geo_ops.c

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/*-------------------------------------------------------------------------
 *
 * geo_ops.c
 *    2D geometric operations
 *
 * Portions Copyright (c) 1996-2013, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/utils/adt/geo_ops.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

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

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

#ifndef M_PI
#define M_PI 3.14159265358979323846
#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);
static bool lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start);
static Point *lseg_interpt_internal(LSEG *l1, LSEG *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 characters printed by pair_encode() */
/* ...+3+7 : 3 accounts for extra_float_digits max value */
#define P_MAXLEN (2*(DBL_DIG+3+7)+1)


/*
 * 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)
{
    int         ndig = DBL_DIG + extra_float_digits;

    if (ndig < 1)
        ndig = 1;

    sprintf(str, "%.*g", ndig, 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)
{
    int         ndig = DBL_DIG + extra_float_digits;

    if (ndig < 1)
        ndig = 1;

    sprintf(str, "%.*g,%.*g", ndig, x, ndig, 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)
{
    int         size = npts * (P_MAXLEN + 3) + 2;
    char       *result;
    char       *cp;
    int         i;

    /* Check for integer overflow */
    if ((size - 2) / npts != (P_MAXLEN + 3))
        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg("too many points requested")));

    result = palloc(size);

    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))
            ereport(ERROR,
                    (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                     errmsg("could not format \"path\" value")));

        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'))
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
                 errmsg("invalid input syntax for type box: \"%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_recv            - converts external binary format to box
 */
Datum
box_recv(PG_FUNCTION_ARGS)
{
    StringInfo  buf = (StringInfo) PG_GETARG_POINTER(0);
    BOX        *box;
    double      x,
                y;

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

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

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

    PG_RETURN_BOX_P(box);
}

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

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


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

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


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

    return result;
}


/*      box_copy        -       copy a box
 */
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 (FPle(box1->low.x, box2->high.x) &&
            FPle(box2->low.x, box1->high.x) &&
            FPle(box1->low.y, box2->high.y) &&
            FPle(box2->low.y, box1->high.y));
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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


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

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

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

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

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

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

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

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

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

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


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

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

    PG_RETURN_FLOAT8(box_ar(box));
}


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

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


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

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


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

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

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


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

    box_cn(result, box);

    PG_RETURN_POINT_P(result);
}


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


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


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


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


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

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

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

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

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

    PG_RETURN_BOX_P(result);
}


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

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

    PG_RETURN_LSEG_P(result);
}

/***********************************************************************
 **
 **     Routines for 2D lines.
 **             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
    /* when fixed, modify "not implemented", catalog/pg_type.h and SGML */
    LSEG        lseg;
    int         isopen;
    char       *s;

    if ((!path_decode(TRUE, 2, str, &isopen, &s, &(lseg.p[0])))
        || (*s != '\0'))
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
                 errmsg("invalid input syntax for type line: \"%s\"", str)));

    line = (LINE *) palloc(sizeof(LINE));
    line_construct_pts(line, &lseg.p[0], &lseg.p[1]);
#else
    ereport(ERROR,
            (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
             errmsg("type \"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
    /* when fixed, modify "not implemented", catalog/pg_type.h and SGML */
    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
    ereport(ERROR,
            (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
             errmsg("type \"line\" not yet implemented")));
    result = NULL;
#endif

    PG_RETURN_CSTRING(result);
}

/*
 *      line_recv           - converts external binary format to line
 */
Datum
line_recv(PG_FUNCTION_ARGS)
{
    ereport(ERROR,
            (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
             errmsg("type \"line\" not yet implemented")));
    return 0;
}

/*
 *      line_send           - converts line to binary format
 */
Datum
line_send(PG_FUNCTION_ARGS)
{
    ereport(ERROR,
            (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
             errmsg("type \"line\" not yet implemented")));
    return 0;
}


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

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

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

#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",
               DBL_DIG, (pt2->x - pt1->x), DBL_DIG, (pt2->y - pt1->y));
#endif
    }
}

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

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


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

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

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

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

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

    return result;
}


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

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

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

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

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

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


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

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

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

    if ((!path_decode(TRUE, npts, s, &isopen, &s, &(path->p[0])))
    && (!((depth == 0) && (*s == '\0'))) && !((depth >= 1) && (*s == RDELIM)))
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
                 errmsg("invalid input syntax for type path: \"%s\"", str)));

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

    PG_RETURN_PATH_P(path);
}


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

    PG_RETURN_CSTRING(path_encode(path->closed, path->npts, path->p));
}

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

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

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

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

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

    PG_RETURN_PATH_P(path);
}

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

    pq_begintypsend(&buf);
    pq_sendbyte(&buf, path->closed ? 1 : 0);
    pq_sendint(&buf, path->npts, sizeof(int32));
    for (i = 0; i < path->npts; i++)
    {
        pq_sendfloat8(&buf, path->p[i].x);
        pq_sendfloat8(&buf, path->p[i].y);
    }
    PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


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

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

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

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

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

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

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

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

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

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

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

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

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

    PG_RETURN_BOOL(path->closed);
}

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

    PG_RETURN_BOOL(!path->closed);
}

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

    PG_RETURN_INT32(path->npts);
}


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

    path->closed = TRUE;

    PG_RETURN_PATH_P(path);
}

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

    path->closed = FALSE;

    PG_RETURN_PATH_P(path);
}


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    if (!have_min)
        PG_RETURN_NULL();

    PG_RETURN_FLOAT8(min);
}


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

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

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

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

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

    PG_RETURN_FLOAT8(result);
}

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

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

Datum
point_in(PG_FUNCTION_ARGS)
{
    char       *str = PG_GETARG_CSTRING(0);
    Point      *point;
    double      x,
                y;
    char       *s;

    if (!pair_decode(str, &x, &y, &s) || (*s != '\0'))
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
                 errmsg("invalid input syntax for type point: \"%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));
}

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

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

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

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


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

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


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

    if (!PointerIsValid(pt))
        return NULL;

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    PG_RETURN_FLOAT8(point_sl(pt1, pt2));
}


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


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

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

Datum
lseg_in(PG_FUNCTION_ARGS)
{
    char       *str = PG_GETARG_CSTRING(0);
    LSEG       *lseg;
    int         isopen;
    char       *s;

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

    if ((!path_decode(TRUE, 2, str, &isopen, &s, &(lseg->p[0])))
        || (*s != '\0'))
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
                 errmsg("invalid input syntax for type lseg: \"%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_recv           - converts external binary format to lseg
 */
Datum
lseg_recv(PG_FUNCTION_ARGS)
{
    StringInfo  buf = (StringInfo) PG_GETARG_POINTER(0);
    LSEG       *lseg;

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

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

#ifdef NOT_USED
    lseg->m = point_sl(&lseg->p[0], &lseg->p[1]);
#endif

    PG_RETURN_LSEG_P(lseg);
}

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

    PG_RETURN_FLOAT8(lseg_dt(l1, l2));
}

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

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

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

    return result;
}


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

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

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

    PG_RETURN_POINT_P(result);
}

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

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

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

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

    return result;
}

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

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

    PG_RETURN_POINT_P(result);
}

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

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

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)
        m = (double) DBL_MAX;   /* slope is infinite */
    else
        m = (lseg->p[0].x - lseg->p[1].x) / (lseg->p[1].y - lseg->p[0].y);
    ln = line_construct_pm(pt, m);

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

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

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

    return result;
}

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

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

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

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

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

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

    return p;
}

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

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

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

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

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

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

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

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

    PG_RETURN_POINT_P(result);
}

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

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

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

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

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

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

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

/* close_sl()
 * Closest point on line to line segment.
 *
 * XXX THIS CODE IS WRONG
 * The code is actually calculating the point on the line segment
 *  which is backwards from the routine naming convention.
 * Copied code to new routine close_ls() but haven't fixed this one yet.
 * - thomas 1998-01-31
 */
Datum
close_sl(PG_FUNCTION_ARGS)
{
    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 */
    ereport(ERROR,
            (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
             errmsg("function \"close_lb\" not implemented")));

    PG_RETURN_NULL();
}

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

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

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


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

    PG_RETURN_BOOL(on_ps_internal(pt, lseg));
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    PG_RETURN_BOOL(has_interpt_sl(lseg, line));
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    if ((!path_decode(FALSE, npts, str, &isopen, &s, &(poly->p[0])))
        || (*s != '\0'))
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
              errmsg("invalid input syntax for type polygon: \"%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));
}

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

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

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

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

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

    make_bound_box(poly);

    PG_RETURN_POLYGON_P(poly);
}

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

    pq_begintypsend(&buf);
    pq_sendint(&buf, poly->npts, sizeof(int32));
    for (i = 0; i < poly->npts; i++)
    {
        pq_sendfloat8(&buf, poly->p[i].x);
        pq_sendfloat8(&buf, poly->p[i].y);
    }
    PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}


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

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

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

    PG_RETURN_BOOL(result);
}

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

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

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

    PG_RETURN_BOOL(result);
}

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

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

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

    PG_RETURN_BOOL(result);
}

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

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

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

    PG_RETURN_BOOL(result);
}

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

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

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

    PG_RETURN_BOOL(result);
}

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

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

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

    PG_RETURN_BOOL(result);
}

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

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

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

    PG_RETURN_BOOL(result);
}

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

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

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

    PG_RETURN_BOOL(result);
}


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

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

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

    PG_RETURN_BOOL(result);
}

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

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

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

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

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

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

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

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

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

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

    PG_RETURN_BOOL(result);
}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    return res;
}

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

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

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

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

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

    PG_RETURN_BOOL(result);
}


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

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


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

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

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

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


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

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

    PG_RETURN_NULL();
}


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

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

    PG_RETURN_POINT_P(point_construct(x, y));
}

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

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

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

    PG_RETURN_POINT_P(result);
}

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

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

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

    PG_RETURN_POINT_P(result);
}

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

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

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

    PG_RETURN_POINT_P(result);
}

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

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

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

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

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

    PG_RETURN_POINT_P(result);
}


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

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

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

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

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

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

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

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

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

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

    PG_RETURN_BOX_P(result);
}

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

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

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

    PG_RETURN_BOX_P(result);
}


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

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

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

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

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

    result = (PATH *) palloc(size);

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

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

    PG_RETURN_PATH_P(result);
}

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

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

    PG_RETURN_PATH_P(path);
}

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

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

    PG_RETURN_PATH_P(path);
}

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

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

    PG_RETURN_PATH_P(path);
}

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

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

    PG_RETURN_PATH_P(path);
}


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

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

    PG_RETURN_NULL();
}

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

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

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

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

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

    make_bound_box(poly);

    PG_RETURN_POLYGON_P(poly);
}


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

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

    PG_RETURN_INT32(poly->npts);
}


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

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

    PG_RETURN_DATUM(result);
}


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

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

    box = box_copy(&poly->boundbox);

    PG_RETURN_BOX_P(box);
}


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

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

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

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

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

    PG_RETURN_POLYGON_P(poly);
}


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

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

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

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

    PG_RETURN_PATH_P(path);
}


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

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

/*      circle_in       -       convert a string to internal form.
 *
 *      External format: (center and radius of circle)
 *              "((f8,f8)<f8>)"
 *              also supports quick entry style "(f8,f8,f8)"
 */
Datum
circle_in(PG_FUNCTION_ARGS)
{
    char       *str = PG_GETARG_CSTRING(0);
    CIRCLE     *circle;
    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))
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
               errmsg("invalid input syntax for type circle: \"%s\"", str)));

    if (*s == DELIM)
        s++;
    while (isspace((unsigned char) *s))
        s++;

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

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

    if (*s != '\0')
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
               errmsg("invalid input syntax for type circle: \"%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(2 * P_MAXLEN + 6);

    cp = result;
    *cp++ = LDELIM_C;
    *cp++ = LDELIM;
    if (!pair_encode(circle->center.x, circle->center.y, cp))
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("could not format \"circle\" value")));

    cp += strlen(cp);
    *cp++ = RDELIM;
    *cp++ = DELIM;
    if (!single_encode(circle->radius, cp))
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("could not format \"circle\" value")));

    cp += strlen(cp);
    *cp++ = RDELIM_C;
    *cp = '\0';

    PG_RETURN_CSTRING(result);
}

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

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

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

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

    PG_RETURN_CIRCLE_P(circle);
}

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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


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

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

    if (!PointerIsValid(circle))
        return NULL;

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


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

    result = circle_copy(circle);

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

    PG_RETURN_CIRCLE_P(result);
}

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

    result = circle_copy(circle);

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

    PG_RETURN_CIRCLE_P(result);
}


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

    result = circle_copy(circle);

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

    PG_RETURN_CIRCLE_P(result);
}

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

    result = circle_copy(circle);

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

    PG_RETURN_CIRCLE_P(result);
}


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

    PG_RETURN_FLOAT8(circle_ar(circle));
}


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

    PG_RETURN_FLOAT8(2 * circle->radius);
}


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

    PG_RETURN_FLOAT8(circle->radius);
}


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

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


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

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


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

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


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

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


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

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

    PG_RETURN_POINT_P(result);
}


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


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

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

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

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

    PG_RETURN_CIRCLE_P(result);
}

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

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

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

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

    PG_RETURN_BOX_P(box);
}

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

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

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

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

    PG_RETURN_CIRCLE_P(circle);
}


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

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

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

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

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

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

    anglestep = (2.0 * M_PI) / npts;

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

    make_bound_box(poly);

    PG_RETURN_POLYGON_P(poly);
}

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

    if (poly->npts < 2)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("cannot convert empty polygon to circle")));

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

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

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

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

    if (FPzero(circle->radius))
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("cannot convert empty polygon to circle")));

    PG_RETURN_CIRCLE_P(circle);
}


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

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

#define POINT_ON_POLYGON INT_MAX

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

    if (npts <= 0)
        return 0;

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

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

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

        prev_x = x;
        prev_y = y;
    }

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

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


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

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

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

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

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


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

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

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

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

    return FALSE;
}


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

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

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

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

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

        x = y;
        y = temp;
    }

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

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