.x, &circle->center.y, &s))
-		elog(ERROR, "Bad circle external representation '%s'", str);
-
-	if (*s == DELIM)
-		s++;
-	while (isspace((unsigned char) *s))
-		s++;
-
-	if ((!single_decode(s, &circle->radius, &s)) || (circle->radius < 0))
-		elog(ERROR, "Bad circle external representation '%s'", str);
-
-	while (depth > 0)
-	{
-		if ((*s == RDELIM)
-			|| ((*s == RDELIM_C) && (depth == 1)))
-		{
-			depth--;
-			s++;
-			while (isspace((unsigned char) *s))
-				s++;
-		}
-		else
-			elog(ERROR, "Bad circle external representation '%s'", str);
-	}
-
-	if (*s != '\0')
-		elog(ERROR, "Bad circle external representation '%s'", 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);
-	char	   *result;
-	char	   *cp;
-
-	result = palloc(3 * (P_MAXLEN + 1) + 3);
-
-	cp = result;
-	*cp++ = LDELIM_C;
-	*cp++ = LDELIM;
-	if (!pair_encode(circle->center.x, circle->center.y, cp))
-		elog(ERROR, "Unable to format circle");
-
-	cp += strlen(cp);
-	*cp++ = RDELIM;
-	*cp++ = DELIM;
-	if (!single_encode(circle->radius, cp))
-		elog(ERROR, "Unable to format circle");
-
-	cp += strlen(cp);
-	*cp++ = RDELIM_C;
-	*cp = '\0';
-
-	PG_RETURN_CSTRING(result);
-}
-
-
-/*----------------------------------------------------------
- *	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 to the 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(FPle((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(FPge((circle1->center.x - circle1->radius),
-						(circle2->center.x + circle2->radius)));
-}
-
-/*		circle_overright		-		is the left edge of circle1 to the 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_positionop		-
- *				is circle1 entirely {above,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(FPle(circle1->center.y + circle1->radius,
-						circle2->center.y - circle2->radius));
-}
-
-Datum
-circle_above(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);
-}
-
-
-/*		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 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			size;
-	int			i;
-	double		angle;
-
-	if (FPzero(circle->radius) || (npts < 2))
-		elog(ERROR, "Unable to convert circle to polygon");
-
-	size = offsetof(POLYGON, p[0]) +(sizeof(poly->p[0]) * npts);
-	poly = (POLYGON *) palloc(size);
-
-	MemSet((char *) poly, 0, size);		/* zero any holes */
-	poly->size = size;
-	poly->npts = npts;
-
-	for (i = 0; i < npts; i++)
-	{
-		angle = i * (2 * PI / npts);
-		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 < 2)
-		elog(ERROR, "Unable to convert 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;
-
-	if (FPzero(circle->radius))
-		elog(ERROR, "Unable to convert polygon to circle");
-
-	PG_RETURN_CIRCLE_P(circle);
-}
-
-
-/***********************************************************************
- **
- **		Private routines for multiple types.
- **
- ***********************************************************************/
-
-#define HIT_IT INT_MAX
-
-static int
-point_inside(Point *p, int npts, Point *plist)
-{
-	double		x0,
-				y0;
-	double		px,
-				py;
-	int			i;
-	double		x,
-				y;
-	int			cross,
-				crossnum;
-
-/*
- * We calculate crossnum, which is twice the crossing number of a
- * ray from the origin parallel to the positive X axis.
- * A coordinate change is made to move the test point to the origin.
- * Then the function lseg_crossing() is called to calculate the crossnum of
- * one segment of the translated polygon with the ray which is the
- * positive X-axis.
- */
-
-	crossnum = 0;
-	i = 0;
-	if (npts <= 0)
-		return 0;
-
-	x0 = plist[0].x - p->x;
-	y0 = plist[0].y - p->y;
-
-	px = x0;
-	py = y0;
-	for (i = 1; i < npts; i++)
-	{
-		x = plist[i].x - p->x;
-		y = plist[i].y - p->y;
-
-		if ((cross = lseg_crossing(x, y, px, py)) == HIT_IT)
-			return 2;
-		crossnum += cross;
-
-		px = x;
-		py = y;
-	}
-	if ((cross = lseg_crossing(x0, y0, px, py)) == HIT_IT)
-		return 2;
-	crossnum += cross;
-	if (crossnum != 0)
-		return 1;
-	return 0;
-}
-
-
-/* lseg_crossing()
- * The function lseg_crossing() returns +2, or -2 if the segment from (x,y)
- * to previous (x,y) crosses the positive X-axis positively or negatively.
- * It returns +1 or -1 if one endpoint is on this ray, or 0 if both are.
- * It returns 0 if the ray and the segment don't intersect.
- * It returns HIT_IT if the segment contains (0,0)
- */
-
-static int
-lseg_crossing(double x, double y, double px, double py)
-{
-	double		z;
-	int			sgn;
-
-	/* If (px,py) = (0,0) and not first call we have already sent HIT_IT */
-
-	if (FPzero(y))
-	{
-		if (FPzero(x))
-		{
-			return HIT_IT;
-
-		}
-		else if (FPgt(x, 0))
-		{
-			if (FPzero(py))
-				return FPgt(px, 0) ? 0 : HIT_IT;
-			return FPlt(py, 0) ? 1 : -1;
-
-		}
-		else
-		{						/* x < 0 */
-			if (FPzero(py))
-				return FPlt(px, 0) ? 0 : HIT_IT;
-			return 0;
-		}
-	}
-
-	/* Now we know y != 0;	set sgn to sign of y */
-	sgn = (FPgt(y, 0) ? 1 : -1);
-	if (FPzero(py))
-		return FPlt(px, 0) ? 0 : sgn;
-
-	if (FPgt((sgn * py), 0))
-	{							/* y and py have same sign */
-		return 0;
-
-	}
-	else
-	{							/* y and py have opposite signs */
-		if (FPge(x, 0) && FPgt(px, 0))
-			return 2 * sgn;
-		if (FPlt(x, 0) && FPle(px, 0))
-			return 0;
-
-		z = (x - px) * y - (y - py) * x;
-		if (FPzero(z))
-			return HIT_IT;
-		return FPgt((sgn * z), 0) ? 0 : 2 * sgn;
-	}
-}
-
-
-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;
-}