opensourcemirror
/
postgresql
mirror of git://git.postgresql.org/git/postgresql.git
1
0
Fork 0
Code Issues Releases Wiki Activity
postgresql/src/backend/utils/adt/geo_ops.c

5436 lines
120 KiB
C
Raw Blame History

/*-------------------------------------------------------------------------
*
* geo_ops.c
* 2D geometric operations
*
* This module implements the geometric functions and operators. The
* geometric types are (from simple to more complicated):
*
* - point
* - line
* - line segment
* - box
* - circle
* - polygon
*
* Portions Copyright (c) 1996-2019, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California
*
*
* IDENTIFICATION
* src/backend/utils/adt/geo_ops.c
*
*-------------------------------------------------------------------------
*/
#include "postgres.h"
#include <math.h>
#include <limits.h>
#include <float.h>
#include <ctype.h>
#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "utils/float.h"
#include "utils/fmgrprotos.h"
#include "utils/geo_decls.h"
/*
* * Type constructors have this form:
* void type_construct(Type *result, ...);
*
* * Operators commonly have signatures such as
* void type1_operator_type2(Type *result, Type1 *obj1, Type2 *obj2);
*
* Common operators are:
* * Intersection point:
* bool type1_interpt_type2(Point *result, Type1 *obj1, Type2 *obj2);
* Return whether the two objects intersect. If *result is not NULL,
* it is set to the intersection point.
*
* * Containment:
* bool type1_contain_type2(Type1 *obj1, Type2 *obj2);
* Return whether obj1 contains obj2.
* bool type1_contain_type2(Type1 *contains_obj, Type1 *contained_obj);
* Return whether obj1 contains obj2 (used when types are the same)
*
* * Distance of closest point in or on obj1 to obj2:
* float8 type1_closept_type2(Point *result, Type1 *obj1, Type2 *obj2);
* Returns the shortest distance between two objects. If *result is not
* NULL, it is set to the closest point in or on obj1 to obj2.
*
* These functions may be used to implement multiple SQL-level operators. For
* example, determining whether two lines are parallel is done by checking
* whether they don't intersect.
*/
/*
* Internal routines
*/
enum path_delim
{
PATH_NONE, PATH_OPEN, PATH_CLOSED
};
/* Routines for points */
static inline void point_construct(Point *result, float8 x, float8 y);
static inline void point_add_point(Point *result, Point *pt1, Point *pt2);
static inline void point_sub_point(Point *result, Point *pt1, Point *pt2);
static inline void point_mul_point(Point *result, Point *pt1, Point *pt2);
static inline void point_div_point(Point *result, Point *pt1, Point *pt2);
static inline bool point_eq_point(Point *pt1, Point *pt2);
static inline float8 point_dt(Point *pt1, Point *pt2);
static inline float8 point_sl(Point *pt1, Point *pt2);
static int point_inside(Point *p, int npts, Point *plist);
/* Routines for lines */
static inline void line_construct(LINE *result, Point *pt, float8 m);
static inline float8 line_sl(LINE *line);
static inline float8 line_invsl(LINE *line);
static bool line_interpt_line(Point *result, LINE *l1, LINE *l2);
static bool line_contain_point(LINE *line, Point *point);
static float8 line_closept_point(Point *result, LINE *line, Point *pt);
/* Routines for line segments */
static inline void statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2);
static inline float8 lseg_sl(LSEG *lseg);
static inline float8 lseg_invsl(LSEG *lseg);
static bool lseg_interpt_line(Point *result, LSEG *lseg, LINE *line);
static bool lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2);
static int lseg_crossing(float8 x, float8 y, float8 px, float8 py);
static bool lseg_contain_point(LSEG *lseg, Point *point);
static float8 lseg_closept_point(Point *result, LSEG *lseg, Point *pt);
static float8 lseg_closept_line(Point *result, LSEG *lseg, LINE *line);
static float8 lseg_closept_lseg(Point *result, LSEG *on_lseg, LSEG *to_lseg);
/* Routines for boxes */
static inline void box_construct(BOX *result, Point *pt1, Point *pt2);
static void box_cn(Point *center, BOX *box);
static bool box_ov(BOX *box1, BOX *box2);
static float8 box_ar(BOX *box);
static float8 box_ht(BOX *box);
static float8 box_wd(BOX *box);
static bool box_contain_point(BOX *box, Point *point);
static bool box_contain_box(BOX *contains_box, BOX *contained_box);
static bool box_contain_lseg(BOX *box, LSEG *lseg);
static bool box_interpt_lseg(Point *result, BOX *box, LSEG *lseg);
static float8 box_closept_point(Point *result, BOX *box, Point *point);
static float8 box_closept_lseg(Point *result, BOX *box, LSEG *lseg);
/* Routines for circles */
static float8 circle_ar(CIRCLE *circle);
/* Routines for polygons */
static void make_bound_box(POLYGON *poly);
static void poly_to_circle(CIRCLE *result, POLYGON *poly);
static bool lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start);
static bool poly_contain_poly(POLYGON *contains_poly, POLYGON *contained_poly);
static bool plist_same(int npts, Point *p1, Point *p2);
static float8 dist_ppoly_internal(Point *pt, POLYGON *poly);
/* Routines for encoding and decoding */
static float8 single_decode(char *num, char **endptr_p,
const char *type_name, const char *orig_string);
static void single_encode(float8 x, StringInfo str);
static void pair_decode(char *str, float8 *x, float8 *y, char **endptr_p,
const char *type_name, const char *orig_string);
static void pair_encode(float8 x, float8 y, StringInfo str);
static int pair_count(char *s, char delim);
static void path_decode(char *str, bool opentype, int npts, Point *p,
bool *isopen, char **endptr_p,
const char *type_name, const char *orig_string);
static char *path_encode(enum path_delim path_delim, int npts, Point *pt);
/*
* 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 '>'
#define LDELIM_L '{'
#define RDELIM_L '}'
/*
* 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 float8
single_decode(char *num, char **endptr_p,
const char *type_name, const char *orig_string)
{
return float8in_internal(num, endptr_p, type_name, orig_string);
} /* single_decode() */
static void
single_encode(float8 x, StringInfo str)
{
char *xstr = float8out_internal(x);
appendStringInfoString(str, xstr);
pfree(xstr);
} /* single_encode() */
static void
pair_decode(char *str, float8 *x, float8 *y, char **endptr_p,
const char *type_name, const char *orig_string)
{
bool has_delim;
while (isspace((unsigned char) *str))
str++;
if ((has_delim = (*str == LDELIM)))
str++;
*x = float8in_internal(str, &str, type_name, orig_string);
if (*str++ != DELIM)
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
type_name, orig_string)));
*y = float8in_internal(str, &str, type_name, orig_string);
if (has_delim)
{
if (*str++ != RDELIM)
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
type_name, orig_string)));
while (isspace((unsigned char) *str))
str++;
}
/* report stopping point if wanted, else complain if not end of string */
if (endptr_p)
*endptr_p = str;
else if (*str != '\0')
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
type_name, orig_string)));
}
static void
pair_encode(float8 x, float8 y, StringInfo str)
{
char *xstr = float8out_internal(x);
char *ystr = float8out_internal(y);
appendStringInfo(str, "%s,%s", xstr, ystr);
pfree(xstr);
pfree(ystr);
}
static void
path_decode(char *str, bool opentype, int npts, Point *p,
bool *isopen, char **endptr_p,
const char *type_name, const char *orig_string)
{
int depth = 0;
char *cp;
int i;
while (isspace((unsigned char) *str))
str++;
if ((*isopen = (*str == LDELIM_EP)))
{
/* no open delimiter allowed? */
if (!opentype)
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
type_name, orig_string)));
depth++;
str++;
}
else if (*str == LDELIM)
{
cp = (str + 1);
while (isspace((unsigned char) *cp))
cp++;
if (*cp == LDELIM)
{
depth++;
str = cp;
}
else if (strrchr(str, LDELIM) == str)
{
depth++;
str = cp;
}
}
for (i = 0; i < npts; i++)
{
pair_decode(str, &(p->x), &(p->y), &str, type_name, orig_string);
if (*str == DELIM)
str++;
p++;
}
while (depth > 0)
{
if (*str == RDELIM || (*str == RDELIM_EP && *isopen && depth == 1))
{
depth--;
str++;
while (isspace((unsigned char) *str))
str++;
}
else
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
type_name, orig_string)));
}
/* report stopping point if wanted, else complain if not end of string */
if (endptr_p)
*endptr_p = str;
else if (*str != '\0')
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
type_name, orig_string)));
} /* path_decode() */
static char *
path_encode(enum path_delim path_delim, int npts, Point *pt)
{
StringInfoData str;
int i;
initStringInfo(&str);
switch (path_delim)
{
case PATH_CLOSED:
appendStringInfoChar(&str, LDELIM);
break;
case PATH_OPEN:
appendStringInfoChar(&str, LDELIM_EP);
break;
case PATH_NONE:
break;
}
for (i = 0; i < npts; i++)
{
if (i > 0)
appendStringInfoChar(&str, DELIM);
appendStringInfoChar(&str, LDELIM);
pair_encode(pt->x, pt->y, &str);
appendStringInfoChar(&str, RDELIM);
pt++;
}
switch (path_delim)
{
case PATH_CLOSED:
appendStringInfoChar(&str, RDELIM);
break;
case PATH_OPEN:
appendStringInfoChar(&str, RDELIM_EP);
break;
case PATH_NONE:
break;
}
return str.data;
} /* path_encode() */
/*-------------------------------------------------------------
* pair_count - count the number of points
* allow the following notation:
* '((1,2),(3,4))'
* '(1,3,2,4)'
* require an odd number of delim characters in the string
*-------------------------------------------------------------*/
static int
pair_count(char *s, char delim)
{
int ndelim = 0;
while ((s = strchr(s, delim)) != NULL)
{
ndelim++;
s++;
}
return (ndelim % 2) ? ((ndelim + 1) / 2) : -1;
}
/***********************************************************************
**
** Routines for two-dimensional boxes.
**
***********************************************************************/
/*----------------------------------------------------------
* Formatting and conversion routines.
*---------------------------------------------------------*/
/* box_in - convert a string to internal form.
*
* External format: (two corners of box)
* "(f8, f8), (f8, f8)"
* also supports the older style "(f8, f8, f8, f8)"
*/
Datum
box_in(PG_FUNCTION_ARGS)
{
char *str = PG_GETARG_CSTRING(0);
BOX *box = (BOX *) palloc(sizeof(BOX));
bool isopen;
float8 x,
y;
path_decode(str, false, 2, &(box->high), &isopen, NULL, "box", str);
/* reorder corners if necessary... */
if (float8_lt(box->high.x, box->low.x))
{
x = box->high.x;
box->high.x = box->low.x;
box->low.x = x;
}
if (float8_lt(box->high.y, box->low.y))
{
y = box->high.y;
box->high.y = box->low.y;
box->low.y = y;
}
PG_RETURN_BOX_P(box);
}
/* box_out - convert a box to external form.
*/
Datum
box_out(PG_FUNCTION_ARGS)
{
BOX *box = PG_GETARG_BOX_P(0);
PG_RETURN_CSTRING(path_encode(PATH_NONE, 2, &(box->high)));
}
/*
* box_recv - converts external binary format to box
*/
Datum
box_recv(PG_FUNCTION_ARGS)
{
StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
BOX *box;
float8 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 (float8_lt(box->high.x, box->low.x))
{
x = box->high.x;
box->high.x = box->low.x;
box->low.x = x;
}
if (float8_lt(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 inline void
box_construct(BOX *result, Point *pt1, Point *pt2)
{
if (float8_gt(pt1->x, pt2->x))
{
result->high.x = pt1->x;
result->low.x = pt2->x;
}
else
{
result->high.x = pt2->x;
result->low.x = pt1->x;
}
if (float8_gt(pt1->y, pt2->y))
{
result->high.y = pt1->y;
result->low.y = pt2->y;
}
else
{
result->high.y = pt2->y;
result->low.y = pt1->y;
}
}
/*----------------------------------------------------------
* 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(point_eq_point(&box1->high, &box2->high) &&
point_eq_point(&box1->low, &box2->low));
}
/* 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(box_contain_box(box2, box1));
}
/* 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(box_contain_box(box1, box2));
}
/*
* Check whether the second box is in the first box or on its border
*/
static bool
box_contain_box(BOX *contains_box, BOX *contained_box)
{
return FPge(contains_box->high.x, contained_box->high.x) &&
FPle(contains_box->low.x, contained_box->low.x) &&
FPge(contains_box->high.y, contained_box->high.y) &&
FPle(contains_box->low.y, contained_box->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_wd(box));
}
/* 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_ht(box));
}
/* 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(point_dt(&a, &b));
}
/* 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 float8
box_ar(BOX *box)
{
return float8_mul(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 = float8_div(float8_pl(box->high.x, box->low.x), 2.0);
center->y = float8_div(float8_pl(box->high.y, box->low.y), 2.0);
}
/* box_wd - returns the width (length) of the box
* (horizontal magnitude).
*/
static float8
box_wd(BOX *box)
{
return float8_mi(box->high.x, box->low.x);
}
/* box_ht - returns the height of the box
* (vertical magnitude).
*/
static float8
box_ht(BOX *box)
{
return float8_mi(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 = float8_min(box1->high.x, box2->high.x);
result->low.x = float8_max(box1->low.x, box2->low.x);
result->high.y = float8_min(box1->high.y, box2->high.y);
result->low.y = float8_max(box1->low.y, box2->low.y);
PG_RETURN_BOX_P(result);
}
/* box_diagonal -
* returns a line segment which happens to be the
* positive-slope diagonal of "box".
*/
Datum
box_diagonal(PG_FUNCTION_ARGS)
{
BOX *box = PG_GETARG_BOX_P(0);
LSEG *result = (LSEG *) palloc(sizeof(LSEG));
statlseg_construct(result, &box->high, &box->low);
PG_RETURN_LSEG_P(result);
}
/***********************************************************************
**
** Routines for 2D lines.
**
***********************************************************************/
static bool
line_decode(char *s, const char *str, LINE *line)
{
/* s was already advanced over leading '{' */
line->A = single_decode(s, &s, "line", str);
if (*s++ != DELIM)
return false;
line->B = single_decode(s, &s, "line", str);
if (*s++ != DELIM)
return false;
line->C = single_decode(s, &s, "line", str);
if (*s++ != RDELIM_L)
return false;
while (isspace((unsigned char) *s))
s++;
if (*s != '\0')
return false;
return true;
}
Datum
line_in(PG_FUNCTION_ARGS)
{
char *str = PG_GETARG_CSTRING(0);
LINE *line = (LINE *) palloc(sizeof(LINE));
LSEG lseg;
bool isopen;
char *s;
s = str;
while (isspace((unsigned char) *s))
s++;
if (*s == LDELIM_L)
{
if (!line_decode(s + 1, str, line))
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
"line", str)));
if (FPzero(line->A) && FPzero(line->B))
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid line specification: A and B cannot both be zero")));
}
else
{
path_decode(s, true, 2, &lseg.p[0], &isopen, NULL, "line", str);
if (point_eq_point(&lseg.p[0], &lseg.p[1]))
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid line specification: must be two distinct points")));
line_construct(line, &lseg.p[0], lseg_sl(&lseg));
}
PG_RETURN_LINE_P(line);
}
Datum
line_out(PG_FUNCTION_ARGS)
{
LINE *line = PG_GETARG_LINE_P(0);
char *astr = float8out_internal(line->A);
char *bstr = float8out_internal(line->B);
char *cstr = float8out_internal(line->C);
PG_RETURN_CSTRING(psprintf("%c%s%c%s%c%s%c", LDELIM_L, astr, DELIM, bstr,
DELIM, cstr, RDELIM_L));
}
/*
* line_recv - converts external binary format to line
*/
Datum
line_recv(PG_FUNCTION_ARGS)
{
StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
LINE *line;
line = (LINE *) palloc(sizeof(LINE));
line->A = pq_getmsgfloat8(buf);
line->B = pq_getmsgfloat8(buf);
line->C = pq_getmsgfloat8(buf);
if (FPzero(line->A) && FPzero(line->B))
ereport(ERROR,
(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
errmsg("invalid line specification: A and B cannot both be zero")));
PG_RETURN_LINE_P(line);
}
/*
* line_send - converts line to binary format
*/
Datum
line_send(PG_FUNCTION_ARGS)
{
LINE *line = PG_GETARG_LINE_P(0);
StringInfoData buf;
pq_begintypsend(&buf);
pq_sendfloat8(&buf, line->A);
pq_sendfloat8(&buf, line->B);
pq_sendfloat8(&buf, line->C);
PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}
/*----------------------------------------------------------
* Conversion routines from one line formula to internal.
* Internal form: Ax+By+C=0
*---------------------------------------------------------*/
/*
* Fill already-allocated LINE struct from the point and the slope
*/
static inline void
line_construct(LINE *result, Point *pt, float8 m)
{
if (m == DBL_MAX)
{
/* vertical - use "x = C" */
result->A = -1.0;
result->B = 0.0;
result->C = pt->x;
}
else
{
/* use "mx - y + yinter = 0" */
result->A = m;
result->B = -1.0;
result->C = float8_mi(pt->y, float8_mul(m, pt->x));
/* on some platforms, the preceding expression tends to produce -0 */
if (result->C == 0.0)
result->C = 0.0;
}
}
/* 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));
if (point_eq_point(pt1, pt2))
ereport(ERROR,
(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
errmsg("invalid line specification: must be two distinct points")));
line_construct(result, pt1, point_sl(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(line_interpt_line(NULL, l1, l2));
}
Datum
line_parallel(PG_FUNCTION_ARGS)
{
LINE *l1 = PG_GETARG_LINE_P(0);
LINE *l2 = PG_GETARG_LINE_P(1);
PG_RETURN_BOOL(!line_interpt_line(NULL, l1, l2));
}
Datum
line_perp(PG_FUNCTION_ARGS)
{
LINE *l1 = PG_GETARG_LINE_P(0);
LINE *l2 = PG_GETARG_LINE_P(1);
if (FPzero(l1->A))
PG_RETURN_BOOL(FPzero(l2->B));
if (FPzero(l2->A))
PG_RETURN_BOOL(FPzero(l1->B));
if (FPzero(l1->B))
PG_RETURN_BOOL(FPzero(l2->A));
if (FPzero(l2->B))
PG_RETURN_BOOL(FPzero(l1->A));
PG_RETURN_BOOL(FPeq(float8_div(float8_mul(l1->A, l2->A),
float8_mul(l1->B, l2->B)), -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));
}
/*
* Check whether the two lines are the same
*
* We consider NaNs values to be equal to each other to let those lines
* to be found.
*/
Datum
line_eq(PG_FUNCTION_ARGS)
{
LINE *l1 = PG_GETARG_LINE_P(0);
LINE *l2 = PG_GETARG_LINE_P(1);
float8 ratio;
if (!FPzero(l2->A) && !isnan(l2->A))
ratio = float8_div(l1->A, l2->A);
else if (!FPzero(l2->B) && !isnan(l2->B))
ratio = float8_div(l1->B, l2->B);
else if (!FPzero(l2->C) && !isnan(l2->C))
ratio = float8_div(l1->C, l2->C);
else
ratio = 1.0;
PG_RETURN_BOOL((FPeq(l1->A, float8_mul(ratio, l2->A)) &&
FPeq(l1->B, float8_mul(ratio, l2->B)) &&
FPeq(l1->C, float8_mul(ratio, l2->C))) ||
(float8_eq(l1->A, l2->A) &&
float8_eq(l1->B, l2->B) &&
float8_eq(l1->C, l2->C)));
}
/*----------------------------------------------------------
* Line arithmetic routines.
*---------------------------------------------------------*/
/*
* Return slope of the line
*/
static inline float8
line_sl(LINE *line)
{
if (FPzero(line->A))
return 0.0;
if (FPzero(line->B))
return DBL_MAX;
return float8_div(line->A, -line->B);
}
/*
* Return inverse slope of the line
*/
static inline float8
line_invsl(LINE *line)
{
if (FPzero(line->A))
return DBL_MAX;
if (FPzero(line->B))
return 0.0;
return float8_div(line->B, line->A);
}
/* 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 ratio;
if (line_interpt_line(NULL, l1, l2)) /* intersecting? */
PG_RETURN_FLOAT8(0.0);
if (!FPzero(l1->A) && !isnan(l1->A) && !FPzero(l2->A) && !isnan(l2->A))
ratio = float8_div(l1->A, l2->A);
else if (!FPzero(l1->B) && !isnan(l1->B) && !FPzero(l2->B) && !isnan(l2->B))
ratio = float8_div(l1->B, l2->B);
else
ratio = 1.0;
PG_RETURN_FLOAT8(float8_div(fabs(float8_mi(l1->C,
float8_mul(ratio, l2->C))),
HYPOT(l1->A, l1->B)));
}
/* 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 = (Point *) palloc(sizeof(Point));
if (!line_interpt_line(result, l1, l2))
PG_RETURN_NULL();
PG_RETURN_POINT_P(result);
}
/*
* Internal version of line_interpt
*
* Return whether two lines intersect. If *result is not NULL, it is set to
* the intersection point.
*
* 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 the lines have NaN constants, we will return true, and the intersection
* point would have NaN coordinates. We shouldn't return false in this case
* because that would mean the lines are parallel.
*/
static bool
line_interpt_line(Point *result, LINE *l1, LINE *l2)
{
float8 x,
y;
if (!FPzero(l1->B))
{
if (FPeq(l2->A, float8_mul(l1->A, float8_div(l2->B, l1->B))))
return false;
x = float8_div(float8_mi(float8_mul(l1->B, l2->C),
float8_mul(l2->B, l1->C)),
float8_mi(float8_mul(l1->A, l2->B),
float8_mul(l2->A, l1->B)));
y = float8_div(-float8_pl(float8_mul(l1->A, x), l1->C), l1->B);
}
else if (!FPzero(l2->B))
{
if (FPeq(l1->A, float8_mul(l2->A, float8_div(l1->B, l2->B))))
return false;
x = float8_div(float8_mi(float8_mul(l2->B, l1->C),
float8_mul(l1->B, l2->C)),
float8_mi(float8_mul(l2->A, l1->B),
float8_mul(l1->A, l2->B)));
y = float8_div(-float8_pl(float8_mul(l2->A, x), l2->C), l2->B);
}
else
return false;
/* On some platforms, the preceding expressions tend to produce -0. */
if (x == 0.0)
x = 0.0;
if (y == 0.0)
y = 0.0;
if (result != NULL)
point_construct(result, x, y);
return true;
}
/***********************************************************************
**
** 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);
float8 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 = float8_pl(area, float8_mul(path->p[i].x, path->p[j].y));
area = float8_mi(area, float8_mul(path->p[i].y, path->p[j].x));
}
PG_RETURN_FLOAT8(float8_div(fabs(area), 2.0));
}
Datum
path_in(PG_FUNCTION_ARGS)
{
char *str = PG_GETARG_CSTRING(0);
PATH *path;
bool isopen;
char *s;
int npts;
int size;
int base_size;
int depth = 0;
if ((npts = pair_count(str, ',')) <= 0)
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
"path", str)));
s = str;
while (isspace((unsigned char) *s))
s++;
/* skip single leading paren */
if ((*s == LDELIM) && (strrchr(s, LDELIM) == s))
{
s++;
depth++;
}
base_size = sizeof(path->p[0]) * npts;
size = offsetof(PATH, p) + base_size;
/* Check for integer overflow */
if (base_size / npts != sizeof(path->p[0]) || size <= base_size)
ereport(ERROR,
(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
errmsg("too many points requested")));
path = (PATH *) palloc(size);
SET_VARSIZE(path, size);
path->npts = npts;
path_decode(s, true, npts, &(path->p[0]), &isopen, &s, "path", str);
if (depth >= 1)
{
if (*s++ != RDELIM)
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
"path", str)));
while (isspace((unsigned char) *s))
s++;
}
if (*s != '\0')
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
"path", str)));
path->closed = (!isopen);
/* prevent instability in unused pad bytes */
path->dummy = 0;
PG_RETURN_PATH_P(path);
}
Datum
path_out(PG_FUNCTION_ARGS)
{
PATH *path = PG_GETARG_PATH_P(0);
PG_RETURN_CSTRING(path_encode(path->closed ? PATH_CLOSED : PATH_OPEN, path->npts, path->p));
}
/*
* path_recv - converts external binary format to path
*
* External representation is closed flag (a boolean byte), int32 number
* of points, and the points.
*/
Datum
path_recv(PG_FUNCTION_ARGS)
{
StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
PATH *path;
int closed;
int32 npts;
int32 i;
int size;
closed = pq_getmsgbyte(buf);
npts = pq_getmsgint(buf, sizeof(int32));
if (npts <= 0 || npts >= (int32) ((INT_MAX - offsetof(PATH, p)) / sizeof(Point)))
ereport(ERROR,
(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
errmsg("invalid number of points in external \"path\" value")));
size = offsetof(PATH, p) + sizeof(path->p[0]) * npts;
path = (PATH *) palloc(size);
SET_VARSIZE(path, size);
path->npts = npts;
path->closed = (closed ? 1 : 0);
/* prevent instability in unused pad bytes */
path->dummy = 0;
for (i = 0; i < npts; i++)
{
path->p[i].x = pq_getmsgfloat8(buf);
path->p[i].y = pq_getmsgfloat8(buf);
}
PG_RETURN_PATH_P(path);
}
/*
* path_send - converts path to binary format
*/
Datum
path_send(PG_FUNCTION_ARGS)
{
PATH *path = PG_GETARG_PATH_P(0);
StringInfoData buf;
int32 i;
pq_begintypsend(&buf);
pq_sendbyte(&buf, path->closed ? 1 : 0);
pq_sendint32(&buf, path->npts);
for (i = 0; i < path->npts; i++)
{
pq_sendfloat8(&buf, path->p[i].x);
pq_sendfloat8(&buf, path->p[i].y);
}
PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}
/*----------------------------------------------------------
* Relational operators.
* These are based on the path cardinality,
* as stupid as that sounds.
*
* Better relops and access methods coming soon.
*---------------------------------------------------------*/
Datum
path_n_lt(PG_FUNCTION_ARGS)
{
PATH *p1 = PG_GETARG_PATH_P(0);
PATH *p2 = PG_GETARG_PATH_P(1);
PG_RETURN_BOOL(p1->npts < p2->npts);
}
Datum
path_n_gt(PG_FUNCTION_ARGS)
{
PATH *p1 = PG_GETARG_PATH_P(0);
PATH *p2 = PG_GETARG_PATH_P(1);
PG_RETURN_BOOL(p1->npts > p2->npts);
}
Datum
path_n_eq(PG_FUNCTION_ARGS)
{
PATH *p1 = PG_GETARG_PATH_P(0);
PATH *p2 = PG_GETARG_PATH_P(1);
PG_RETURN_BOOL(p1->npts == p2->npts);
}
Datum
path_n_le(PG_FUNCTION_ARGS)
{
PATH *p1 = PG_GETARG_PATH_P(0);
PATH *p2 = PG_GETARG_PATH_P(1);
PG_RETURN_BOOL(p1->npts <= p2->npts);
}
Datum
path_n_ge(PG_FUNCTION_ARGS)
{
PATH *p1 = PG_GETARG_PATH_P(0);
PATH *p2 = PG_GETARG_PATH_P(1);
PG_RETURN_BOOL(p1->npts >= p2->npts);
}
/*----------------------------------------------------------
* Conversion operators.
*---------------------------------------------------------*/
Datum
path_isclosed(PG_FUNCTION_ARGS)
{
PATH *path = PG_GETARG_PATH_P(0);
PG_RETURN_BOOL(path->closed);
}
Datum
path_isopen(PG_FUNCTION_ARGS)
{
PATH *path = PG_GETARG_PATH_P(0);
PG_RETURN_BOOL(!path->closed);
}
Datum
path_npoints(PG_FUNCTION_ARGS)
{
PATH *path = PG_GETARG_PATH_P(0);
PG_RETURN_INT32(path->npts);
}
Datum
path_close(PG_FUNCTION_ARGS)
{
PATH *path = PG_GETARG_PATH_P_COPY(0);
path->closed = true;
PG_RETURN_PATH_P(path);
}
Datum
path_open(PG_FUNCTION_ARGS)
{
PATH *path = PG_GETARG_PATH_P_COPY(0);
path->closed = false;
PG_RETURN_PATH_P(path);
}
/* path_inter -
* Does p1 intersect p2 at any point?
* Use bounding boxes for a quick (O(n)) check, then do a
* O(n^2) iterative edge check.
*/
Datum
path_inter(PG_FUNCTION_ARGS)
{
PATH *p1 = PG_GETARG_PATH_P(0);
PATH *p2 = PG_GETARG_PATH_P(1);
BOX b1,
b2;
int i,
j;
LSEG seg1,
seg2;
Assert(p1->npts > 0 && p2->npts > 0);
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 = float8_max(p1->p[i].x, b1.high.x);
b1.high.y = float8_max(p1->p[i].y, b1.high.y);
b1.low.x = float8_min(p1->p[i].x, b1.low.x);
b1.low.y = float8_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 = float8_max(p2->p[i].x, b2.high.x);
b2.high.y = float8_max(p2->p[i].y, b2.high.y);
b2.low.x = float8_min(p2->p[i].x, b2.low.x);
b2.low.y = float8_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_interpt_lseg(NULL, &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 = lseg_closept_lseg(NULL, &seg1, &seg2);
if (!have_min || float8_lt(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 = float8_pl(result, point_dt(&path->p[iprev], &path->p[i]));
}
PG_RETURN_FLOAT8(result);
}
/***********************************************************************
**
** Routines for 2D points.
**
***********************************************************************/
/*----------------------------------------------------------
* String to point, point to string conversion.
* External format:
* "(x,y)"
* "x,y"
*---------------------------------------------------------*/
Datum
point_in(PG_FUNCTION_ARGS)
{
char *str = PG_GETARG_CSTRING(0);
Point *point = (Point *) palloc(sizeof(Point));
pair_decode(str, &point->x, &point->y, NULL, "point", str);
PG_RETURN_POINT_P(point);
}
Datum
point_out(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
PG_RETURN_CSTRING(path_encode(PATH_NONE, 1, pt));
}
/*
* point_recv - converts external binary format to point
*/
Datum
point_recv(PG_FUNCTION_ARGS)
{
StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
Point *point;
point = (Point *) palloc(sizeof(Point));
point->x = pq_getmsgfloat8(buf);
point->y = pq_getmsgfloat8(buf);
PG_RETURN_POINT_P(point);
}
/*
* point_send - converts point to binary format
*/
Datum
point_send(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
StringInfoData buf;
pq_begintypsend(&buf);
pq_sendfloat8(&buf, pt->x);
pq_sendfloat8(&buf, pt->y);
PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}
/*
* Initialize a point
*/
static inline void
point_construct(Point *result, float8 x, float8 y)
{
result->x = x;
result->y = y;
}
/*----------------------------------------------------------
* 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(point_eq_point(pt1, pt2));
}
Datum
point_ne(PG_FUNCTION_ARGS)
{
Point *pt1 = PG_GETARG_POINT_P(0);
Point *pt2 = PG_GETARG_POINT_P(1);
PG_RETURN_BOOL(!point_eq_point(pt1, pt2));
}
/*
* Check whether the two points are the same
*
* We consider NaNs coordinates to be equal to each other to let those points
* to be found.
*/
static inline bool
point_eq_point(Point *pt1, Point *pt2)
{
return ((FPeq(pt1->x, pt2->x) && FPeq(pt1->y, pt2->y)) ||
(float8_eq(pt1->x, pt2->x) && float8_eq(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(point_dt(pt1, pt2));
}
static inline float8
point_dt(Point *pt1, Point *pt2)
{
return HYPOT(float8_mi(pt1->x, pt2->x), float8_mi(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));
}
/*
* Return slope of two points
*
* Note that this function returns DBL_MAX when the points are the same.
*/
static inline float8
point_sl(Point *pt1, Point *pt2)
{
if (FPeq(pt1->x, pt2->x))
return DBL_MAX;
if (FPeq(pt1->y, pt2->y))
return 0.0;
return float8_div(float8_mi(pt1->y, pt2->y), float8_mi(pt1->x, pt2->x));
}
/*
* Return inverse slope of two points
*
* Note that this function returns 0.0 when the points are the same.
*/
static inline float8
point_invsl(Point *pt1, Point *pt2)
{
if (FPeq(pt1->x, pt2->x))
return 0.0;
if (FPeq(pt1->y, pt2->y))
return DBL_MAX;
return float8_div(float8_mi(pt1->x, pt2->x), float8_mi(pt2->y, pt1->y));
}
/***********************************************************************
**
** Routines for 2D line segments.
**
***********************************************************************/
/*----------------------------------------------------------
* String to lseg, lseg to string conversion.
* External forms: "[(x1, y1), (x2, y2)]"
* "(x1, y1), (x2, y2)"
* "x1, y1, x2, y2"
* closed form ok "((x1, y1), (x2, y2))"
* (old form) "(x1, y1, x2, y2)"
*---------------------------------------------------------*/
Datum
lseg_in(PG_FUNCTION_ARGS)
{
char *str = PG_GETARG_CSTRING(0);
LSEG *lseg = (LSEG *) palloc(sizeof(LSEG));
bool isopen;
path_decode(str, true, 2, &lseg->p[0], &isopen, NULL, "lseg", str);
PG_RETURN_LSEG_P(lseg);
}
Datum
lseg_out(PG_FUNCTION_ARGS)
{
LSEG *ls = PG_GETARG_LSEG_P(0);
PG_RETURN_CSTRING(path_encode(PATH_OPEN, 2, &ls->p[0]));
}
/*
* lseg_recv - converts external binary format to lseg
*/
Datum
lseg_recv(PG_FUNCTION_ARGS)
{
StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
LSEG *lseg;
lseg = (LSEG *) palloc(sizeof(LSEG));
lseg->p[0].x = pq_getmsgfloat8(buf);
lseg->p[0].y = pq_getmsgfloat8(buf);
lseg->p[1].x = pq_getmsgfloat8(buf);
lseg->p[1].y = pq_getmsgfloat8(buf);
PG_RETURN_LSEG_P(lseg);
}
/*
* lseg_send - converts lseg to binary format
*/
Datum
lseg_send(PG_FUNCTION_ARGS)
{
LSEG *ls = PG_GETARG_LSEG_P(0);
StringInfoData buf;
pq_begintypsend(&buf);
pq_sendfloat8(&buf, ls->p[0].x);
pq_sendfloat8(&buf, ls->p[0].y);
pq_sendfloat8(&buf, ls->p[1].x);
pq_sendfloat8(&buf, ls->p[1].y);
PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}
/* lseg_construct -
* form a LSEG from two Points.
*/
Datum
lseg_construct(PG_FUNCTION_ARGS)
{
Point *pt1 = PG_GETARG_POINT_P(0);
Point *pt2 = PG_GETARG_POINT_P(1);
LSEG *result = (LSEG *) palloc(sizeof(LSEG));
statlseg_construct(result, pt1, pt2);
PG_RETURN_LSEG_P(result);
}
/* like lseg_construct, but assume space already allocated */
static inline 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;
}
/*
* Return slope of the line segment
*/
static inline float8
lseg_sl(LSEG *lseg)
{
return point_sl(&lseg->p[0], &lseg->p[1]);
}
/*
* Return inverse slope of the line segment
*/
static inline float8
lseg_invsl(LSEG *lseg)
{
return point_invsl(&lseg->p[0], &lseg->p[1]);
}
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_interpt_lseg(NULL, l1, l2));
}
Datum
lseg_parallel(PG_FUNCTION_ARGS)
{
LSEG *l1 = PG_GETARG_LSEG_P(0);
LSEG *l2 = PG_GETARG_LSEG_P(1);
PG_RETURN_BOOL(FPeq(lseg_sl(l1), lseg_sl(l2)));
}
/*
* Determine if two line segments are perpendicular.
*/
Datum
lseg_perp(PG_FUNCTION_ARGS)
{
LSEG *l1 = PG_GETARG_LSEG_P(0);
LSEG *l2 = PG_GETARG_LSEG_P(1);
PG_RETURN_BOOL(FPeq(lseg_sl(l1), lseg_invsl(l2)));
}
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(point_eq_point(&l1->p[0], &l2->p[0]) &&
point_eq_point(&l1->p[1], &l2->p[1]));
}
Datum
lseg_ne(PG_FUNCTION_ARGS)
{
LSEG *l1 = PG_GETARG_LSEG_P(0);
LSEG *l2 = PG_GETARG_LSEG_P(1);
PG_RETURN_BOOL(!point_eq_point(&l1->p[0], &l2->p[0]) ||
!point_eq_point(&l1->p[1], &l2->p[1]));
}
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_closept_lseg(NULL, l1, l2));
}
Datum
lseg_center(PG_FUNCTION_ARGS)
{
LSEG *lseg = PG_GETARG_LSEG_P(0);
Point *result;
result = (Point *) palloc(sizeof(Point));
result->x = float8_div(float8_pl(lseg->p[0].x, lseg->p[1].x), 2.0);
result->y = float8_div(float8_pl(lseg->p[0].y, lseg->p[1].y), 2.0);
PG_RETURN_POINT_P(result);
}
/*
* Return whether the two segments intersect. If *result is not NULL,
* it is set to the intersection point.
*
* This function is almost perfectly symmetric, even though it doesn't look
* like it. See lseg_interpt_line() for the other half of it.
*/
static bool
lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2)
{
Point interpt;
LINE tmp;
line_construct(&tmp, &l2->p[0], lseg_sl(l2));
if (!lseg_interpt_line(&interpt, l1, &tmp))
return false;
/*
* If the line intersection point isn't within l2, there is no valid
* segment intersection point at all.
*/
if (!lseg_contain_point(l2, &interpt))
return false;
if (result != NULL)
*result = interpt;
return true;
}
Datum
lseg_interpt(PG_FUNCTION_ARGS)
{
LSEG *l1 = PG_GETARG_LSEG_P(0);
LSEG *l2 = PG_GETARG_LSEG_P(1);
Point *result;
result = (Point *) palloc(sizeof(Point));
if (!lseg_interpt_lseg(result, l1, l2))
PG_RETURN_NULL();
PG_RETURN_POINT_P(result);
}
/***********************************************************************
**
** Routines for position comparisons of differently-typed
** 2D objects.
**
***********************************************************************/
/*---------------------------------------------------------------------
* dist_
* Minimum distance from one object to another.
*-------------------------------------------------------------------*/
/*
* Distance from a point to a line
*/
Datum
dist_pl(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
LINE *line = PG_GETARG_LINE_P(1);
PG_RETURN_FLOAT8(line_closept_point(NULL, line, pt));
}
/*
* Distance from a point to a lseg
*/
Datum
dist_ps(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
LSEG *lseg = PG_GETARG_LSEG_P(1);
PG_RETURN_FLOAT8(lseg_closept_point(NULL, lseg, pt));
}
/*
* 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;
Assert(path->npts > 0);
/*
* 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 = lseg_closept_point(NULL, &lseg, pt);
if (!have_min || float8_lt(tmp, result))
{
result = tmp;
have_min = true;
}
}
PG_RETURN_FLOAT8(result);
}
/*
* Distance from a point to a box
*/
Datum
dist_pb(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
BOX *box = PG_GETARG_BOX_P(1);
PG_RETURN_FLOAT8(box_closept_point(NULL, box, pt));
}
/*
* Distance from a lseg to a line
*/
Datum
dist_sl(PG_FUNCTION_ARGS)
{
LSEG *lseg = PG_GETARG_LSEG_P(0);
LINE *line = PG_GETARG_LINE_P(1);
PG_RETURN_FLOAT8(lseg_closept_line(NULL, lseg, line));
}
/*
* Distance from a lseg to a box
*/
Datum
dist_sb(PG_FUNCTION_ARGS)
{
LSEG *lseg = PG_GETARG_LSEG_P(0);
BOX *box = PG_GETARG_BOX_P(1);
PG_RETURN_FLOAT8(box_closept_lseg(NULL, box, lseg));
}
/*
* Distance from a line to a box
*/
Datum
dist_lb(PG_FUNCTION_ARGS)
{
#ifdef NOT_USED
LINE *line = PG_GETARG_LINE_P(0);
BOX *box = PG_GETARG_BOX_P(1);
#endif
/* need to think about this one for a while */
ereport(ERROR,
(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
errmsg("function \"dist_lb\" not implemented")));
PG_RETURN_NULL();
}
/*
* Distance from a circle to a polygon
*/
Datum
dist_cpoly(PG_FUNCTION_ARGS)
{
CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
POLYGON *poly = PG_GETARG_POLYGON_P(1);
float8 result;
/* calculate distance to center, and subtract radius */
result = float8_mi(dist_ppoly_internal(&circle->center, poly),
circle->radius);
if (result < 0.0)
result = 0.0;
PG_RETURN_FLOAT8(result);
}
/*
* Distance from a point to a polygon
*/
Datum
dist_ppoly(PG_FUNCTION_ARGS)
{
Point *point = PG_GETARG_POINT_P(0);
POLYGON *poly = PG_GETARG_POLYGON_P(1);
PG_RETURN_FLOAT8(dist_ppoly_internal(point, poly));
}
Datum
dist_polyp(PG_FUNCTION_ARGS)
{
POLYGON *poly = PG_GETARG_POLYGON_P(0);
Point *point = PG_GETARG_POINT_P(1);
PG_RETURN_FLOAT8(dist_ppoly_internal(point, poly));
}
static float8
dist_ppoly_internal(Point *pt, POLYGON *poly)
{
float8 result;
float8 d;
int i;
LSEG seg;
if (point_inside(pt, poly->npts, poly->p) != 0)
return 0.0;
/* initialize distance with segment between first and last points */
seg.p[0].x = poly->p[0].x;
seg.p[0].y = poly->p[0].y;
seg.p[1].x = poly->p[poly->npts - 1].x;
seg.p[1].y = poly->p[poly->npts - 1].y;
result = lseg_closept_point(NULL, &seg, pt);
/* 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 = lseg_closept_point(NULL, &seg, pt);
if (float8_lt(d, result))
result = d;
}
return result;
}
/*---------------------------------------------------------------------
* interpt_
* Intersection point of objects.
* We choose to ignore the "point" of intersection between
* lines and boxes, since there are typically two.
*-------------------------------------------------------------------*/
/*
* Return whether the line segment intersect with the line. If *result is not
* NULL, it is set to the intersection point.
*/
static bool
lseg_interpt_line(Point *result, LSEG *lseg, LINE *line)
{
Point interpt;
LINE tmp;
/*
* First, we promote the line segment to a line, because we know how to
* find the intersection point of two lines. If they don't have an
* intersection point, we are done.
*/
line_construct(&tmp, &lseg->p[0], lseg_sl(lseg));
if (!line_interpt_line(&interpt, &tmp, line))
return false;
/*
* Then, we check whether the intersection point is actually on the line
* segment.
*/
if (!lseg_contain_point(lseg, &interpt))
return false;
if (result != NULL)
{
/*
* If there is an intersection, then check explicitly for matching
* endpoints since there may be rounding effects with annoying LSB
* residue.
*/
if (point_eq_point(&lseg->p[0], &interpt))
*result = lseg->p[0];
else if (point_eq_point(&lseg->p[1], &interpt))
*result = lseg->p[1];
else
*result = interpt;
}
return true;
}
/*---------------------------------------------------------------------
* close_
* Point of closest proximity between objects.
*-------------------------------------------------------------------*/
/*
* If *result is not NULL, it is set to the intersection point of a
* perpendicular of the line through the point. Returns the distance
* of those two points.
*/
static float8
line_closept_point(Point *result, LINE *line, Point *point)
{
Point closept;
LINE tmp;
/*
* We drop a perpendicular to find the intersection point. Ordinarily we
* should always find it, but that can fail in the presence of NaN
* coordinates, and perhaps even from simple roundoff issues.
*/
line_construct(&tmp, point, line_invsl(line));
if (!line_interpt_line(&closept, &tmp, line))
{
if (result != NULL)
*result = *point;
return get_float8_nan();
}
if (result != NULL)
*result = closept;
return point_dt(&closept, point);
}
Datum
close_pl(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
LINE *line = PG_GETARG_LINE_P(1);
Point *result;
result = (Point *) palloc(sizeof(Point));
if (isnan(line_closept_point(result, line, pt)))
PG_RETURN_NULL();
PG_RETURN_POINT_P(result);
}
/*
* Closest point on line segment to specified point.
*
* If *result is not NULL, set it to the closest point on the line segment
* to the point. Returns the distance of the two points.
*/
static float8
lseg_closept_point(Point *result, LSEG *lseg, Point *pt)
{
Point closept;
LINE tmp;
/*
* To find the closest point, we draw a perpendicular line from the point
* to the line segment.
*/
line_construct(&tmp, pt, point_invsl(&lseg->p[0], &lseg->p[1]));
lseg_closept_line(&closept, lseg, &tmp);
if (result != NULL)
*result = closept;
return point_dt(&closept, pt);
}
Datum
close_ps(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
LSEG *lseg = PG_GETARG_LSEG_P(1);
Point *result;
result = (Point *) palloc(sizeof(Point));
if (isnan(lseg_closept_point(result, lseg, pt)))
PG_RETURN_NULL();
PG_RETURN_POINT_P(result);
}
/*
* Closest point on line segment to line segment
*/
static float8
lseg_closept_lseg(Point *result, LSEG *on_lseg, LSEG *to_lseg)
{
Point point;
float8 dist,
d;
/* First, we handle the case when the line segments are intersecting. */
if (lseg_interpt_lseg(result, on_lseg, to_lseg))
return 0.0;
/*
* Then, we find the closest points from the endpoints of the second line
* segment, and keep the closest one.
*/
dist = lseg_closept_point(result, on_lseg, &to_lseg->p[0]);
d = lseg_closept_point(&point, on_lseg, &to_lseg->p[1]);
if (float8_lt(d, dist))
{
dist = d;
if (result != NULL)
*result = point;
}
/* The closest point can still be one of the endpoints, so we test them. */
d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[0]);
if (float8_lt(d, dist))
{
dist = d;
if (result != NULL)
*result = on_lseg->p[0];
}
d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[1]);
if (float8_lt(d, dist))
{
dist = d;
if (result != NULL)
*result = on_lseg->p[1];
}
return dist;
}
Datum
close_lseg(PG_FUNCTION_ARGS)
{
LSEG *l1 = PG_GETARG_LSEG_P(0);
LSEG *l2 = PG_GETARG_LSEG_P(1);
Point *result;
if (lseg_sl(l1) == lseg_sl(l2))
PG_RETURN_NULL();
result = (Point *) palloc(sizeof(Point));
if (isnan(lseg_closept_lseg(result, l2, l1)))
PG_RETURN_NULL();
PG_RETURN_POINT_P(result);
}
/*
* Closest point on or in box to specified point.
*
* If *result is not NULL, set it to the closest point on the box to the
* given point, and return the distance of the two points.
*/
static float8
box_closept_point(Point *result, BOX *box, Point *pt)
{
float8 dist,
d;
Point point,
closept;
LSEG lseg;
if (box_contain_point(box, pt))
{
if (result != NULL)
*result = *pt;
return 0.0;
}
/* pairwise check lseg distances */
point.x = box->low.x;
point.y = box->high.y;
statlseg_construct(&lseg, &box->low, &point);
dist = lseg_closept_point(result, &lseg, pt);
statlseg_construct(&lseg, &box->high, &point);
d = lseg_closept_point(&closept, &lseg, pt);
if (float8_lt(d, dist))
{
dist = d;
if (result != NULL)
*result = closept;
}
point.x = box->high.x;
point.y = box->low.y;
statlseg_construct(&lseg, &box->low, &point);
d = lseg_closept_point(&closept, &lseg, pt);
if (float8_lt(d, dist))
{
dist = d;
if (result != NULL)
*result = closept;
}
statlseg_construct(&lseg, &box->high, &point);
d = lseg_closept_point(&closept, &lseg, pt);
if (float8_lt(d, dist))
{
dist = d;
if (result != NULL)
*result = closept;
}
return dist;
}
Datum
close_pb(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
BOX *box = PG_GETARG_BOX_P(1);
Point *result;
result = (Point *) palloc(sizeof(Point));
if (isnan(box_closept_point(result, box, pt)))
PG_RETURN_NULL();
PG_RETURN_POINT_P(result);
}
/* close_sl()
* Closest point on line to line segment.
*
* XXX THIS CODE IS WRONG
* The code is actually calculating the point on the line segment
* which is backwards from the routine naming convention.
* Copied code to new routine close_ls() but haven't fixed this one yet.
* - thomas 1998-01-31
*/
Datum
close_sl(PG_FUNCTION_ARGS)
{
#ifdef NOT_USED
LSEG *lseg = PG_GETARG_LSEG_P(0);
LINE *line = PG_GETARG_LINE_P(1);
Point *result;
float8 d1,
d2;
result = (Point *) palloc(sizeof(Point));
if (lseg_interpt_line(result, lseg, line))
PG_RETURN_POINT_P(result);
d1 = line_closept_point(NULL, line, &lseg->p[0]);
d2 = line_closept_point(NULL, line, &lseg->p[1]);
if (float8_lt(d1, d2))
*result = lseg->p[0];
else
*result = lseg->p[1];
PG_RETURN_POINT_P(result);
#endif
ereport(ERROR,
(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
errmsg("function \"close_sl\" not implemented")));
PG_RETURN_NULL();
}
/*
* Closest point on line segment to line.
*
* Return the distance between the line and the closest point of the line
* segment to the line. If *result is not NULL, set it to that point.
*
* NOTE: When the lines are parallel, endpoints of one of the line segment
* are FPeq(), in presence of NaN or Infinite coordinates, or perhaps =
* even because of simple roundoff issues, there may not be a single closest
* point. We are likely to set the result to the second endpoint in these
* cases.
*/
static float8
lseg_closept_line(Point *result, LSEG *lseg, LINE *line)
{
float8 dist1,
dist2;
if (lseg_interpt_line(result, lseg, line))
return 0.0;
dist1 = line_closept_point(NULL, line, &lseg->p[0]);
dist2 = line_closept_point(NULL, line, &lseg->p[1]);
if (dist1 < dist2)
{
if (result != NULL)
*result = lseg->p[0];
return dist1;
}
else
{
if (result != NULL)
*result = lseg->p[1];
return dist2;
}
}
Datum
close_ls(PG_FUNCTION_ARGS)
{
LINE *line = PG_GETARG_LINE_P(0);
LSEG *lseg = PG_GETARG_LSEG_P(1);
Point *result;
if (lseg_sl(lseg) == line_sl(line))
PG_RETURN_NULL();
result = (Point *) palloc(sizeof(Point));
if (isnan(lseg_closept_line(result, lseg, line)))
PG_RETURN_NULL();
PG_RETURN_POINT_P(result);
}
/*
* Closest point on or in box to line segment.
*
* Returns the distance between the closest point on or in the box to
* the line segment. If *result is not NULL, it is set to that point.
*/
static float8
box_closept_lseg(Point *result, BOX *box, LSEG *lseg)
{
float8 dist,
d;
Point point,
closept;
LSEG bseg;
if (box_interpt_lseg(result, box, lseg))
return 0.0;
/* pairwise check lseg distances */
point.x = box->low.x;
point.y = box->high.y;
statlseg_construct(&bseg, &box->low, &point);
dist = lseg_closept_lseg(result, &bseg, lseg);
statlseg_construct(&bseg, &box->high, &point);
d = lseg_closept_lseg(&closept, &bseg, lseg);
if (float8_lt(d, dist))
{
dist = d;
if (result != NULL)
*result = closept;
}
point.x = box->high.x;
point.y = box->low.y;
statlseg_construct(&bseg, &box->low, &point);
d = lseg_closept_lseg(&closept, &bseg, lseg);
if (float8_lt(d, dist))
{
dist = d;
if (result != NULL)
*result = closept;
}
statlseg_construct(&bseg, &box->high, &point);
d = lseg_closept_lseg(&closept, &bseg, lseg);
if (float8_lt(d, dist))
{
dist = d;
if (result != NULL)
*result = closept;
}
return dist;
}
Datum
close_sb(PG_FUNCTION_ARGS)
{
LSEG *lseg = PG_GETARG_LSEG_P(0);
BOX *box = PG_GETARG_BOX_P(1);
Point *result;
result = (Point *) palloc(sizeof(Point));
if (isnan(box_closept_lseg(result, box, lseg)))
PG_RETURN_NULL();
PG_RETURN_POINT_P(result);
}
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.
*-------------------------------------------------------------------*/
/*
* Does the point satisfy the equation?
*/
static bool
line_contain_point(LINE *line, Point *point)
{
return FPzero(float8_pl(float8_pl(float8_mul(line->A, point->x),
float8_mul(line->B, point->y)),
line->C));
}
Datum
on_pl(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
LINE *line = PG_GETARG_LINE_P(1);
PG_RETURN_BOOL(line_contain_point(line, pt));
}
/*
* Determine colinearity by detecting a triangle inequality.
* This algorithm seems to behave nicely even with lsb residues - tgl 1997-07-09
*/
static bool
lseg_contain_point(LSEG *lseg, Point *pt)
{
return FPeq(point_dt(pt, &lseg->p[0]) +
point_dt(pt, &lseg->p[1]),
point_dt(&lseg->p[0], &lseg->p[1]));
}
Datum
on_ps(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
LSEG *lseg = PG_GETARG_LSEG_P(1);
PG_RETURN_BOOL(lseg_contain_point(lseg, pt));
}
/*
* Check whether the point is in the box or on its border
*/
static bool
box_contain_point(BOX *box, Point *point)
{
return box->high.x >= point->x && box->low.x <= point->x &&
box->high.y >= point->y && box->low.y <= point->y;
}
Datum
on_pb(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
BOX *box = PG_GETARG_BOX_P(1);
PG_RETURN_BOOL(box_contain_point(box, pt));
}
Datum
box_contain_pt(PG_FUNCTION_ARGS)
{
BOX *box = PG_GETARG_BOX_P(0);
Point *pt = PG_GETARG_POINT_P(1);
PG_RETURN_BOOL(box_contain_point(box, pt));
}
/* 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;
float8 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(float8_pl(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);
}
/*
* Check whether the line segment is on the line or close enough
*
* It is, if both of its points are on the line or close enough.
*/
Datum
on_sl(PG_FUNCTION_ARGS)
{
LSEG *lseg = PG_GETARG_LSEG_P(0);
LINE *line = PG_GETARG_LINE_P(1);
PG_RETURN_BOOL(line_contain_point(line, &lseg->p[0]) &&
line_contain_point(line, &lseg->p[1]));
}
/*
* Check whether the line segment is in the box or on its border
*
* It is, if both of its points are in the box or on its border.
*/
static bool
box_contain_lseg(BOX *box, LSEG *lseg)
{
return box_contain_point(box, &lseg->p[0]) &&
box_contain_point(box, &lseg->p[1]);
}
Datum
on_sb(PG_FUNCTION_ARGS)
{
LSEG *lseg = PG_GETARG_LSEG_P(0);
BOX *box = PG_GETARG_BOX_P(1);
PG_RETURN_BOOL(box_contain_lseg(box, lseg));
}
/*---------------------------------------------------------------------
* 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(lseg_interpt_line(NULL, lseg, line));
}
/*
* 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.
*
* This function also sets the *result to the closest point on the line
* segment to the center of the box when they overlap and the result is
* not NULL. It is somewhat arbitrary, but maybe the best we can do as
* there are typically two points they intersect.
*
* Optimize for non-intersection by checking for box intersection first.
* - thomas 1998-01-30
*/
static bool
box_interpt_lseg(Point *result, BOX *box, LSEG *lseg)
{
BOX lbox;
LSEG bseg;
Point point;
lbox.low.x = float8_min(lseg->p[0].x, lseg->p[1].x);
lbox.low.y = float8_min(lseg->p[0].y, lseg->p[1].y);
lbox.high.x = float8_max(lseg->p[0].x, lseg->p[1].x);
lbox.high.y = float8_max(lseg->p[0].y, lseg->p[1].y);
/* nothing close to overlap? then not going to intersect */
if (!box_ov(&lbox, box))
return false;
if (result != NULL)
{
box_cn(&point, box);
lseg_closept_point(result, lseg, &point);
}
/* an endpoint of segment is inside box? then clearly intersects */
if (box_contain_point(box, &lseg->p[0]) ||
box_contain_point(box, &lseg->p[1]))
return true;
/* pairwise check lseg intersections */
point.x = box->low.x;
point.y = box->high.y;
statlseg_construct(&bseg, &box->low, &point);
if (lseg_interpt_lseg(NULL, &bseg, lseg))
return true;
statlseg_construct(&bseg, &box->high, &point);
if (lseg_interpt_lseg(NULL, &bseg, lseg))
return true;
point.x = box->high.x;
point.y = box->low.y;
statlseg_construct(&bseg, &box->low, &point);
if (lseg_interpt_lseg(NULL, &bseg, lseg))
return true;
statlseg_construct(&bseg, &box->high, &point);
if (lseg_interpt_lseg(NULL, &bseg, lseg))
return true;
/* if we dropped through, no two segs intersected */
return false;
}
Datum
inter_sb(PG_FUNCTION_ARGS)
{
LSEG *lseg = PG_GETARG_LSEG_P(0);
BOX *box = PG_GETARG_BOX_P(1);
PG_RETURN_BOOL(box_interpt_lseg(NULL, box, lseg));
}
/* 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 (lseg_interpt_line(NULL, &bseg, line))
PG_RETURN_BOOL(true);
p1.x = box->high.x;
p1.y = box->high.y;
statlseg_construct(&bseg, &p1, &p2);
if (lseg_interpt_line(NULL, &bseg, line))
PG_RETURN_BOOL(true);
p2.x = box->high.x;
p2.y = box->low.y;
statlseg_construct(&bseg, &p1, &p2);
if (lseg_interpt_line(NULL, &bseg, line))
PG_RETURN_BOOL(true);
p1.x = box->low.x;
p1.y = box->low.y;
statlseg_construct(&bseg, &p1, &p2);
if (lseg_interpt_line(NULL, &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;
float8 x1,
y1,
x2,
y2;
Assert(poly->npts > 0);
x1 = x2 = poly->p[0].x;
y2 = y1 = poly->p[0].y;
for (i = 1; i < poly->npts; i++)
{
if (float8_lt(poly->p[i].x, x1))
x1 = poly->p[i].x;
if (float8_gt(poly->p[i].x, x2))
x2 = poly->p[i].x;
if (float8_lt(poly->p[i].y, y1))
y1 = poly->p[i].y;
if (float8_gt(poly->p[i].y, y2))
y2 = poly->p[i].y;
}
poly->boundbox.low.x = x1;
poly->boundbox.high.x = x2;
poly->boundbox.low.y = y1;
poly->boundbox.high.y = y2;
}
/*------------------------------------------------------------------
* poly_in - read in the polygon from a string specification
*
* External format:
* "((x0,y0),...,(xn,yn))"
* "x0,y0,...,xn,yn"
* also supports the older style "(x1,...,xn,y1,...yn)"
*------------------------------------------------------------------*/
Datum
poly_in(PG_FUNCTION_ARGS)
{
char *str = PG_GETARG_CSTRING(0);
POLYGON *poly;
int npts;
int size;
int base_size;
bool isopen;
if ((npts = pair_count(str, ',')) <= 0)
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
"polygon", str)));
base_size = sizeof(poly->p[0]) * npts;
size = offsetof(POLYGON, p) + base_size;
/* Check for integer overflow */
if (base_size / npts != sizeof(poly->p[0]) || size <= base_size)
ereport(ERROR,
(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
errmsg("too many points requested")));
poly = (POLYGON *) palloc0(size); /* zero any holes */
SET_VARSIZE(poly, size);
poly->npts = npts;
path_decode(str, false, npts, &(poly->p[0]), &isopen, NULL, "polygon", str);
make_bound_box(poly);
PG_RETURN_POLYGON_P(poly);
}
/*---------------------------------------------------------------
* poly_out - convert internal POLYGON representation to the
* character string format "((f8,f8),...,(f8,f8))"
*---------------------------------------------------------------*/
Datum
poly_out(PG_FUNCTION_ARGS)
{
POLYGON *poly = PG_GETARG_POLYGON_P(0);
PG_RETURN_CSTRING(path_encode(PATH_CLOSED, poly->npts, poly->p));
}
/*
* poly_recv - converts external binary format to polygon
*
* External representation is int32 number of points, and the points.
* We recompute the bounding box on read, instead of trusting it to
* be valid. (Checking it would take just as long, so may as well
* omit it from external representation.)
*/
Datum
poly_recv(PG_FUNCTION_ARGS)
{
StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
POLYGON *poly;
int32 npts;
int32 i;
int size;
npts = pq_getmsgint(buf, sizeof(int32));
if (npts <= 0 || npts >= (int32) ((INT_MAX - offsetof(POLYGON, p)) / sizeof(Point)))
ereport(ERROR,
(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
errmsg("invalid number of points in external \"polygon\" value")));
size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * npts;
poly = (POLYGON *) palloc0(size); /* zero any holes */
SET_VARSIZE(poly, size);
poly->npts = npts;
for (i = 0; i < npts; i++)
{
poly->p[i].x = pq_getmsgfloat8(buf);
poly->p[i].y = pq_getmsgfloat8(buf);
}
make_bound_box(poly);
PG_RETURN_POLYGON_P(poly);
}
/*
* poly_send - converts polygon to binary format
*/
Datum
poly_send(PG_FUNCTION_ARGS)
{
POLYGON *poly = PG_GETARG_POLYGON_P(0);
StringInfoData buf;
int32 i;
pq_begintypsend(&buf);
pq_sendint32(&buf, poly->npts);
for (i = 0; i < poly->npts; i++)
{
pq_sendfloat8(&buf, poly->p[i].x);
pq_sendfloat8(&buf, poly->p[i].y);
}
PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}
/*-------------------------------------------------------
* Is polygon A strictly left of polygon B? i.e. is
* the right most point of A left of the left most point
* of B?
*-------------------------------------------------------*/
Datum
poly_left(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
result = polya->boundbox.high.x < polyb->boundbox.low.x;
/*
* Avoid leaking memory for toasted inputs ... needed for rtree indexes
*/
PG_FREE_IF_COPY(polya, 0);
PG_FREE_IF_COPY(polyb, 1);
PG_RETURN_BOOL(result);
}
/*-------------------------------------------------------
* Is polygon A overlapping or left of polygon B? i.e. is
* the right most point of A at or left of the right most point
* of B?
*-------------------------------------------------------*/
Datum
poly_overleft(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
result = polya->boundbox.high.x <= polyb->boundbox.high.x;
/*
* Avoid leaking memory for toasted inputs ... needed for rtree indexes
*/
PG_FREE_IF_COPY(polya, 0);
PG_FREE_IF_COPY(polyb, 1);
PG_RETURN_BOOL(result);
}
/*-------------------------------------------------------
* Is polygon A strictly right of polygon B? i.e. is
* the left most point of A right of the right most point
* of B?
*-------------------------------------------------------*/
Datum
poly_right(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
result = polya->boundbox.low.x > polyb->boundbox.high.x;
/*
* Avoid leaking memory for toasted inputs ... needed for rtree indexes
*/
PG_FREE_IF_COPY(polya, 0);
PG_FREE_IF_COPY(polyb, 1);
PG_RETURN_BOOL(result);
}
/*-------------------------------------------------------
* Is polygon A overlapping or right of polygon B? i.e. is
* the left most point of A at or right of the left most point
* of B?
*-------------------------------------------------------*/
Datum
poly_overright(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
result = polya->boundbox.low.x >= polyb->boundbox.low.x;
/*
* Avoid leaking memory for toasted inputs ... needed for rtree indexes
*/
PG_FREE_IF_COPY(polya, 0);
PG_FREE_IF_COPY(polyb, 1);
PG_RETURN_BOOL(result);
}
/*-------------------------------------------------------
* Is polygon A strictly below polygon B? i.e. is
* the upper most point of A below the lower most point
* of B?
*-------------------------------------------------------*/
Datum
poly_below(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
result = polya->boundbox.high.y < polyb->boundbox.low.y;
/*
* Avoid leaking memory for toasted inputs ... needed for rtree indexes
*/
PG_FREE_IF_COPY(polya, 0);
PG_FREE_IF_COPY(polyb, 1);
PG_RETURN_BOOL(result);
}
/*-------------------------------------------------------
* Is polygon A overlapping or below polygon B? i.e. is
* the upper most point of A at or below the upper most point
* of B?
*-------------------------------------------------------*/
Datum
poly_overbelow(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
result = polya->boundbox.high.y <= polyb->boundbox.high.y;
/*
* Avoid leaking memory for toasted inputs ... needed for rtree indexes
*/
PG_FREE_IF_COPY(polya, 0);
PG_FREE_IF_COPY(polyb, 1);
PG_RETURN_BOOL(result);
}
/*-------------------------------------------------------
* Is polygon A strictly above polygon B? i.e. is
* the lower most point of A above the upper most point
* of B?
*-------------------------------------------------------*/
Datum
poly_above(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
result = polya->boundbox.low.y > polyb->boundbox.high.y;
/*
* Avoid leaking memory for toasted inputs ... needed for rtree indexes
*/
PG_FREE_IF_COPY(polya, 0);
PG_FREE_IF_COPY(polyb, 1);
PG_RETURN_BOOL(result);
}
/*-------------------------------------------------------
* Is polygon A overlapping or above polygon B? i.e. is
* the lower most point of A at or above the lower most point
* of B?
*-------------------------------------------------------*/
Datum
poly_overabove(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
result = polya->boundbox.low.y >= polyb->boundbox.low.y;
/*
* Avoid leaking memory for toasted inputs ... needed for rtree indexes
*/
PG_FREE_IF_COPY(polya, 0);
PG_FREE_IF_COPY(polyb, 1);
PG_RETURN_BOOL(result);
}
/*-------------------------------------------------------
* Is polygon A the same as polygon B? i.e. are all the
* points the same?
* Check all points for matches in both forward and reverse
* direction since polygons are non-directional and are
* closed shapes.
*-------------------------------------------------------*/
Datum
poly_same(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
if (polya->npts != polyb->npts)
result = false;
else
result = plist_same(polya->npts, polya->p, polyb->p);
/*
* Avoid leaking memory for toasted inputs ... needed for rtree indexes
*/
PG_FREE_IF_COPY(polya, 0);
PG_FREE_IF_COPY(polyb, 1);
PG_RETURN_BOOL(result);
}
/*-----------------------------------------------------------------
* Determine if polygon A overlaps polygon B
*-----------------------------------------------------------------*/
Datum
poly_overlap(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
Assert(polya->npts > 0 && polyb->npts > 0);
/* Quick check by bounding box */
result = box_ov(&polya->boundbox, &polyb->boundbox);
/*
* 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; 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; ib++)
{
sb.p[1] = polyb->p[ib];
result = lseg_interpt_lseg(NULL, &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)
{
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;
if (point_eq_point(a, s->p))
{
if (lseg_contain_point(&t, s->p + 1))
return lseg_inside_poly(b, s->p + 1, poly, start);
}
else if (point_eq_point(a, s->p + 1))
{
if (lseg_contain_point(&t, s->p))
return lseg_inside_poly(b, s->p, poly, start);
}
else if (lseg_contain_point(&t, s->p))
{
return lseg_inside_poly(b, s->p, poly, start);
}
else if (lseg_contain_point(&t, s->p + 1))
{
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 starting 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;
CHECK_FOR_INTERRUPTS();
s.p[1] = poly->p[i];
if (lseg_contain_point(&s, t.p))
{
if (lseg_contain_point(&s, t.p + 1))
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 (lseg_contain_point(&s, t.p + 1))
{
/* Y-cross */
res = touched_lseg_inside_poly(t.p + 1, t.p, &s, poly, i + 1);
}
else if (lseg_interpt_lseg(&interpt, &t, &s))
{
/*
* 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);
}
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 = float8_div(float8_pl(t.p[0].x, t.p[1].x), 2.0);
p.y = float8_div(float8_pl(t.p[0].y, t.p[1].y), 2.0);
res = point_inside(&p, poly->npts, poly->p);
}
return res;
}
/*
* Check whether the first polygon contains the second
*/
static bool
poly_contain_poly(POLYGON *contains_poly, POLYGON *contained_poly)
{
int i;
LSEG s;
Assert(contains_poly->npts > 0 && contained_poly->npts > 0);
/*
* Quick check to see if contained's bounding box is contained in
* contains' bb.
*/
if (!box_contain_box(&contains_poly->boundbox, &contained_poly->boundbox))
return false;
s.p[0] = contained_poly->p[contained_poly->npts - 1];
for (i = 0; i < contained_poly->npts; i++)
{
s.p[1] = contained_poly->p[i];
if (!lseg_inside_poly(s.p, s.p + 1, contains_poly, 0))
return false;
s.p[0] = s.p[1];
}
return true;
}
Datum
poly_contain(PG_FUNCTION_ARGS)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
result = poly_contain_poly(polya, polyb);
/*
* 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)
{
POLYGON *polya = PG_GETARG_POLYGON_P(0);
POLYGON *polyb = PG_GETARG_POLYGON_P(1);
bool result;
/* Just switch the arguments and pass it off to poly_contain */
result = poly_contain_poly(polyb, polya);
/*
* 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);
}
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);
Point *result;
result = (Point *) palloc(sizeof(Point));
point_construct(result, x, y);
PG_RETURN_POINT_P(result);
}
static inline void
point_add_point(Point *result, Point *pt1, Point *pt2)
{
point_construct(result,
float8_pl(pt1->x, pt2->x),
float8_pl(pt1->y, pt2->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));
point_add_point(result, p1, p2);
PG_RETURN_POINT_P(result);
}
static inline void
point_sub_point(Point *result, Point *pt1, Point *pt2)
{
point_construct(result,
float8_mi(pt1->x, pt2->x),
float8_mi(pt1->y, pt2->y));
}
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));
point_sub_point(result, p1, p2);
PG_RETURN_POINT_P(result);
}
static inline void
point_mul_point(Point *result, Point *pt1, Point *pt2)
{
point_construct(result,
float8_mi(float8_mul(pt1->x, pt2->x),
float8_mul(pt1->y, pt2->y)),
float8_pl(float8_mul(pt1->x, pt2->y),
float8_mul(pt1->y, pt2->x)));
}
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));
point_mul_point(result, p1, p2);
PG_RETURN_POINT_P(result);
}
static inline void
point_div_point(Point *result, Point *pt1, Point *pt2)
{
float8 div;
div = float8_pl(float8_mul(pt2->x, pt2->x), float8_mul(pt2->y, pt2->y));
point_construct(result,
float8_div(float8_pl(float8_mul(pt1->x, pt2->x),
float8_mul(pt1->y, pt2->y)), div),
float8_div(float8_mi(float8_mul(pt1->y, pt2->x),
float8_mul(pt1->x, pt2->y)), div));
}
Datum
point_div(PG_FUNCTION_ARGS)
{
Point *p1 = PG_GETARG_POINT_P(0);
Point *p2 = PG_GETARG_POINT_P(1);
Point *result;
result = (Point *) palloc(sizeof(Point));
point_div_point(result, p1, p2);
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);
BOX *result;
result = (BOX *) palloc(sizeof(BOX));
box_construct(result, p1, p2);
PG_RETURN_BOX_P(result);
}
Datum
box_add(PG_FUNCTION_ARGS)
{
BOX *box = PG_GETARG_BOX_P(0);
Point *p = PG_GETARG_POINT_P(1);
BOX *result;
result = (BOX *) palloc(sizeof(BOX));
point_add_point(&result->high, &box->high, p);
point_add_point(&result->low, &box->low, p);
PG_RETURN_BOX_P(result);
}
Datum
box_sub(PG_FUNCTION_ARGS)
{
BOX *box = PG_GETARG_BOX_P(0);
Point *p = PG_GETARG_POINT_P(1);
BOX *result;
result = (BOX *) palloc(sizeof(BOX));
point_sub_point(&result->high, &box->high, p);
point_sub_point(&result->low, &box->low, p);
PG_RETURN_BOX_P(result);
}
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;
result = (BOX *) palloc(sizeof(BOX));
point_mul_point(&high, &box->high, p);
point_mul_point(&low, &box->low, p);
box_construct(result, &high, &low);
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;
result = (BOX *) palloc(sizeof(BOX));
point_div_point(&high, &box->high, p);
point_div_point(&low, &box->low, p);
box_construct(result, &high, &low);
PG_RETURN_BOX_P(result);
}
/*
* Convert point to empty box
*/
Datum
point_box(PG_FUNCTION_ARGS)
{
Point *pt = PG_GETARG_POINT_P(0);
BOX *box;
box = (BOX *) palloc(sizeof(BOX));
box->high.x = pt->x;
box->low.x = pt->x;
box->high.y = pt->y;
box->low.y = pt->y;
PG_RETURN_BOX_P(box);
}
/*
* Smallest bounding box that includes both of the given boxes
*/
Datum
boxes_bound_box(PG_FUNCTION_ARGS)
{
BOX *box1 = PG_GETARG_BOX_P(0),
*box2 = PG_GETARG_BOX_P(1),
*container;
container = (BOX *) palloc(sizeof(BOX));
container->high.x = float8_max(box1->high.x, box2->high.x);
container->low.x = float8_min(box1->low.x, box2->low.x);
container->high.y = float8_max(box1->high.y, box2->high.y);
container->low.y = float8_min(box1->low.y, box2->low.y);
PG_RETURN_BOX_P(container);
}
/***********************************************************************
**
** Routines for 2D paths.
**
***********************************************************************/
/* path_add()
* Concatenate two paths (only if they are both open).
*/
Datum
path_add(PG_FUNCTION_ARGS)
{
PATH *p1 = PG_GETARG_PATH_P(0);
PATH *p2 = PG_GETARG_PATH_P(1);
PATH *result;
int size,
base_size;
int i;
if (p1->closed || p2->closed)
PG_RETURN_NULL();
base_size = sizeof(p1->p[0]) * (p1->npts + p2->npts);
size = offsetof(PATH, p) + base_size;
/* Check for integer overflow */
if (base_size / sizeof(p1->p[0]) != (p1->npts + p2->npts) ||
size <= base_size)
ereport(ERROR,
(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
errmsg("too many points requested")));
result = (PATH *) palloc(size);
SET_VARSIZE(result, size);
result->npts = (p1->npts + p2->npts);
result->closed = p1->closed;
/* prevent instability in unused pad bytes */
result->dummy = 0;
for (i = 0; i < p1->npts; i++)
{
result->p[i].x = p1->p[i].x;
result->p[i].y = p1->p[i].y;
}
for (i = 0; i < p2->npts; i++)
{
result->p[i + p1->npts].x = p2->p[i].x;
result->p[i + p1->npts].y = p2->p[i].y;
}
PG_RETURN_PATH_P(result);
}
/* path_add_pt()
* Translation operators.
*/
Datum
path_add_pt(PG_FUNCTION_ARGS)
{
PATH *path = PG_GETARG_PATH_P_COPY(0);
Point *point = PG_GETARG_POINT_P(1);
int i;
for (i = 0; i < path->npts; i++)
point_add_point(&path->p[i], &path->p[i], point);
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++)
point_sub_point(&path->p[i], &path->p[i], point);
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);
int i;
for (i = 0; i < path->npts; i++)
point_mul_point(&path->p[i], &path->p[i], point);
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);
int i;
for (i = 0; i < path->npts; i++)
point_div_point(&path->p[i], &path->p[i], point);
PG_RETURN_PATH_P(path);
}
Datum
path_center(PG_FUNCTION_ARGS)
{
#ifdef NOT_USED
PATH *path = PG_GETARG_PATH_P(0);
#endif
ereport(ERROR,
(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
errmsg("function \"path_center\" not implemented")));
PG_RETURN_NULL();
}
Datum
path_poly(PG_FUNCTION_ARGS)
{
PATH *path = PG_GETARG_PATH_P(0);
POLYGON *poly;
int size;
int i;
/* This is not very consistent --- other similar cases return NULL ... */
if (!path->closed)
ereport(ERROR,
(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
errmsg("open path cannot be converted to polygon")));
/*
* Never overflows: the old size fit in MaxAllocSize, and the new size is
* just a small constant larger.
*/
size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * path->npts;
poly = (POLYGON *) palloc(size);
SET_VARSIZE(poly, size);
poly->npts = path->npts;
for (i = 0; i < path->npts; i++)
{
poly->p[i].x = path->p[i].x;
poly->p[i].y = path->p[i].y;
}
make_bound_box(poly);
PG_RETURN_POLYGON_P(poly);
}
/***********************************************************************
**
** Routines for 2D polygons.
**
***********************************************************************/
Datum
poly_npoints(PG_FUNCTION_ARGS)
{
POLYGON *poly = PG_GETARG_POLYGON_P(0);
PG_RETURN_INT32(poly->npts);
}
Datum
poly_center(PG_FUNCTION_ARGS)
{
POLYGON *poly = PG_GETARG_POLYGON_P(0);
Point *result;
CIRCLE circle;
result = (Point *) palloc(sizeof(Point));
poly_to_circle(&circle, poly);
*result = circle.center;
PG_RETURN_POINT_P(result);
}
Datum
poly_box(PG_FUNCTION_ARGS)
{
POLYGON *poly = PG_GETARG_POLYGON_P(0);
BOX *box;
box = (BOX *) palloc(sizeof(BOX));
*box = poly->boundbox;
PG_RETURN_BOX_P(box);
}
/* box_poly()
* Convert a box to a polygon.
*/
Datum
box_poly(PG_FUNCTION_ARGS)
{
BOX *box = PG_GETARG_BOX_P(0);
POLYGON *poly;
int size;
/* map four corners of the box to a polygon */
size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * 4;
poly = (POLYGON *) palloc(size);
SET_VARSIZE(poly, size);
poly->npts = 4;
poly->p[0].x = box->low.x;
poly->p[0].y = box->low.y;
poly->p[1].x = box->low.x;
poly->p[1].y = box->high.y;
poly->p[2].x = box->high.x;
poly->p[2].y = box->high.y;
poly->p[3].x = box->high.x;
poly->p[3].y = box->low.y;
box_construct(&poly->boundbox, &box->high, &box->low);
PG_RETURN_POLYGON_P(poly);
}
Datum
poly_path(PG_FUNCTION_ARGS)
{
POLYGON *poly = PG_GETARG_POLYGON_P(0);
PATH *path;
int size;
int i;
/*
* Never overflows: the old size fit in MaxAllocSize, and the new size is
* smaller by a small constant.
*/
size = offsetof(PATH, p) + sizeof(path->p[0]) * poly->npts;
path = (PATH *) palloc(size);
SET_VARSIZE(path, size);
path->npts = poly->npts;
path->closed = true;
/* prevent instability in unused pad bytes */
path->dummy = 0;
for (i = 0; i < poly->npts; i++)
{
path->p[i].x = poly->p[i].x;
path->p[i].y = poly->p[i].y;
}
PG_RETURN_PATH_P(path);
}
/***********************************************************************
**
** Routines for circles.
**
***********************************************************************/
/*----------------------------------------------------------
* Formatting and conversion routines.
*---------------------------------------------------------*/
/* circle_in - convert a string to internal form.
*
* External format: (center and radius of circle)
* "((f8,f8)<f8>)"
* also supports quick entry style "(f8,f8,f8)"
*/
Datum
circle_in(PG_FUNCTION_ARGS)
{
char *str = PG_GETARG_CSTRING(0);
CIRCLE *circle = (CIRCLE *) palloc(sizeof(CIRCLE));
char *s,
*cp;
int depth = 0;
s = str;
while (isspace((unsigned char) *s))
s++;
if ((*s == LDELIM_C) || (*s == LDELIM))
{
depth++;
cp = (s + 1);
while (isspace((unsigned char) *cp))
cp++;
if (*cp == LDELIM)
s = cp;
}
pair_decode(s, &circle->center.x, &circle->center.y, &s, "circle", str);
if (*s == DELIM)
s++;
circle->radius = single_decode(s, &s, "circle", str);
/* We have to accept NaN. */
if (circle->radius < 0.0)
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
"circle", str)));
while (depth > 0)
{
if ((*s == RDELIM) || ((*s == RDELIM_C) && (depth == 1)))
{
depth--;
s++;
while (isspace((unsigned char) *s))
s++;
}
else
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
"circle", str)));
}
if (*s != '\0')
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type %s: \"%s\"",
"circle", str)));
PG_RETURN_CIRCLE_P(circle);
}
/* circle_out - convert a circle to external form.
*/
Datum
circle_out(PG_FUNCTION_ARGS)
{
CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
StringInfoData str;
initStringInfo(&str);
appendStringInfoChar(&str, LDELIM_C);
appendStringInfoChar(&str, LDELIM);
pair_encode(circle->center.x, circle->center.y, &str);
appendStringInfoChar(&str, RDELIM);
appendStringInfoChar(&str, DELIM);
single_encode(circle->radius, &str);
appendStringInfoChar(&str, RDELIM_C);
PG_RETURN_CSTRING(str.data);
}
/*
* circle_recv - converts external binary format to circle
*/
Datum
circle_recv(PG_FUNCTION_ARGS)
{
StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
CIRCLE *circle;
circle = (CIRCLE *) palloc(sizeof(CIRCLE));
circle->center.x = pq_getmsgfloat8(buf);
circle->center.y = pq_getmsgfloat8(buf);
circle->radius = pq_getmsgfloat8(buf);
/* We have to accept NaN. */
if (circle->radius < 0.0)
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?
*
* We consider NaNs values to be equal to each other to let those circles
* to be found.
*/
Datum
circle_same(PG_FUNCTION_ARGS)
{
CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
PG_RETURN_BOOL(((isnan(circle1->radius) && isnan(circle1->radius)) ||
FPeq(circle1->radius, circle2->radius)) &&
point_eq_point(&circle1->center, &circle2->center));
}
/* 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),
float8_pl(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(float8_pl(circle1->center.x, circle1->radius),
float8_pl(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(float8_pl(circle1->center.x, circle1->radius),
float8_mi(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(float8_mi(circle1->center.x, circle1->radius),
float8_pl(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(float8_mi(circle1->center.x, circle1->radius),
float8_mi(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),
float8_mi(circle2->radius, circle1->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),
float8_mi(circle1->radius, circle2->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(float8_pl(circle1->center.y, circle1->radius),
float8_mi(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(float8_mi(circle1->center.y, circle1->radius),
float8_pl(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(float8_pl(circle1->center.y, circle1->radius),
float8_pl(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(float8_mi(circle1->center.y, circle1->radius),
float8_mi(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.
*---------------------------------------------------------*/
/* 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 *) palloc(sizeof(CIRCLE));
point_add_point(&result->center, &circle->center, point);
result->radius = circle->radius;
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 *) palloc(sizeof(CIRCLE));
point_sub_point(&result->center, &circle->center, point);
result->radius = circle->radius;
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;
result = (CIRCLE *) palloc(sizeof(CIRCLE));
point_mul_point(&result->center, &circle->center, point);
result->radius = float8_mul(circle->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;
result = (CIRCLE *) palloc(sizeof(CIRCLE));
point_div_point(&result->center, &circle->center, point);
result->radius = float8_div(circle->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(float8_mul(circle->radius, 2.0));
}
/* 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 = float8_mi(point_dt(&circle1->center, &circle2->center),
float8_pl(circle1->radius, circle2->radius));
if (result < 0.0)
result = 0.0;
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);
float8 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);
float8 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 = float8_mi(point_dt(point, &circle->center),
circle->radius);
if (result < 0.0)
result = 0.0;
PG_RETURN_FLOAT8(result);
}
/*
* Distance from a circle to a point
*/
Datum
dist_cpoint(PG_FUNCTION_ARGS)
{
CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
Point *point = PG_GETARG_POINT_P(1);
float8 result;
result = float8_mi(point_dt(point, &circle->center), circle->radius);
if (result < 0.0)
result = 0.0;
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 float8
circle_ar(CIRCLE *circle)
{
return float8_mul(float8_mul(circle->radius, circle->radius), M_PI);
}
/*----------------------------------------------------------
* 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;
float8 delta;
box = (BOX *) palloc(sizeof(BOX));
delta = float8_div(circle->radius, sqrt(2.0));
box->high.x = float8_pl(circle->center.x, delta);
box->low.x = float8_mi(circle->center.x, delta);
box->high.y = float8_pl(circle->center.y, delta);
box->low.y = float8_mi(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 = float8_div(float8_pl(box->high.x, box->low.x), 2.0);
circle->center.y = float8_div(float8_pl(box->high.y, box->low.y), 2.0);
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;
float8 angle;
float8 anglestep;
if (FPzero(circle->radius))
ereport(ERROR,
(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
errmsg("cannot convert circle with radius zero to polygon")));
if (npts < 2)
ereport(ERROR,
(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
errmsg("must request at least 2 points")));
base_size = sizeof(poly->p[0]) * npts;
size = offsetof(POLYGON, p) + base_size;
/* Check for integer overflow */
if (base_size / npts != sizeof(poly->p[0]) || size <= base_size)
ereport(ERROR,
(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
errmsg("too many points requested")));
poly = (POLYGON *) palloc0(size); /* zero any holes */
SET_VARSIZE(poly, size);
poly->npts = npts;
anglestep = float8_div(2.0 * M_PI, npts);
for (i = 0; i < npts; i++)
{
angle = float8_mul(anglestep, i);
poly->p[i].x = float8_mi(circle->center.x,
float8_mul(circle->radius, cos(angle)));
poly->p[i].y = float8_pl(circle->center.y,
float8_mul(circle->radius, sin(angle)));
}
make_bound_box(poly);
PG_RETURN_POLYGON_P(poly);
}
/*
* Convert polygon to circle
*
* The result must be preallocated.
*
* XXX This algorithm should use weighted means of line segments
* rather than straight average values of points - tgl 97/01/21.
*/
static void
poly_to_circle(CIRCLE *result, POLYGON *poly)
{
int i;
Assert(poly->npts > 0);
result->center.x = 0;
result->center.y = 0;
result->radius = 0;
for (i = 0; i < poly->npts; i++)
point_add_point(&result->center, &result->center, &poly->p[i]);
result->center.x = float8_div(result->center.x, poly->npts);
result->center.y = float8_div(result->center.y, poly->npts);
for (i = 0; i < poly->npts; i++)
result->radius = float8_pl(result->radius,
point_dt(&poly->p[i], &result->center));
result->radius = float8_div(result->radius, poly->npts);
}
Datum
poly_circle(PG_FUNCTION_ARGS)
{
POLYGON *poly = PG_GETARG_POLYGON_P(0);
CIRCLE *result;
result = (CIRCLE *) palloc(sizeof(CIRCLE));
poly_to_circle(result, poly);
PG_RETURN_CIRCLE_P(result);
}
/***********************************************************************
**
** 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)
{
float8 x0,
y0;
float8 prev_x,
prev_y;
int i = 0;
float8 x,
y;
int cross,
total_cross = 0;
Assert(npts > 0);
/* compute first polygon point relative to single point */
x0 = float8_mi(plist[0].x, p->x);
y0 = float8_mi(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 = float8_mi(plist[i].x, p->x);
y = float8_mi(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(float8 x, float8 y, float8 prev_x, float8 prev_y)
{
float8 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) ? 0 : POINT_ON_POLYGON;
return FPlt(prev_y, 0.0) ? 1 : -1;
}
else
{ /* x < 0, x not on positive X axis */
if (FPzero(prev_y))
/* prev_x < 0? */
return FPlt(prev_x, 0.0) ? 0 : POINT_ON_POLYGON;
return 0;
}
}
else
{ /* y != 0 */
/* compute y crossing direction from previous point */
y_sign = FPgt(y, 0.0) ? 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) ? 0 : y_sign;
else if ((y_sign < 0 && FPlt(prev_y, 0.0)) ||
(y_sign > 0 && FPgt(prev_y, 0.0)))
/* both above or below X axis */
return 0; /* same sign */
else
{ /* y and prev_y cross X-axis */
if (FPge(x, 0.0) && FPgt(prev_x, 0.0))
/* both non-negative so cross positive X-axis */
return 2 * y_sign;
if (FPlt(x, 0.0) && FPle(prev_x, 0.0))
/* both non-positive so do not cross positive X-axis */
return 0;
/* x and y cross axises, see URL above point_inside() */
z = float8_mi(float8_mul(float8_mi(x, prev_x), y),
float8_mul(float8_mi(y, prev_y), x));
if (FPzero(z))
return POINT_ON_POLYGON;
if ((y_sign < 0 && FPlt(z, 0.0)) ||
(y_sign > 0 && FPgt(z, 0.0)))
return 0;
return 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 (point_eq_point(&p2[i], &p1[0]))
{
/* match found? then look forward through remaining points */
for (ii = 1, j = i + 1; ii < npts; ii++, j++)
{
if (j >= npts)
j = 0;
if (!point_eq_point(&p2[j], &p1[ii]))
break;
}
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 (!point_eq_point(&p2[j], &p1[ii]))
break;
}
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.
*-----------------------------------------------------------------------
*/
float8
pg_hypot(float8 x, float8 y)
{
float8 yx,
result;
/* 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)
{
float8 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;
result = x * sqrt(1.0 + (yx * yx));
check_float8_val(result, false, false);
return result;
}
Reference in New Issue View Git Blame Copy Permalink