Line data Source code
1 : /*-------------------------------------------------------------------------
2 : *
3 : * geo_ops.c
4 : * 2D geometric operations
5 : *
6 : * This module implements the geometric functions and operators. The
7 : * geometric types are (from simple to more complicated):
8 : *
9 : * - point
10 : * - line
11 : * - line segment
12 : * - box
13 : * - circle
14 : * - polygon
15 : *
16 : * Portions Copyright (c) 1996-2024, PostgreSQL Global Development Group
17 : * Portions Copyright (c) 1994, Regents of the University of California
18 : *
19 : *
20 : * IDENTIFICATION
21 : * src/backend/utils/adt/geo_ops.c
22 : *
23 : *-------------------------------------------------------------------------
24 : */
25 : #include "postgres.h"
26 :
27 : #include <math.h>
28 : #include <limits.h>
29 : #include <float.h>
30 : #include <ctype.h>
31 :
32 : #include "libpq/pqformat.h"
33 : #include "miscadmin.h"
34 : #include "nodes/miscnodes.h"
35 : #include "utils/float.h"
36 : #include "utils/fmgrprotos.h"
37 : #include "utils/geo_decls.h"
38 : #include "varatt.h"
39 :
40 : /*
41 : * * Type constructors have this form:
42 : * void type_construct(Type *result, ...);
43 : *
44 : * * Operators commonly have signatures such as
45 : * void type1_operator_type2(Type *result, Type1 *obj1, Type2 *obj2);
46 : *
47 : * Common operators are:
48 : * * Intersection point:
49 : * bool type1_interpt_type2(Point *result, Type1 *obj1, Type2 *obj2);
50 : * Return whether the two objects intersect. If *result is not NULL,
51 : * it is set to the intersection point.
52 : *
53 : * * Containment:
54 : * bool type1_contain_type2(Type1 *obj1, Type2 *obj2);
55 : * Return whether obj1 contains obj2.
56 : * bool type1_contain_type2(Type1 *contains_obj, Type1 *contained_obj);
57 : * Return whether obj1 contains obj2 (used when types are the same)
58 : *
59 : * * Distance of closest point in or on obj1 to obj2:
60 : * float8 type1_closept_type2(Point *result, Type1 *obj1, Type2 *obj2);
61 : * Returns the shortest distance between two objects. If *result is not
62 : * NULL, it is set to the closest point in or on obj1 to obj2.
63 : *
64 : * These functions may be used to implement multiple SQL-level operators. For
65 : * example, determining whether two lines are parallel is done by checking
66 : * whether they don't intersect.
67 : */
68 :
69 : /*
70 : * Internal routines
71 : */
72 :
73 : enum path_delim
74 : {
75 : PATH_NONE, PATH_OPEN, PATH_CLOSED
76 : };
77 :
78 : /* Routines for points */
79 : static inline void point_construct(Point *result, float8 x, float8 y);
80 : static inline void point_add_point(Point *result, Point *pt1, Point *pt2);
81 : static inline void point_sub_point(Point *result, Point *pt1, Point *pt2);
82 : static inline void point_mul_point(Point *result, Point *pt1, Point *pt2);
83 : static inline void point_div_point(Point *result, Point *pt1, Point *pt2);
84 : static inline bool point_eq_point(Point *pt1, Point *pt2);
85 : static inline float8 point_dt(Point *pt1, Point *pt2);
86 : static inline float8 point_sl(Point *pt1, Point *pt2);
87 : static int point_inside(Point *p, int npts, Point *plist);
88 :
89 : /* Routines for lines */
90 : static inline void line_construct(LINE *result, Point *pt, float8 m);
91 : static inline float8 line_sl(LINE *line);
92 : static inline float8 line_invsl(LINE *line);
93 : static bool line_interpt_line(Point *result, LINE *l1, LINE *l2);
94 : static bool line_contain_point(LINE *line, Point *point);
95 : static float8 line_closept_point(Point *result, LINE *line, Point *point);
96 :
97 : /* Routines for line segments */
98 : static inline void statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2);
99 : static inline float8 lseg_sl(LSEG *lseg);
100 : static inline float8 lseg_invsl(LSEG *lseg);
101 : static bool lseg_interpt_line(Point *result, LSEG *lseg, LINE *line);
102 : static bool lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2);
103 : static int lseg_crossing(float8 x, float8 y, float8 prev_x, float8 prev_y);
104 : static bool lseg_contain_point(LSEG *lseg, Point *pt);
105 : static float8 lseg_closept_point(Point *result, LSEG *lseg, Point *pt);
106 : static float8 lseg_closept_line(Point *result, LSEG *lseg, LINE *line);
107 : static float8 lseg_closept_lseg(Point *result, LSEG *on_lseg, LSEG *to_lseg);
108 :
109 : /* Routines for boxes */
110 : static inline void box_construct(BOX *result, Point *pt1, Point *pt2);
111 : static void box_cn(Point *center, BOX *box);
112 : static bool box_ov(BOX *box1, BOX *box2);
113 : static float8 box_ar(BOX *box);
114 : static float8 box_ht(BOX *box);
115 : static float8 box_wd(BOX *box);
116 : static bool box_contain_point(BOX *box, Point *point);
117 : static bool box_contain_box(BOX *contains_box, BOX *contained_box);
118 : static bool box_contain_lseg(BOX *box, LSEG *lseg);
119 : static bool box_interpt_lseg(Point *result, BOX *box, LSEG *lseg);
120 : static float8 box_closept_point(Point *result, BOX *box, Point *pt);
121 : static float8 box_closept_lseg(Point *result, BOX *box, LSEG *lseg);
122 :
123 : /* Routines for circles */
124 : static float8 circle_ar(CIRCLE *circle);
125 :
126 : /* Routines for polygons */
127 : static void make_bound_box(POLYGON *poly);
128 : static void poly_to_circle(CIRCLE *result, POLYGON *poly);
129 : static bool lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start);
130 : static bool poly_contain_poly(POLYGON *contains_poly, POLYGON *contained_poly);
131 : static bool plist_same(int npts, Point *p1, Point *p2);
132 : static float8 dist_ppoly_internal(Point *pt, POLYGON *poly);
133 :
134 : /* Routines for encoding and decoding */
135 : static bool single_decode(char *num, float8 *x, char **endptr_p,
136 : const char *type_name, const char *orig_string,
137 : Node *escontext);
138 : static void single_encode(float8 x, StringInfo str);
139 : static bool pair_decode(char *str, float8 *x, float8 *y, char **endptr_p,
140 : const char *type_name, const char *orig_string,
141 : Node *escontext);
142 : static void pair_encode(float8 x, float8 y, StringInfo str);
143 : static int pair_count(char *s, char delim);
144 : static bool path_decode(char *str, bool opentype, int npts, Point *p,
145 : bool *isopen, char **endptr_p,
146 : const char *type_name, const char *orig_string,
147 : Node *escontext);
148 : static char *path_encode(enum path_delim path_delim, int npts, Point *pt);
149 :
150 :
151 : /*
152 : * Delimiters for input and output strings.
153 : * LDELIM, RDELIM, and DELIM are left, right, and separator delimiters, respectively.
154 : * LDELIM_EP, RDELIM_EP are left and right delimiters for paths with endpoints.
155 : */
156 :
157 : #define LDELIM '('
158 : #define RDELIM ')'
159 : #define DELIM ','
160 : #define LDELIM_EP '['
161 : #define RDELIM_EP ']'
162 : #define LDELIM_C '<'
163 : #define RDELIM_C '>'
164 : #define LDELIM_L '{'
165 : #define RDELIM_L '}'
166 :
167 :
168 : /*
169 : * Geometric data types are composed of points.
170 : * This code tries to support a common format throughout the data types,
171 : * to allow for more predictable usage and data type conversion.
172 : * The fundamental unit is the point. Other units are line segments,
173 : * open paths, boxes, closed paths, and polygons (which should be considered
174 : * non-intersecting closed paths).
175 : *
176 : * Data representation is as follows:
177 : * point: (x,y)
178 : * line segment: [(x1,y1),(x2,y2)]
179 : * box: (x1,y1),(x2,y2)
180 : * open path: [(x1,y1),...,(xn,yn)]
181 : * closed path: ((x1,y1),...,(xn,yn))
182 : * polygon: ((x1,y1),...,(xn,yn))
183 : *
184 : * For boxes, the points are opposite corners with the first point at the top right.
185 : * For closed paths and polygons, the points should be reordered to allow
186 : * fast and correct equality comparisons.
187 : *
188 : * XXX perhaps points in complex shapes should be reordered internally
189 : * to allow faster internal operations, but should keep track of input order
190 : * and restore that order for text output - tgl 97/01/16
191 : */
192 :
193 : static bool
194 224816 : single_decode(char *num, float8 *x, char **endptr_p,
195 : const char *type_name, const char *orig_string,
196 : Node *escontext)
197 : {
198 224816 : *x = float8in_internal(num, endptr_p, type_name, orig_string, escontext);
199 224762 : return (!SOFT_ERROR_OCCURRED(escontext));
200 : } /* single_decode() */
201 :
202 : static void
203 9176 : single_encode(float8 x, StringInfo str)
204 : {
205 9176 : char *xstr = float8out_internal(x);
206 :
207 9176 : appendStringInfoString(str, xstr);
208 9176 : pfree(xstr);
209 9176 : } /* single_encode() */
210 :
211 : static bool
212 112078 : pair_decode(char *str, float8 *x, float8 *y, char **endptr_p,
213 : const char *type_name, const char *orig_string,
214 : Node *escontext)
215 : {
216 : bool has_delim;
217 :
218 112180 : while (isspace((unsigned char) *str))
219 102 : str++;
220 112078 : if ((has_delim = (*str == LDELIM)))
221 73178 : str++;
222 :
223 112078 : if (!single_decode(str, x, &str, type_name, orig_string, escontext))
224 0 : return false;
225 :
226 112042 : if (*str++ != DELIM)
227 54 : goto fail;
228 :
229 111988 : if (!single_decode(str, y, &str, type_name, orig_string, escontext))
230 54 : return false;
231 :
232 111922 : if (has_delim)
233 : {
234 73100 : if (*str++ != RDELIM)
235 18 : goto fail;
236 73148 : while (isspace((unsigned char) *str))
237 66 : str++;
238 : }
239 :
240 : /* report stopping point if wanted, else complain if not end of string */
241 111904 : if (endptr_p)
242 110178 : *endptr_p = str;
243 1726 : else if (*str != '\0')
244 6 : goto fail;
245 111898 : return true;
246 :
247 78 : fail:
248 78 : ereturn(escontext, false,
249 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
250 : errmsg("invalid input syntax for type %s: \"%s\"",
251 : type_name, orig_string)));
252 : }
253 :
254 : static void
255 1784604 : pair_encode(float8 x, float8 y, StringInfo str)
256 : {
257 1784604 : char *xstr = float8out_internal(x);
258 1784604 : char *ystr = float8out_internal(y);
259 :
260 1784604 : appendStringInfo(str, "%s,%s", xstr, ystr);
261 1784604 : pfree(xstr);
262 1784604 : pfree(ystr);
263 1784604 : }
264 :
265 : static bool
266 51298 : path_decode(char *str, bool opentype, int npts, Point *p,
267 : bool *isopen, char **endptr_p,
268 : const char *type_name, const char *orig_string,
269 : Node *escontext)
270 : {
271 51298 : int depth = 0;
272 : char *cp;
273 : int i;
274 :
275 51304 : while (isspace((unsigned char) *str))
276 6 : str++;
277 51298 : if ((*isopen = (*str == LDELIM_EP)))
278 : {
279 : /* no open delimiter allowed? */
280 30410 : if (!opentype)
281 6 : goto fail;
282 30404 : depth++;
283 30404 : str++;
284 : }
285 20888 : else if (*str == LDELIM)
286 : {
287 20732 : cp = (str + 1);
288 20750 : while (isspace((unsigned char) *cp))
289 18 : cp++;
290 20732 : if (*cp == LDELIM)
291 : {
292 1232 : depth++;
293 1232 : str = cp;
294 : }
295 19500 : else if (strrchr(str, LDELIM) == str)
296 : {
297 19060 : depth++;
298 19060 : str = cp;
299 : }
300 : }
301 :
302 161092 : for (i = 0; i < npts; i++)
303 : {
304 109914 : if (!pair_decode(str, &(p->x), &(p->y), &str, type_name, orig_string,
305 : escontext))
306 72 : return false;
307 109800 : if (*str == DELIM)
308 58586 : str++;
309 109800 : p++;
310 : }
311 :
312 101748 : while (depth > 0)
313 : {
314 50612 : if (*str == RDELIM || (*str == RDELIM_EP && *isopen && depth == 1))
315 : {
316 50570 : depth--;
317 50570 : str++;
318 50588 : while (isspace((unsigned char) *str))
319 18 : str++;
320 : }
321 : else
322 42 : goto fail;
323 : }
324 :
325 : /* report stopping point if wanted, else complain if not end of string */
326 51136 : if (endptr_p)
327 30880 : *endptr_p = str;
328 20256 : else if (*str != '\0')
329 6 : goto fail;
330 51130 : return true;
331 :
332 54 : fail:
333 54 : ereturn(escontext, false,
334 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
335 : errmsg("invalid input syntax for type %s: \"%s\"",
336 : type_name, orig_string)));
337 : } /* path_decode() */
338 :
339 : static char *
340 598140 : path_encode(enum path_delim path_delim, int npts, Point *pt)
341 : {
342 : StringInfoData str;
343 : int i;
344 :
345 598140 : initStringInfo(&str);
346 :
347 598140 : switch (path_delim)
348 : {
349 100646 : case PATH_CLOSED:
350 100646 : appendStringInfoChar(&str, LDELIM);
351 100646 : break;
352 60400 : case PATH_OPEN:
353 60400 : appendStringInfoChar(&str, LDELIM_EP);
354 60400 : break;
355 437094 : case PATH_NONE:
356 437094 : break;
357 : }
358 :
359 2373568 : for (i = 0; i < npts; i++)
360 : {
361 1775428 : if (i > 0)
362 1177288 : appendStringInfoChar(&str, DELIM);
363 1775428 : appendStringInfoChar(&str, LDELIM);
364 1775428 : pair_encode(pt->x, pt->y, &str);
365 1775428 : appendStringInfoChar(&str, RDELIM);
366 1775428 : pt++;
367 : }
368 :
369 598140 : switch (path_delim)
370 : {
371 100646 : case PATH_CLOSED:
372 100646 : appendStringInfoChar(&str, RDELIM);
373 100646 : break;
374 60400 : case PATH_OPEN:
375 60400 : appendStringInfoChar(&str, RDELIM_EP);
376 60400 : break;
377 437094 : case PATH_NONE:
378 437094 : break;
379 : }
380 :
381 598140 : return str.data;
382 : } /* path_encode() */
383 :
384 : /*-------------------------------------------------------------
385 : * pair_count - count the number of points
386 : * allow the following notation:
387 : * '((1,2),(3,4))'
388 : * '(1,3,2,4)'
389 : * require an odd number of delim characters in the string
390 : *-------------------------------------------------------------*/
391 : static int
392 31328 : pair_count(char *s, char delim)
393 : {
394 31328 : int ndelim = 0;
395 :
396 140014 : while ((s = strchr(s, delim)) != NULL)
397 : {
398 108686 : ndelim++;
399 108686 : s++;
400 : }
401 31328 : return (ndelim % 2) ? ((ndelim + 1) / 2) : -1;
402 : }
403 :
404 :
405 : /***********************************************************************
406 : **
407 : ** Routines for two-dimensional boxes.
408 : **
409 : ***********************************************************************/
410 :
411 : /*----------------------------------------------------------
412 : * Formatting and conversion routines.
413 : *---------------------------------------------------------*/
414 :
415 : /* box_in - convert a string to internal form.
416 : *
417 : * External format: (two corners of box)
418 : * "(f8, f8), (f8, f8)"
419 : * also supports the older style "(f8, f8, f8, f8)"
420 : */
421 : Datum
422 19846 : box_in(PG_FUNCTION_ARGS)
423 : {
424 19846 : char *str = PG_GETARG_CSTRING(0);
425 19846 : Node *escontext = fcinfo->context;
426 19846 : BOX *box = (BOX *) palloc(sizeof(BOX));
427 : bool isopen;
428 : float8 x,
429 : y;
430 :
431 19846 : if (!path_decode(str, false, 2, &(box->high), &isopen, NULL, "box", str,
432 : escontext))
433 24 : PG_RETURN_NULL();
434 :
435 : /* reorder corners if necessary... */
436 19792 : if (float8_lt(box->high.x, box->low.x))
437 : {
438 898 : x = box->high.x;
439 898 : box->high.x = box->low.x;
440 898 : box->low.x = x;
441 : }
442 19792 : if (float8_lt(box->high.y, box->low.y))
443 : {
444 910 : y = box->high.y;
445 910 : box->high.y = box->low.y;
446 910 : box->low.y = y;
447 : }
448 :
449 19792 : PG_RETURN_BOX_P(box);
450 : }
451 :
452 : /* box_out - convert a box to external form.
453 : */
454 : Datum
455 177554 : box_out(PG_FUNCTION_ARGS)
456 : {
457 177554 : BOX *box = PG_GETARG_BOX_P(0);
458 :
459 177554 : PG_RETURN_CSTRING(path_encode(PATH_NONE, 2, &(box->high)));
460 : }
461 :
462 : /*
463 : * box_recv - converts external binary format to box
464 : */
465 : Datum
466 0 : box_recv(PG_FUNCTION_ARGS)
467 : {
468 0 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
469 : BOX *box;
470 : float8 x,
471 : y;
472 :
473 0 : box = (BOX *) palloc(sizeof(BOX));
474 :
475 0 : box->high.x = pq_getmsgfloat8(buf);
476 0 : box->high.y = pq_getmsgfloat8(buf);
477 0 : box->low.x = pq_getmsgfloat8(buf);
478 0 : box->low.y = pq_getmsgfloat8(buf);
479 :
480 : /* reorder corners if necessary... */
481 0 : if (float8_lt(box->high.x, box->low.x))
482 : {
483 0 : x = box->high.x;
484 0 : box->high.x = box->low.x;
485 0 : box->low.x = x;
486 : }
487 0 : if (float8_lt(box->high.y, box->low.y))
488 : {
489 0 : y = box->high.y;
490 0 : box->high.y = box->low.y;
491 0 : box->low.y = y;
492 : }
493 :
494 0 : PG_RETURN_BOX_P(box);
495 : }
496 :
497 : /*
498 : * box_send - converts box to binary format
499 : */
500 : Datum
501 0 : box_send(PG_FUNCTION_ARGS)
502 : {
503 0 : BOX *box = PG_GETARG_BOX_P(0);
504 : StringInfoData buf;
505 :
506 0 : pq_begintypsend(&buf);
507 0 : pq_sendfloat8(&buf, box->high.x);
508 0 : pq_sendfloat8(&buf, box->high.y);
509 0 : pq_sendfloat8(&buf, box->low.x);
510 0 : pq_sendfloat8(&buf, box->low.y);
511 0 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
512 : }
513 :
514 :
515 : /* box_construct - fill in a new box.
516 : */
517 : static inline void
518 260544 : box_construct(BOX *result, Point *pt1, Point *pt2)
519 : {
520 260544 : if (float8_gt(pt1->x, pt2->x))
521 : {
522 18558 : result->high.x = pt1->x;
523 18558 : result->low.x = pt2->x;
524 : }
525 : else
526 : {
527 241986 : result->high.x = pt2->x;
528 241986 : result->low.x = pt1->x;
529 : }
530 260544 : if (float8_gt(pt1->y, pt2->y))
531 : {
532 18594 : result->high.y = pt1->y;
533 18594 : result->low.y = pt2->y;
534 : }
535 : else
536 : {
537 241950 : result->high.y = pt2->y;
538 241950 : result->low.y = pt1->y;
539 : }
540 260544 : }
541 :
542 :
543 : /*----------------------------------------------------------
544 : * Relational operators for BOXes.
545 : * <, >, <=, >=, and == are based on box area.
546 : *---------------------------------------------------------*/
547 :
548 : /* box_same - are two boxes identical?
549 : */
550 : Datum
551 13760 : box_same(PG_FUNCTION_ARGS)
552 : {
553 13760 : BOX *box1 = PG_GETARG_BOX_P(0);
554 13760 : BOX *box2 = PG_GETARG_BOX_P(1);
555 :
556 13760 : PG_RETURN_BOOL(point_eq_point(&box1->high, &box2->high) &&
557 : point_eq_point(&box1->low, &box2->low));
558 : }
559 :
560 : /* box_overlap - does box1 overlap box2?
561 : */
562 : Datum
563 64734 : box_overlap(PG_FUNCTION_ARGS)
564 : {
565 64734 : BOX *box1 = PG_GETARG_BOX_P(0);
566 64734 : BOX *box2 = PG_GETARG_BOX_P(1);
567 :
568 64734 : PG_RETURN_BOOL(box_ov(box1, box2));
569 : }
570 :
571 : static bool
572 1476180 : box_ov(BOX *box1, BOX *box2)
573 : {
574 2230044 : return (FPle(box1->low.x, box2->high.x) &&
575 876786 : FPle(box2->low.x, box1->high.x) &&
576 2352966 : FPle(box1->low.y, box2->high.y) &&
577 98472 : FPle(box2->low.y, box1->high.y));
578 : }
579 :
580 : /* box_left - is box1 strictly left of box2?
581 : */
582 : Datum
583 50022 : box_left(PG_FUNCTION_ARGS)
584 : {
585 50022 : BOX *box1 = PG_GETARG_BOX_P(0);
586 50022 : BOX *box2 = PG_GETARG_BOX_P(1);
587 :
588 50022 : PG_RETURN_BOOL(FPlt(box1->high.x, box2->low.x));
589 : }
590 :
591 : /* box_overleft - is the right edge of box1 at or left of
592 : * the right edge of box2?
593 : *
594 : * This is "less than or equal" for the end of a time range,
595 : * when time ranges are stored as rectangles.
596 : */
597 : Datum
598 99708 : box_overleft(PG_FUNCTION_ARGS)
599 : {
600 99708 : BOX *box1 = PG_GETARG_BOX_P(0);
601 99708 : BOX *box2 = PG_GETARG_BOX_P(1);
602 :
603 99708 : PG_RETURN_BOOL(FPle(box1->high.x, box2->high.x));
604 : }
605 :
606 : /* box_right - is box1 strictly right of box2?
607 : */
608 : Datum
609 131742 : box_right(PG_FUNCTION_ARGS)
610 : {
611 131742 : BOX *box1 = PG_GETARG_BOX_P(0);
612 131742 : BOX *box2 = PG_GETARG_BOX_P(1);
613 :
614 131742 : PG_RETURN_BOOL(FPgt(box1->low.x, box2->high.x));
615 : }
616 :
617 : /* box_overright - is the left edge of box1 at or right of
618 : * the left edge of box2?
619 : *
620 : * This is "greater than or equal" for time ranges, when time ranges
621 : * are stored as rectangles.
622 : */
623 : Datum
624 112398 : box_overright(PG_FUNCTION_ARGS)
625 : {
626 112398 : BOX *box1 = PG_GETARG_BOX_P(0);
627 112398 : BOX *box2 = PG_GETARG_BOX_P(1);
628 :
629 112398 : PG_RETURN_BOOL(FPge(box1->low.x, box2->low.x));
630 : }
631 :
632 : /* box_below - is box1 strictly below box2?
633 : */
634 : Datum
635 27678 : box_below(PG_FUNCTION_ARGS)
636 : {
637 27678 : BOX *box1 = PG_GETARG_BOX_P(0);
638 27678 : BOX *box2 = PG_GETARG_BOX_P(1);
639 :
640 27678 : PG_RETURN_BOOL(FPlt(box1->high.y, box2->low.y));
641 : }
642 :
643 : /* box_overbelow - is the upper edge of box1 at or below
644 : * the upper edge of box2?
645 : */
646 : Datum
647 80436 : box_overbelow(PG_FUNCTION_ARGS)
648 : {
649 80436 : BOX *box1 = PG_GETARG_BOX_P(0);
650 80436 : BOX *box2 = PG_GETARG_BOX_P(1);
651 :
652 80436 : PG_RETURN_BOOL(FPle(box1->high.y, box2->high.y));
653 : }
654 :
655 : /* box_above - is box1 strictly above box2?
656 : */
657 : Datum
658 57720 : box_above(PG_FUNCTION_ARGS)
659 : {
660 57720 : BOX *box1 = PG_GETARG_BOX_P(0);
661 57720 : BOX *box2 = PG_GETARG_BOX_P(1);
662 :
663 57720 : PG_RETURN_BOOL(FPgt(box1->low.y, box2->high.y));
664 : }
665 :
666 : /* box_overabove - is the lower edge of box1 at or above
667 : * the lower edge of box2?
668 : */
669 : Datum
670 111150 : box_overabove(PG_FUNCTION_ARGS)
671 : {
672 111150 : BOX *box1 = PG_GETARG_BOX_P(0);
673 111150 : BOX *box2 = PG_GETARG_BOX_P(1);
674 :
675 111150 : PG_RETURN_BOOL(FPge(box1->low.y, box2->low.y));
676 : }
677 :
678 : /* box_contained - is box1 contained by box2?
679 : */
680 : Datum
681 158292 : box_contained(PG_FUNCTION_ARGS)
682 : {
683 158292 : BOX *box1 = PG_GETARG_BOX_P(0);
684 158292 : BOX *box2 = PG_GETARG_BOX_P(1);
685 :
686 158292 : PG_RETURN_BOOL(box_contain_box(box2, box1));
687 : }
688 :
689 : /* box_contain - does box1 contain box2?
690 : */
691 : Datum
692 12252 : box_contain(PG_FUNCTION_ARGS)
693 : {
694 12252 : BOX *box1 = PG_GETARG_BOX_P(0);
695 12252 : BOX *box2 = PG_GETARG_BOX_P(1);
696 :
697 12252 : PG_RETURN_BOOL(box_contain_box(box1, box2));
698 : }
699 :
700 : /*
701 : * Check whether the second box is in the first box or on its border
702 : */
703 : static bool
704 255474 : box_contain_box(BOX *contains_box, BOX *contained_box)
705 : {
706 417552 : return FPge(contains_box->high.x, contained_box->high.x) &&
707 277854 : FPle(contains_box->low.x, contained_box->low.x) &&
708 533328 : FPge(contains_box->high.y, contained_box->high.y) &&
709 97494 : FPle(contains_box->low.y, contained_box->low.y);
710 : }
711 :
712 :
713 : /* box_positionop -
714 : * is box1 entirely {above,below} box2?
715 : *
716 : * box_below_eq and box_above_eq are obsolete versions that (probably
717 : * erroneously) accept the equal-boundaries case. Since these are not
718 : * in sync with the box_left and box_right code, they are deprecated and
719 : * not supported in the PG 8.1 rtree operator class extension.
720 : */
721 : Datum
722 150 : box_below_eq(PG_FUNCTION_ARGS)
723 : {
724 150 : BOX *box1 = PG_GETARG_BOX_P(0);
725 150 : BOX *box2 = PG_GETARG_BOX_P(1);
726 :
727 150 : PG_RETURN_BOOL(FPle(box1->high.y, box2->low.y));
728 : }
729 :
730 : Datum
731 150 : box_above_eq(PG_FUNCTION_ARGS)
732 : {
733 150 : BOX *box1 = PG_GETARG_BOX_P(0);
734 150 : BOX *box2 = PG_GETARG_BOX_P(1);
735 :
736 150 : PG_RETURN_BOOL(FPge(box1->low.y, box2->high.y));
737 : }
738 :
739 :
740 : /* box_relop - is area(box1) relop area(box2), within
741 : * our accuracy constraint?
742 : */
743 : Datum
744 30 : box_lt(PG_FUNCTION_ARGS)
745 : {
746 30 : BOX *box1 = PG_GETARG_BOX_P(0);
747 30 : BOX *box2 = PG_GETARG_BOX_P(1);
748 :
749 30 : PG_RETURN_BOOL(FPlt(box_ar(box1), box_ar(box2)));
750 : }
751 :
752 : Datum
753 30 : box_gt(PG_FUNCTION_ARGS)
754 : {
755 30 : BOX *box1 = PG_GETARG_BOX_P(0);
756 30 : BOX *box2 = PG_GETARG_BOX_P(1);
757 :
758 30 : PG_RETURN_BOOL(FPgt(box_ar(box1), box_ar(box2)));
759 : }
760 :
761 : Datum
762 30 : box_eq(PG_FUNCTION_ARGS)
763 : {
764 30 : BOX *box1 = PG_GETARG_BOX_P(0);
765 30 : BOX *box2 = PG_GETARG_BOX_P(1);
766 :
767 30 : PG_RETURN_BOOL(FPeq(box_ar(box1), box_ar(box2)));
768 : }
769 :
770 : Datum
771 30 : box_le(PG_FUNCTION_ARGS)
772 : {
773 30 : BOX *box1 = PG_GETARG_BOX_P(0);
774 30 : BOX *box2 = PG_GETARG_BOX_P(1);
775 :
776 30 : PG_RETURN_BOOL(FPle(box_ar(box1), box_ar(box2)));
777 : }
778 :
779 : Datum
780 30 : box_ge(PG_FUNCTION_ARGS)
781 : {
782 30 : BOX *box1 = PG_GETARG_BOX_P(0);
783 30 : BOX *box2 = PG_GETARG_BOX_P(1);
784 :
785 30 : PG_RETURN_BOOL(FPge(box_ar(box1), box_ar(box2)));
786 : }
787 :
788 :
789 : /*----------------------------------------------------------
790 : * "Arithmetic" operators on boxes.
791 : *---------------------------------------------------------*/
792 :
793 : /* box_area - returns the area of the box.
794 : */
795 : Datum
796 30 : box_area(PG_FUNCTION_ARGS)
797 : {
798 30 : BOX *box = PG_GETARG_BOX_P(0);
799 :
800 30 : PG_RETURN_FLOAT8(box_ar(box));
801 : }
802 :
803 :
804 : /* box_width - returns the width of the box
805 : * (horizontal magnitude).
806 : */
807 : Datum
808 30 : box_width(PG_FUNCTION_ARGS)
809 : {
810 30 : BOX *box = PG_GETARG_BOX_P(0);
811 :
812 30 : PG_RETURN_FLOAT8(box_wd(box));
813 : }
814 :
815 :
816 : /* box_height - returns the height of the box
817 : * (vertical magnitude).
818 : */
819 : Datum
820 30 : box_height(PG_FUNCTION_ARGS)
821 : {
822 30 : BOX *box = PG_GETARG_BOX_P(0);
823 :
824 30 : PG_RETURN_FLOAT8(box_ht(box));
825 : }
826 :
827 :
828 : /* box_distance - returns the distance between the
829 : * center points of two boxes.
830 : */
831 : Datum
832 150 : box_distance(PG_FUNCTION_ARGS)
833 : {
834 150 : BOX *box1 = PG_GETARG_BOX_P(0);
835 150 : BOX *box2 = PG_GETARG_BOX_P(1);
836 : Point a,
837 : b;
838 :
839 150 : box_cn(&a, box1);
840 150 : box_cn(&b, box2);
841 :
842 150 : PG_RETURN_FLOAT8(point_dt(&a, &b));
843 : }
844 :
845 :
846 : /* box_center - returns the center point of the box.
847 : */
848 : Datum
849 90 : box_center(PG_FUNCTION_ARGS)
850 : {
851 90 : BOX *box = PG_GETARG_BOX_P(0);
852 90 : Point *result = (Point *) palloc(sizeof(Point));
853 :
854 90 : box_cn(result, box);
855 :
856 90 : PG_RETURN_POINT_P(result);
857 : }
858 :
859 :
860 : /* box_ar - returns the area of the box.
861 : */
862 : static float8
863 330 : box_ar(BOX *box)
864 : {
865 330 : return float8_mul(box_wd(box), box_ht(box));
866 : }
867 :
868 :
869 : /* box_cn - stores the centerpoint of the box into *center.
870 : */
871 : static void
872 474 : box_cn(Point *center, BOX *box)
873 : {
874 474 : center->x = float8_div(float8_pl(box->high.x, box->low.x), 2.0);
875 474 : center->y = float8_div(float8_pl(box->high.y, box->low.y), 2.0);
876 474 : }
877 :
878 :
879 : /* box_wd - returns the width (length) of the box
880 : * (horizontal magnitude).
881 : */
882 : static float8
883 360 : box_wd(BOX *box)
884 : {
885 360 : return float8_mi(box->high.x, box->low.x);
886 : }
887 :
888 :
889 : /* box_ht - returns the height of the box
890 : * (vertical magnitude).
891 : */
892 : static float8
893 360 : box_ht(BOX *box)
894 : {
895 360 : return float8_mi(box->high.y, box->low.y);
896 : }
897 :
898 :
899 : /*----------------------------------------------------------
900 : * Funky operations.
901 : *---------------------------------------------------------*/
902 :
903 : /* box_intersect -
904 : * returns the overlapping portion of two boxes,
905 : * or NULL if they do not intersect.
906 : */
907 : Datum
908 150 : box_intersect(PG_FUNCTION_ARGS)
909 : {
910 150 : BOX *box1 = PG_GETARG_BOX_P(0);
911 150 : BOX *box2 = PG_GETARG_BOX_P(1);
912 : BOX *result;
913 :
914 150 : if (!box_ov(box1, box2))
915 84 : PG_RETURN_NULL();
916 :
917 66 : result = (BOX *) palloc(sizeof(BOX));
918 :
919 66 : result->high.x = float8_min(box1->high.x, box2->high.x);
920 66 : result->low.x = float8_max(box1->low.x, box2->low.x);
921 66 : result->high.y = float8_min(box1->high.y, box2->high.y);
922 66 : result->low.y = float8_max(box1->low.y, box2->low.y);
923 :
924 66 : PG_RETURN_BOX_P(result);
925 : }
926 :
927 :
928 : /* box_diagonal -
929 : * returns a line segment which happens to be the
930 : * positive-slope diagonal of "box".
931 : */
932 : Datum
933 30 : box_diagonal(PG_FUNCTION_ARGS)
934 : {
935 30 : BOX *box = PG_GETARG_BOX_P(0);
936 30 : LSEG *result = (LSEG *) palloc(sizeof(LSEG));
937 :
938 30 : statlseg_construct(result, &box->high, &box->low);
939 :
940 30 : PG_RETURN_LSEG_P(result);
941 : }
942 :
943 : /***********************************************************************
944 : **
945 : ** Routines for 2D lines.
946 : **
947 : ***********************************************************************/
948 :
949 : static bool
950 138 : line_decode(char *s, const char *str, LINE *line, Node *escontext)
951 : {
952 : /* s was already advanced over leading '{' */
953 138 : if (!single_decode(s, &line->A, &s, "line", str, escontext))
954 0 : return false;
955 132 : if (*s++ != DELIM)
956 6 : goto fail;
957 126 : if (!single_decode(s, &line->B, &s, "line", str, escontext))
958 0 : return false;
959 126 : if (*s++ != DELIM)
960 18 : goto fail;
961 108 : if (!single_decode(s, &line->C, &s, "line", str, escontext))
962 24 : return false;
963 84 : if (*s++ != RDELIM_L)
964 6 : goto fail;
965 84 : while (isspace((unsigned char) *s))
966 6 : s++;
967 78 : if (*s != '\0')
968 6 : goto fail;
969 72 : return true;
970 :
971 36 : fail:
972 36 : ereturn(escontext, false,
973 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
974 : errmsg("invalid input syntax for type %s: \"%s\"",
975 : "line", str)));
976 : }
977 :
978 : Datum
979 210 : line_in(PG_FUNCTION_ARGS)
980 : {
981 210 : char *str = PG_GETARG_CSTRING(0);
982 210 : Node *escontext = fcinfo->context;
983 210 : LINE *line = (LINE *) palloc(sizeof(LINE));
984 : LSEG lseg;
985 : bool isopen;
986 : char *s;
987 :
988 210 : s = str;
989 216 : while (isspace((unsigned char) *s))
990 6 : s++;
991 210 : if (*s == LDELIM_L)
992 : {
993 138 : if (!line_decode(s + 1, str, line, escontext))
994 36 : PG_RETURN_NULL();
995 72 : if (FPzero(line->A) && FPzero(line->B))
996 18 : ereturn(escontext, (Datum) 0,
997 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
998 : errmsg("invalid line specification: A and B cannot both be zero")));
999 : }
1000 : else
1001 : {
1002 72 : if (!path_decode(s, true, 2, &lseg.p[0], &isopen, NULL, "line", str,
1003 : escontext))
1004 12 : PG_RETURN_NULL();
1005 36 : if (point_eq_point(&lseg.p[0], &lseg.p[1]))
1006 6 : ereturn(escontext, (Datum) 0,
1007 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
1008 : errmsg("invalid line specification: must be two distinct points")));
1009 :
1010 : /*
1011 : * XXX lseg_sl() and line_construct() can throw overflow/underflow
1012 : * errors. Eventually we should allow those to be soft, but the
1013 : * notational pain seems to outweigh the value for now.
1014 : */
1015 30 : line_construct(line, &lseg.p[0], lseg_sl(&lseg));
1016 : }
1017 :
1018 84 : PG_RETURN_LINE_P(line);
1019 : }
1020 :
1021 :
1022 : Datum
1023 6964 : line_out(PG_FUNCTION_ARGS)
1024 : {
1025 6964 : LINE *line = PG_GETARG_LINE_P(0);
1026 6964 : char *astr = float8out_internal(line->A);
1027 6964 : char *bstr = float8out_internal(line->B);
1028 6964 : char *cstr = float8out_internal(line->C);
1029 :
1030 6964 : PG_RETURN_CSTRING(psprintf("%c%s%c%s%c%s%c", LDELIM_L, astr, DELIM, bstr,
1031 : DELIM, cstr, RDELIM_L));
1032 : }
1033 :
1034 : /*
1035 : * line_recv - converts external binary format to line
1036 : */
1037 : Datum
1038 0 : line_recv(PG_FUNCTION_ARGS)
1039 : {
1040 0 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
1041 : LINE *line;
1042 :
1043 0 : line = (LINE *) palloc(sizeof(LINE));
1044 :
1045 0 : line->A = pq_getmsgfloat8(buf);
1046 0 : line->B = pq_getmsgfloat8(buf);
1047 0 : line->C = pq_getmsgfloat8(buf);
1048 :
1049 0 : if (FPzero(line->A) && FPzero(line->B))
1050 0 : ereport(ERROR,
1051 : (errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
1052 : errmsg("invalid line specification: A and B cannot both be zero")));
1053 :
1054 0 : PG_RETURN_LINE_P(line);
1055 : }
1056 :
1057 : /*
1058 : * line_send - converts line to binary format
1059 : */
1060 : Datum
1061 0 : line_send(PG_FUNCTION_ARGS)
1062 : {
1063 0 : LINE *line = PG_GETARG_LINE_P(0);
1064 : StringInfoData buf;
1065 :
1066 0 : pq_begintypsend(&buf);
1067 0 : pq_sendfloat8(&buf, line->A);
1068 0 : pq_sendfloat8(&buf, line->B);
1069 0 : pq_sendfloat8(&buf, line->C);
1070 0 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
1071 : }
1072 :
1073 :
1074 : /*----------------------------------------------------------
1075 : * Conversion routines from one line formula to internal.
1076 : * Internal form: Ax+By+C=0
1077 : *---------------------------------------------------------*/
1078 :
1079 : /*
1080 : * Fill already-allocated LINE struct from the point and the slope
1081 : */
1082 : static inline void
1083 6545460 : line_construct(LINE *result, Point *pt, float8 m)
1084 : {
1085 6545460 : if (isinf(m))
1086 : {
1087 : /* vertical - use "x = C" */
1088 1494696 : result->A = -1.0;
1089 1494696 : result->B = 0.0;
1090 1494696 : result->C = pt->x;
1091 : }
1092 5050764 : else if (m == 0)
1093 : {
1094 : /* horizontal - use "y = C" */
1095 1478418 : result->A = 0.0;
1096 1478418 : result->B = -1.0;
1097 1478418 : result->C = pt->y;
1098 : }
1099 : else
1100 : {
1101 : /* use "mx - y + yinter = 0" */
1102 3572346 : result->A = m;
1103 3572346 : result->B = -1.0;
1104 3572346 : result->C = float8_mi(pt->y, float8_mul(m, pt->x));
1105 : /* on some platforms, the preceding expression tends to produce -0 */
1106 3572346 : if (result->C == 0.0)
1107 4860 : result->C = 0.0;
1108 : }
1109 6545460 : }
1110 :
1111 : /* line_construct_pp()
1112 : * two points
1113 : */
1114 : Datum
1115 540 : line_construct_pp(PG_FUNCTION_ARGS)
1116 : {
1117 540 : Point *pt1 = PG_GETARG_POINT_P(0);
1118 540 : Point *pt2 = PG_GETARG_POINT_P(1);
1119 540 : LINE *result = (LINE *) palloc(sizeof(LINE));
1120 :
1121 540 : if (point_eq_point(pt1, pt2))
1122 6 : ereport(ERROR,
1123 : (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
1124 : errmsg("invalid line specification: must be two distinct points")));
1125 :
1126 534 : line_construct(result, pt1, point_sl(pt1, pt2));
1127 :
1128 534 : PG_RETURN_LINE_P(result);
1129 : }
1130 :
1131 :
1132 : /*----------------------------------------------------------
1133 : * Relative position routines.
1134 : *---------------------------------------------------------*/
1135 :
1136 : Datum
1137 600 : line_intersect(PG_FUNCTION_ARGS)
1138 : {
1139 600 : LINE *l1 = PG_GETARG_LINE_P(0);
1140 600 : LINE *l2 = PG_GETARG_LINE_P(1);
1141 :
1142 600 : PG_RETURN_BOOL(line_interpt_line(NULL, l1, l2));
1143 : }
1144 :
1145 : Datum
1146 600 : line_parallel(PG_FUNCTION_ARGS)
1147 : {
1148 600 : LINE *l1 = PG_GETARG_LINE_P(0);
1149 600 : LINE *l2 = PG_GETARG_LINE_P(1);
1150 :
1151 600 : PG_RETURN_BOOL(!line_interpt_line(NULL, l1, l2));
1152 : }
1153 :
1154 : Datum
1155 600 : line_perp(PG_FUNCTION_ARGS)
1156 : {
1157 600 : LINE *l1 = PG_GETARG_LINE_P(0);
1158 600 : LINE *l2 = PG_GETARG_LINE_P(1);
1159 :
1160 600 : if (FPzero(l1->A))
1161 180 : PG_RETURN_BOOL(FPzero(l2->B));
1162 420 : if (FPzero(l2->A))
1163 126 : PG_RETURN_BOOL(FPzero(l1->B));
1164 294 : if (FPzero(l1->B))
1165 84 : PG_RETURN_BOOL(FPzero(l2->A));
1166 210 : if (FPzero(l2->B))
1167 60 : PG_RETURN_BOOL(FPzero(l1->A));
1168 :
1169 150 : PG_RETURN_BOOL(FPeq(float8_div(float8_mul(l1->A, l2->A),
1170 : float8_mul(l1->B, l2->B)), -1.0));
1171 : }
1172 :
1173 : Datum
1174 60 : line_vertical(PG_FUNCTION_ARGS)
1175 : {
1176 60 : LINE *line = PG_GETARG_LINE_P(0);
1177 :
1178 60 : PG_RETURN_BOOL(FPzero(line->B));
1179 : }
1180 :
1181 : Datum
1182 60 : line_horizontal(PG_FUNCTION_ARGS)
1183 : {
1184 60 : LINE *line = PG_GETARG_LINE_P(0);
1185 :
1186 60 : PG_RETURN_BOOL(FPzero(line->A));
1187 : }
1188 :
1189 :
1190 : /*
1191 : * Check whether the two lines are the same
1192 : */
1193 : Datum
1194 612 : line_eq(PG_FUNCTION_ARGS)
1195 : {
1196 612 : LINE *l1 = PG_GETARG_LINE_P(0);
1197 612 : LINE *l2 = PG_GETARG_LINE_P(1);
1198 : float8 ratio;
1199 :
1200 : /* If any NaNs are involved, insist on exact equality */
1201 612 : if (unlikely(isnan(l1->A) || isnan(l1->B) || isnan(l1->C) ||
1202 : isnan(l2->A) || isnan(l2->B) || isnan(l2->C)))
1203 : {
1204 228 : PG_RETURN_BOOL(float8_eq(l1->A, l2->A) &&
1205 : float8_eq(l1->B, l2->B) &&
1206 : float8_eq(l1->C, l2->C));
1207 : }
1208 :
1209 : /* Otherwise, lines whose parameters are proportional are the same */
1210 384 : if (!FPzero(l2->A))
1211 240 : ratio = float8_div(l1->A, l2->A);
1212 144 : else if (!FPzero(l2->B))
1213 144 : ratio = float8_div(l1->B, l2->B);
1214 0 : else if (!FPzero(l2->C))
1215 0 : ratio = float8_div(l1->C, l2->C);
1216 : else
1217 0 : ratio = 1.0;
1218 :
1219 384 : PG_RETURN_BOOL(FPeq(l1->A, float8_mul(ratio, l2->A)) &&
1220 : FPeq(l1->B, float8_mul(ratio, l2->B)) &&
1221 : FPeq(l1->C, float8_mul(ratio, l2->C)));
1222 : }
1223 :
1224 :
1225 : /*----------------------------------------------------------
1226 : * Line arithmetic routines.
1227 : *---------------------------------------------------------*/
1228 :
1229 : /*
1230 : * Return slope of the line
1231 : */
1232 : static inline float8
1233 480 : line_sl(LINE *line)
1234 : {
1235 480 : if (FPzero(line->A))
1236 144 : return 0.0;
1237 336 : if (FPzero(line->B))
1238 96 : return get_float8_infinity();
1239 240 : return float8_div(line->A, -line->B);
1240 : }
1241 :
1242 :
1243 : /*
1244 : * Return inverse slope of the line
1245 : */
1246 : static inline float8
1247 1793160 : line_invsl(LINE *line)
1248 : {
1249 1793160 : if (FPzero(line->A))
1250 715320 : return get_float8_infinity();
1251 1077840 : if (FPzero(line->B))
1252 695604 : return 0.0;
1253 382236 : return float8_div(line->B, line->A);
1254 : }
1255 :
1256 :
1257 : /* line_distance()
1258 : * Distance between two lines.
1259 : */
1260 : Datum
1261 600 : line_distance(PG_FUNCTION_ARGS)
1262 : {
1263 600 : LINE *l1 = PG_GETARG_LINE_P(0);
1264 600 : LINE *l2 = PG_GETARG_LINE_P(1);
1265 : float8 ratio;
1266 :
1267 600 : if (line_interpt_line(NULL, l1, l2)) /* intersecting? */
1268 504 : PG_RETURN_FLOAT8(0.0);
1269 :
1270 96 : if (!FPzero(l1->A) && !isnan(l1->A) && !FPzero(l2->A) && !isnan(l2->A))
1271 42 : ratio = float8_div(l1->A, l2->A);
1272 54 : else if (!FPzero(l1->B) && !isnan(l1->B) && !FPzero(l2->B) && !isnan(l2->B))
1273 54 : ratio = float8_div(l1->B, l2->B);
1274 : else
1275 0 : ratio = 1.0;
1276 :
1277 96 : PG_RETURN_FLOAT8(float8_div(fabs(float8_mi(l1->C,
1278 : float8_mul(ratio, l2->C))),
1279 : HYPOT(l1->A, l1->B)));
1280 : }
1281 :
1282 : /* line_interpt()
1283 : * Point where two lines l1, l2 intersect (if any)
1284 : */
1285 : Datum
1286 600 : line_interpt(PG_FUNCTION_ARGS)
1287 : {
1288 600 : LINE *l1 = PG_GETARG_LINE_P(0);
1289 600 : LINE *l2 = PG_GETARG_LINE_P(1);
1290 : Point *result;
1291 :
1292 600 : result = (Point *) palloc(sizeof(Point));
1293 :
1294 600 : if (!line_interpt_line(result, l1, l2))
1295 96 : PG_RETURN_NULL();
1296 504 : PG_RETURN_POINT_P(result);
1297 : }
1298 :
1299 : /*
1300 : * Internal version of line_interpt
1301 : *
1302 : * Return whether two lines intersect. If *result is not NULL, it is set to
1303 : * the intersection point.
1304 : *
1305 : * NOTE: If the lines are identical then we will find they are parallel
1306 : * and report "no intersection". This is a little weird, but since
1307 : * there's no *unique* intersection, maybe it's appropriate behavior.
1308 : *
1309 : * If the lines have NaN constants, we will return true, and the intersection
1310 : * point would have NaN coordinates. We shouldn't return false in this case
1311 : * because that would mean the lines are parallel.
1312 : */
1313 : static bool
1314 4172850 : line_interpt_line(Point *result, LINE *l1, LINE *l2)
1315 : {
1316 : float8 x,
1317 : y;
1318 :
1319 4172850 : if (!FPzero(l1->B))
1320 : {
1321 3036450 : if (FPeq(l2->A, float8_mul(l1->A, float8_div(l2->B, l1->B))))
1322 9588 : return false;
1323 :
1324 3026862 : x = float8_div(float8_mi(float8_mul(l1->B, l2->C),
1325 : float8_mul(l2->B, l1->C)),
1326 : float8_mi(float8_mul(l1->A, l2->B),
1327 : float8_mul(l2->A, l1->B)));
1328 3026862 : y = float8_div(-float8_pl(float8_mul(l1->A, x), l1->C), l1->B);
1329 : }
1330 1136400 : else if (!FPzero(l2->B))
1331 : {
1332 1133442 : if (FPeq(l1->A, float8_mul(l2->A, float8_div(l1->B, l2->B))))
1333 0 : return false;
1334 :
1335 1133442 : x = float8_div(float8_mi(float8_mul(l2->B, l1->C),
1336 : float8_mul(l1->B, l2->C)),
1337 : float8_mi(float8_mul(l2->A, l1->B),
1338 : float8_mul(l1->A, l2->B)));
1339 1133442 : y = float8_div(-float8_pl(float8_mul(l2->A, x), l2->C), l2->B);
1340 : }
1341 : else
1342 2958 : return false;
1343 :
1344 : /* On some platforms, the preceding expressions tend to produce -0. */
1345 4160304 : if (x == 0.0)
1346 121710 : x = 0.0;
1347 4160304 : if (y == 0.0)
1348 119928 : y = 0.0;
1349 :
1350 4160304 : if (result != NULL)
1351 4158792 : point_construct(result, x, y);
1352 :
1353 4160304 : return true;
1354 : }
1355 :
1356 :
1357 : /***********************************************************************
1358 : **
1359 : ** Routines for 2D paths (sequences of line segments, also
1360 : ** called `polylines').
1361 : **
1362 : ** This is not a general package for geometric paths,
1363 : ** which of course include polygons; the emphasis here
1364 : ** is on (for example) usefulness in wire layout.
1365 : **
1366 : ***********************************************************************/
1367 :
1368 : /*----------------------------------------------------------
1369 : * String to path / path to string conversion.
1370 : * External format:
1371 : * "((xcoord, ycoord),... )"
1372 : * "[(xcoord, ycoord),... ]"
1373 : * "(xcoord, ycoord),... "
1374 : * "[xcoord, ycoord,... ]"
1375 : * Also support older format:
1376 : * "(closed, npts, xcoord, ycoord,... )"
1377 : *---------------------------------------------------------*/
1378 :
1379 : Datum
1380 54 : path_area(PG_FUNCTION_ARGS)
1381 : {
1382 54 : PATH *path = PG_GETARG_PATH_P(0);
1383 54 : float8 area = 0.0;
1384 : int i,
1385 : j;
1386 :
1387 54 : if (!path->closed)
1388 24 : PG_RETURN_NULL();
1389 :
1390 84 : for (i = 0; i < path->npts; i++)
1391 : {
1392 54 : j = (i + 1) % path->npts;
1393 54 : area = float8_pl(area, float8_mul(path->p[i].x, path->p[j].y));
1394 54 : area = float8_mi(area, float8_mul(path->p[i].y, path->p[j].x));
1395 : }
1396 :
1397 30 : PG_RETURN_FLOAT8(float8_div(fabs(area), 2.0));
1398 : }
1399 :
1400 :
1401 : Datum
1402 30922 : path_in(PG_FUNCTION_ARGS)
1403 : {
1404 30922 : char *str = PG_GETARG_CSTRING(0);
1405 30922 : Node *escontext = fcinfo->context;
1406 : PATH *path;
1407 : bool isopen;
1408 : char *s;
1409 : int npts;
1410 : int size;
1411 : int base_size;
1412 30922 : int depth = 0;
1413 :
1414 30922 : if ((npts = pair_count(str, ',')) <= 0)
1415 18 : ereturn(escontext, (Datum) 0,
1416 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
1417 : errmsg("invalid input syntax for type %s: \"%s\"",
1418 : "path", str)));
1419 :
1420 30904 : s = str;
1421 30916 : while (isspace((unsigned char) *s))
1422 12 : s++;
1423 :
1424 : /* skip single leading paren */
1425 30904 : if ((*s == LDELIM) && (strrchr(s, LDELIM) == s))
1426 : {
1427 24 : s++;
1428 24 : depth++;
1429 : }
1430 :
1431 30904 : base_size = sizeof(path->p[0]) * npts;
1432 30904 : size = offsetof(PATH, p) + base_size;
1433 :
1434 : /* Check for integer overflow */
1435 30904 : if (base_size / npts != sizeof(path->p[0]) || size <= base_size)
1436 0 : ereturn(escontext, (Datum) 0,
1437 : (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
1438 : errmsg("too many points requested")));
1439 :
1440 30904 : path = (PATH *) palloc(size);
1441 :
1442 30904 : SET_VARSIZE(path, size);
1443 30904 : path->npts = npts;
1444 :
1445 30904 : if (!path_decode(s, true, npts, &(path->p[0]), &isopen, &s, "path", str,
1446 : escontext))
1447 12 : PG_RETURN_NULL();
1448 :
1449 30880 : if (depth >= 1)
1450 : {
1451 24 : if (*s++ != RDELIM)
1452 6 : ereturn(escontext, (Datum) 0,
1453 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
1454 : errmsg("invalid input syntax for type %s: \"%s\"",
1455 : "path", str)));
1456 24 : while (isspace((unsigned char) *s))
1457 6 : s++;
1458 : }
1459 30874 : if (*s != '\0')
1460 6 : ereturn(escontext, (Datum) 0,
1461 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
1462 : errmsg("invalid input syntax for type %s: \"%s\"",
1463 : "path", str)));
1464 :
1465 30868 : path->closed = (!isopen);
1466 : /* prevent instability in unused pad bytes */
1467 30868 : path->dummy = 0;
1468 :
1469 30868 : PG_RETURN_PATH_P(path);
1470 : }
1471 :
1472 :
1473 : Datum
1474 60054 : path_out(PG_FUNCTION_ARGS)
1475 : {
1476 60054 : PATH *path = PG_GETARG_PATH_P(0);
1477 :
1478 60054 : PG_RETURN_CSTRING(path_encode(path->closed ? PATH_CLOSED : PATH_OPEN, path->npts, path->p));
1479 : }
1480 :
1481 : /*
1482 : * path_recv - converts external binary format to path
1483 : *
1484 : * External representation is closed flag (a boolean byte), int32 number
1485 : * of points, and the points.
1486 : */
1487 : Datum
1488 0 : path_recv(PG_FUNCTION_ARGS)
1489 : {
1490 0 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
1491 : PATH *path;
1492 : int closed;
1493 : int32 npts;
1494 : int32 i;
1495 : int size;
1496 :
1497 0 : closed = pq_getmsgbyte(buf);
1498 0 : npts = pq_getmsgint(buf, sizeof(int32));
1499 0 : if (npts <= 0 || npts >= (int32) ((INT_MAX - offsetof(PATH, p)) / sizeof(Point)))
1500 0 : ereport(ERROR,
1501 : (errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
1502 : errmsg("invalid number of points in external \"path\" value")));
1503 :
1504 0 : size = offsetof(PATH, p) + sizeof(path->p[0]) * npts;
1505 0 : path = (PATH *) palloc(size);
1506 :
1507 0 : SET_VARSIZE(path, size);
1508 0 : path->npts = npts;
1509 0 : path->closed = (closed ? 1 : 0);
1510 : /* prevent instability in unused pad bytes */
1511 0 : path->dummy = 0;
1512 :
1513 0 : for (i = 0; i < npts; i++)
1514 : {
1515 0 : path->p[i].x = pq_getmsgfloat8(buf);
1516 0 : path->p[i].y = pq_getmsgfloat8(buf);
1517 : }
1518 :
1519 0 : PG_RETURN_PATH_P(path);
1520 : }
1521 :
1522 : /*
1523 : * path_send - converts path to binary format
1524 : */
1525 : Datum
1526 0 : path_send(PG_FUNCTION_ARGS)
1527 : {
1528 0 : PATH *path = PG_GETARG_PATH_P(0);
1529 : StringInfoData buf;
1530 : int32 i;
1531 :
1532 0 : pq_begintypsend(&buf);
1533 0 : pq_sendbyte(&buf, path->closed ? 1 : 0);
1534 0 : pq_sendint32(&buf, path->npts);
1535 0 : for (i = 0; i < path->npts; i++)
1536 : {
1537 0 : pq_sendfloat8(&buf, path->p[i].x);
1538 0 : pq_sendfloat8(&buf, path->p[i].y);
1539 : }
1540 0 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
1541 : }
1542 :
1543 :
1544 : /*----------------------------------------------------------
1545 : * Relational operators.
1546 : * These are based on the path cardinality,
1547 : * as stupid as that sounds.
1548 : *
1549 : * Better relops and access methods coming soon.
1550 : *---------------------------------------------------------*/
1551 :
1552 : Datum
1553 486 : path_n_lt(PG_FUNCTION_ARGS)
1554 : {
1555 486 : PATH *p1 = PG_GETARG_PATH_P(0);
1556 486 : PATH *p2 = PG_GETARG_PATH_P(1);
1557 :
1558 486 : PG_RETURN_BOOL(p1->npts < p2->npts);
1559 : }
1560 :
1561 : Datum
1562 486 : path_n_gt(PG_FUNCTION_ARGS)
1563 : {
1564 486 : PATH *p1 = PG_GETARG_PATH_P(0);
1565 486 : PATH *p2 = PG_GETARG_PATH_P(1);
1566 :
1567 486 : PG_RETURN_BOOL(p1->npts > p2->npts);
1568 : }
1569 :
1570 : Datum
1571 488 : path_n_eq(PG_FUNCTION_ARGS)
1572 : {
1573 488 : PATH *p1 = PG_GETARG_PATH_P(0);
1574 488 : PATH *p2 = PG_GETARG_PATH_P(1);
1575 :
1576 488 : PG_RETURN_BOOL(p1->npts == p2->npts);
1577 : }
1578 :
1579 : Datum
1580 486 : path_n_le(PG_FUNCTION_ARGS)
1581 : {
1582 486 : PATH *p1 = PG_GETARG_PATH_P(0);
1583 486 : PATH *p2 = PG_GETARG_PATH_P(1);
1584 :
1585 486 : PG_RETURN_BOOL(p1->npts <= p2->npts);
1586 : }
1587 :
1588 : Datum
1589 486 : path_n_ge(PG_FUNCTION_ARGS)
1590 : {
1591 486 : PATH *p1 = PG_GETARG_PATH_P(0);
1592 486 : PATH *p2 = PG_GETARG_PATH_P(1);
1593 :
1594 486 : PG_RETURN_BOOL(p1->npts >= p2->npts);
1595 : }
1596 :
1597 : /*----------------------------------------------------------
1598 : * Conversion operators.
1599 : *---------------------------------------------------------*/
1600 :
1601 : Datum
1602 162 : path_isclosed(PG_FUNCTION_ARGS)
1603 : {
1604 162 : PATH *path = PG_GETARG_PATH_P(0);
1605 :
1606 162 : PG_RETURN_BOOL(path->closed);
1607 : }
1608 :
1609 : Datum
1610 114 : path_isopen(PG_FUNCTION_ARGS)
1611 : {
1612 114 : PATH *path = PG_GETARG_PATH_P(0);
1613 :
1614 114 : PG_RETURN_BOOL(!path->closed);
1615 : }
1616 :
1617 : Datum
1618 5430 : path_npoints(PG_FUNCTION_ARGS)
1619 : {
1620 5430 : PATH *path = PG_GETARG_PATH_P(0);
1621 :
1622 5430 : PG_RETURN_INT32(path->npts);
1623 : }
1624 :
1625 :
1626 : Datum
1627 78 : path_close(PG_FUNCTION_ARGS)
1628 : {
1629 78 : PATH *path = PG_GETARG_PATH_P_COPY(0);
1630 :
1631 78 : path->closed = true;
1632 :
1633 78 : PG_RETURN_PATH_P(path);
1634 : }
1635 :
1636 : Datum
1637 54 : path_open(PG_FUNCTION_ARGS)
1638 : {
1639 54 : PATH *path = PG_GETARG_PATH_P_COPY(0);
1640 :
1641 54 : path->closed = false;
1642 :
1643 54 : PG_RETURN_PATH_P(path);
1644 : }
1645 :
1646 :
1647 : /* path_inter -
1648 : * Does p1 intersect p2 at any point?
1649 : * Use bounding boxes for a quick (O(n)) check, then do a
1650 : * O(n^2) iterative edge check.
1651 : */
1652 : Datum
1653 1380918 : path_inter(PG_FUNCTION_ARGS)
1654 : {
1655 1380918 : PATH *p1 = PG_GETARG_PATH_P(0);
1656 1380918 : PATH *p2 = PG_GETARG_PATH_P(1);
1657 : BOX b1,
1658 : b2;
1659 : int i,
1660 : j;
1661 : LSEG seg1,
1662 : seg2;
1663 :
1664 : Assert(p1->npts > 0 && p2->npts > 0);
1665 :
1666 1380918 : b1.high.x = b1.low.x = p1->p[0].x;
1667 1380918 : b1.high.y = b1.low.y = p1->p[0].y;
1668 5252100 : for (i = 1; i < p1->npts; i++)
1669 : {
1670 3871182 : b1.high.x = float8_max(p1->p[i].x, b1.high.x);
1671 3871182 : b1.high.y = float8_max(p1->p[i].y, b1.high.y);
1672 3871182 : b1.low.x = float8_min(p1->p[i].x, b1.low.x);
1673 3871182 : b1.low.y = float8_min(p1->p[i].y, b1.low.y);
1674 : }
1675 1380918 : b2.high.x = b2.low.x = p2->p[0].x;
1676 1380918 : b2.high.y = b2.low.y = p2->p[0].y;
1677 3951324 : for (i = 1; i < p2->npts; i++)
1678 : {
1679 2570406 : b2.high.x = float8_max(p2->p[i].x, b2.high.x);
1680 2570406 : b2.high.y = float8_max(p2->p[i].y, b2.high.y);
1681 2570406 : b2.low.x = float8_min(p2->p[i].x, b2.low.x);
1682 2570406 : b2.low.y = float8_min(p2->p[i].y, b2.low.y);
1683 : }
1684 1380918 : if (!box_ov(&b1, &b2))
1685 1347420 : PG_RETURN_BOOL(false);
1686 :
1687 : /* pairwise check lseg intersections */
1688 165012 : for (i = 0; i < p1->npts; i++)
1689 : {
1690 : int iprev;
1691 :
1692 138888 : if (i > 0)
1693 105390 : iprev = i - 1;
1694 : else
1695 : {
1696 33498 : if (!p1->closed)
1697 7986 : continue;
1698 25512 : iprev = p1->npts - 1; /* include the closure segment */
1699 : }
1700 :
1701 435666 : for (j = 0; j < p2->npts; j++)
1702 : {
1703 : int jprev;
1704 :
1705 312138 : if (j > 0)
1706 181236 : jprev = j - 1;
1707 : else
1708 : {
1709 130902 : if (!p2->closed)
1710 123738 : continue;
1711 7164 : jprev = p2->npts - 1; /* include the closure segment */
1712 : }
1713 :
1714 188400 : statlseg_construct(&seg1, &p1->p[iprev], &p1->p[i]);
1715 188400 : statlseg_construct(&seg2, &p2->p[jprev], &p2->p[j]);
1716 188400 : if (lseg_interpt_lseg(NULL, &seg1, &seg2))
1717 7374 : PG_RETURN_BOOL(true);
1718 : }
1719 : }
1720 :
1721 : /* if we dropped through, no two segs intersected */
1722 26124 : PG_RETURN_BOOL(false);
1723 : }
1724 :
1725 : /* path_distance()
1726 : * This essentially does a cartesian product of the lsegs in the
1727 : * two paths, and finds the min distance between any two lsegs
1728 : */
1729 : Datum
1730 486 : path_distance(PG_FUNCTION_ARGS)
1731 : {
1732 486 : PATH *p1 = PG_GETARG_PATH_P(0);
1733 486 : PATH *p2 = PG_GETARG_PATH_P(1);
1734 486 : float8 min = 0.0; /* initialize to keep compiler quiet */
1735 486 : bool have_min = false;
1736 : float8 tmp;
1737 : int i,
1738 : j;
1739 : LSEG seg1,
1740 : seg2;
1741 :
1742 1512 : for (i = 0; i < p1->npts; i++)
1743 : {
1744 : int iprev;
1745 :
1746 1026 : if (i > 0)
1747 540 : iprev = i - 1;
1748 : else
1749 : {
1750 486 : if (!p1->closed)
1751 216 : continue;
1752 270 : iprev = p1->npts - 1; /* include the closure segment */
1753 : }
1754 :
1755 2520 : for (j = 0; j < p2->npts; j++)
1756 : {
1757 : int jprev;
1758 :
1759 1710 : if (j > 0)
1760 900 : jprev = j - 1;
1761 : else
1762 : {
1763 810 : if (!p2->closed)
1764 360 : continue;
1765 450 : jprev = p2->npts - 1; /* include the closure segment */
1766 : }
1767 :
1768 1350 : statlseg_construct(&seg1, &p1->p[iprev], &p1->p[i]);
1769 1350 : statlseg_construct(&seg2, &p2->p[jprev], &p2->p[j]);
1770 :
1771 1350 : tmp = lseg_closept_lseg(NULL, &seg1, &seg2);
1772 1350 : if (!have_min || float8_lt(tmp, min))
1773 : {
1774 582 : min = tmp;
1775 582 : have_min = true;
1776 : }
1777 : }
1778 : }
1779 :
1780 486 : if (!have_min)
1781 0 : PG_RETURN_NULL();
1782 :
1783 486 : PG_RETURN_FLOAT8(min);
1784 : }
1785 :
1786 :
1787 : /*----------------------------------------------------------
1788 : * "Arithmetic" operations.
1789 : *---------------------------------------------------------*/
1790 :
1791 : Datum
1792 54 : path_length(PG_FUNCTION_ARGS)
1793 : {
1794 54 : PATH *path = PG_GETARG_PATH_P(0);
1795 54 : float8 result = 0.0;
1796 : int i;
1797 :
1798 168 : for (i = 0; i < path->npts; i++)
1799 : {
1800 : int iprev;
1801 :
1802 114 : if (i > 0)
1803 60 : iprev = i - 1;
1804 : else
1805 : {
1806 54 : if (!path->closed)
1807 24 : continue;
1808 30 : iprev = path->npts - 1; /* include the closure segment */
1809 : }
1810 :
1811 90 : result = float8_pl(result, point_dt(&path->p[iprev], &path->p[i]));
1812 : }
1813 :
1814 54 : PG_RETURN_FLOAT8(result);
1815 : }
1816 :
1817 : /***********************************************************************
1818 : **
1819 : ** Routines for 2D points.
1820 : **
1821 : ***********************************************************************/
1822 :
1823 : /*----------------------------------------------------------
1824 : * String to point, point to string conversion.
1825 : * External format:
1826 : * "(x,y)"
1827 : * "x,y"
1828 : *---------------------------------------------------------*/
1829 :
1830 : Datum
1831 1762 : point_in(PG_FUNCTION_ARGS)
1832 : {
1833 1762 : char *str = PG_GETARG_CSTRING(0);
1834 1762 : Point *point = (Point *) palloc(sizeof(Point));
1835 :
1836 : /* Ignore failure from pair_decode, since our return value won't matter */
1837 1762 : pair_decode(str, &point->x, &point->y, NULL, "point", str, fcinfo->context);
1838 1732 : PG_RETURN_POINT_P(point);
1839 : }
1840 :
1841 : Datum
1842 259540 : point_out(PG_FUNCTION_ARGS)
1843 : {
1844 259540 : Point *pt = PG_GETARG_POINT_P(0);
1845 :
1846 259540 : PG_RETURN_CSTRING(path_encode(PATH_NONE, 1, pt));
1847 : }
1848 :
1849 : /*
1850 : * point_recv - converts external binary format to point
1851 : */
1852 : Datum
1853 18 : point_recv(PG_FUNCTION_ARGS)
1854 : {
1855 18 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
1856 : Point *point;
1857 :
1858 18 : point = (Point *) palloc(sizeof(Point));
1859 18 : point->x = pq_getmsgfloat8(buf);
1860 18 : point->y = pq_getmsgfloat8(buf);
1861 18 : PG_RETURN_POINT_P(point);
1862 : }
1863 :
1864 : /*
1865 : * point_send - converts point to binary format
1866 : */
1867 : Datum
1868 18 : point_send(PG_FUNCTION_ARGS)
1869 : {
1870 18 : Point *pt = PG_GETARG_POINT_P(0);
1871 : StringInfoData buf;
1872 :
1873 18 : pq_begintypsend(&buf);
1874 18 : pq_sendfloat8(&buf, pt->x);
1875 18 : pq_sendfloat8(&buf, pt->y);
1876 18 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
1877 : }
1878 :
1879 :
1880 : /*
1881 : * Initialize a point
1882 : */
1883 : static inline void
1884 5221370 : point_construct(Point *result, float8 x, float8 y)
1885 : {
1886 5221370 : result->x = x;
1887 5221370 : result->y = y;
1888 5221370 : }
1889 :
1890 :
1891 : /*----------------------------------------------------------
1892 : * Relational operators for Points.
1893 : * Since we do have a sense of coordinates being
1894 : * "equal" to a given accuracy (point_vert, point_horiz),
1895 : * the other ops must preserve that sense. This means
1896 : * that results may, strictly speaking, be a lie (unless
1897 : * EPSILON = 0.0).
1898 : *---------------------------------------------------------*/
1899 :
1900 : Datum
1901 707390 : point_left(PG_FUNCTION_ARGS)
1902 : {
1903 707390 : Point *pt1 = PG_GETARG_POINT_P(0);
1904 707390 : Point *pt2 = PG_GETARG_POINT_P(1);
1905 :
1906 707390 : PG_RETURN_BOOL(FPlt(pt1->x, pt2->x));
1907 : }
1908 :
1909 : Datum
1910 16828016 : point_right(PG_FUNCTION_ARGS)
1911 : {
1912 16828016 : Point *pt1 = PG_GETARG_POINT_P(0);
1913 16828016 : Point *pt2 = PG_GETARG_POINT_P(1);
1914 :
1915 16828016 : PG_RETURN_BOOL(FPgt(pt1->x, pt2->x));
1916 : }
1917 :
1918 : Datum
1919 17064526 : point_above(PG_FUNCTION_ARGS)
1920 : {
1921 17064526 : Point *pt1 = PG_GETARG_POINT_P(0);
1922 17064526 : Point *pt2 = PG_GETARG_POINT_P(1);
1923 :
1924 17064526 : PG_RETURN_BOOL(FPgt(pt1->y, pt2->y));
1925 : }
1926 :
1927 : Datum
1928 1250266 : point_below(PG_FUNCTION_ARGS)
1929 : {
1930 1250266 : Point *pt1 = PG_GETARG_POINT_P(0);
1931 1250266 : Point *pt2 = PG_GETARG_POINT_P(1);
1932 :
1933 1250266 : PG_RETURN_BOOL(FPlt(pt1->y, pt2->y));
1934 : }
1935 :
1936 : Datum
1937 497800 : point_vert(PG_FUNCTION_ARGS)
1938 : {
1939 497800 : Point *pt1 = PG_GETARG_POINT_P(0);
1940 497800 : Point *pt2 = PG_GETARG_POINT_P(1);
1941 :
1942 497800 : PG_RETURN_BOOL(FPeq(pt1->x, pt2->x));
1943 : }
1944 :
1945 : Datum
1946 531322 : point_horiz(PG_FUNCTION_ARGS)
1947 : {
1948 531322 : Point *pt1 = PG_GETARG_POINT_P(0);
1949 531322 : Point *pt2 = PG_GETARG_POINT_P(1);
1950 :
1951 531322 : PG_RETURN_BOOL(FPeq(pt1->y, pt2->y));
1952 : }
1953 :
1954 : Datum
1955 80204 : point_eq(PG_FUNCTION_ARGS)
1956 : {
1957 80204 : Point *pt1 = PG_GETARG_POINT_P(0);
1958 80204 : Point *pt2 = PG_GETARG_POINT_P(1);
1959 :
1960 80204 : PG_RETURN_BOOL(point_eq_point(pt1, pt2));
1961 : }
1962 :
1963 : Datum
1964 702 : point_ne(PG_FUNCTION_ARGS)
1965 : {
1966 702 : Point *pt1 = PG_GETARG_POINT_P(0);
1967 702 : Point *pt2 = PG_GETARG_POINT_P(1);
1968 :
1969 702 : PG_RETURN_BOOL(!point_eq_point(pt1, pt2));
1970 : }
1971 :
1972 :
1973 : /*
1974 : * Check whether the two points are the same
1975 : */
1976 : static inline bool
1977 303394 : point_eq_point(Point *pt1, Point *pt2)
1978 : {
1979 : /* If any NaNs are involved, insist on exact equality */
1980 303394 : if (unlikely(isnan(pt1->x) || isnan(pt1->y) ||
1981 : isnan(pt2->x) || isnan(pt2->y)))
1982 426 : return (float8_eq(pt1->x, pt2->x) && float8_eq(pt1->y, pt2->y));
1983 :
1984 302968 : return (FPeq(pt1->x, pt2->x) && FPeq(pt1->y, pt2->y));
1985 : }
1986 :
1987 :
1988 : /*----------------------------------------------------------
1989 : * "Arithmetic" operators on points.
1990 : *---------------------------------------------------------*/
1991 :
1992 : Datum
1993 739050 : point_distance(PG_FUNCTION_ARGS)
1994 : {
1995 739050 : Point *pt1 = PG_GETARG_POINT_P(0);
1996 739050 : Point *pt2 = PG_GETARG_POINT_P(1);
1997 :
1998 739050 : PG_RETURN_FLOAT8(point_dt(pt1, pt2));
1999 : }
2000 :
2001 : static inline float8
2002 15546120 : point_dt(Point *pt1, Point *pt2)
2003 : {
2004 15546120 : return HYPOT(float8_mi(pt1->x, pt2->x), float8_mi(pt1->y, pt2->y));
2005 : }
2006 :
2007 : Datum
2008 600 : point_slope(PG_FUNCTION_ARGS)
2009 : {
2010 600 : Point *pt1 = PG_GETARG_POINT_P(0);
2011 600 : Point *pt2 = PG_GETARG_POINT_P(1);
2012 :
2013 600 : PG_RETURN_FLOAT8(point_sl(pt1, pt2));
2014 : }
2015 :
2016 :
2017 : /*
2018 : * Return slope of two points
2019 : *
2020 : * Note that this function returns Inf when the points are the same.
2021 : */
2022 : static inline float8
2023 3849204 : point_sl(Point *pt1, Point *pt2)
2024 : {
2025 3849204 : if (FPeq(pt1->x, pt2->x))
2026 428502 : return get_float8_infinity();
2027 3420702 : if (FPeq(pt1->y, pt2->y))
2028 424494 : return 0.0;
2029 2996208 : return float8_div(float8_mi(pt1->y, pt2->y), float8_mi(pt1->x, pt2->x));
2030 : }
2031 :
2032 :
2033 : /*
2034 : * Return inverse slope of two points
2035 : *
2036 : * Note that this function returns 0.0 when the points are the same.
2037 : */
2038 : static inline float8
2039 906480 : point_invsl(Point *pt1, Point *pt2)
2040 : {
2041 906480 : if (FPeq(pt1->x, pt2->x))
2042 358608 : return 0.0;
2043 547872 : if (FPeq(pt1->y, pt2->y))
2044 351204 : return get_float8_infinity();
2045 196668 : return float8_div(float8_mi(pt1->x, pt2->x), float8_mi(pt2->y, pt1->y));
2046 : }
2047 :
2048 :
2049 : /***********************************************************************
2050 : **
2051 : ** Routines for 2D line segments.
2052 : **
2053 : ***********************************************************************/
2054 :
2055 : /*----------------------------------------------------------
2056 : * String to lseg, lseg to string conversion.
2057 : * External forms: "[(x1, y1), (x2, y2)]"
2058 : * "(x1, y1), (x2, y2)"
2059 : * "x1, y1, x2, y2"
2060 : * closed form ok "((x1, y1), (x2, y2))"
2061 : * (old form) "(x1, y1, x2, y2)"
2062 : *---------------------------------------------------------*/
2063 :
2064 : Datum
2065 106 : lseg_in(PG_FUNCTION_ARGS)
2066 : {
2067 106 : char *str = PG_GETARG_CSTRING(0);
2068 106 : Node *escontext = fcinfo->context;
2069 106 : LSEG *lseg = (LSEG *) palloc(sizeof(LSEG));
2070 : bool isopen;
2071 :
2072 106 : if (!path_decode(str, true, 2, &lseg->p[0], &isopen, NULL, "lseg", str,
2073 : escontext))
2074 12 : PG_RETURN_NULL();
2075 :
2076 70 : PG_RETURN_LSEG_P(lseg);
2077 : }
2078 :
2079 :
2080 : Datum
2081 7326 : lseg_out(PG_FUNCTION_ARGS)
2082 : {
2083 7326 : LSEG *ls = PG_GETARG_LSEG_P(0);
2084 :
2085 7326 : PG_RETURN_CSTRING(path_encode(PATH_OPEN, 2, &ls->p[0]));
2086 : }
2087 :
2088 : /*
2089 : * lseg_recv - converts external binary format to lseg
2090 : */
2091 : Datum
2092 0 : lseg_recv(PG_FUNCTION_ARGS)
2093 : {
2094 0 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
2095 : LSEG *lseg;
2096 :
2097 0 : lseg = (LSEG *) palloc(sizeof(LSEG));
2098 :
2099 0 : lseg->p[0].x = pq_getmsgfloat8(buf);
2100 0 : lseg->p[0].y = pq_getmsgfloat8(buf);
2101 0 : lseg->p[1].x = pq_getmsgfloat8(buf);
2102 0 : lseg->p[1].y = pq_getmsgfloat8(buf);
2103 :
2104 0 : PG_RETURN_LSEG_P(lseg);
2105 : }
2106 :
2107 : /*
2108 : * lseg_send - converts lseg to binary format
2109 : */
2110 : Datum
2111 0 : lseg_send(PG_FUNCTION_ARGS)
2112 : {
2113 0 : LSEG *ls = PG_GETARG_LSEG_P(0);
2114 : StringInfoData buf;
2115 :
2116 0 : pq_begintypsend(&buf);
2117 0 : pq_sendfloat8(&buf, ls->p[0].x);
2118 0 : pq_sendfloat8(&buf, ls->p[0].y);
2119 0 : pq_sendfloat8(&buf, ls->p[1].x);
2120 0 : pq_sendfloat8(&buf, ls->p[1].y);
2121 0 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
2122 : }
2123 :
2124 :
2125 : /* lseg_construct -
2126 : * form a LSEG from two Points.
2127 : */
2128 : Datum
2129 6 : lseg_construct(PG_FUNCTION_ARGS)
2130 : {
2131 6 : Point *pt1 = PG_GETARG_POINT_P(0);
2132 6 : Point *pt2 = PG_GETARG_POINT_P(1);
2133 6 : LSEG *result = (LSEG *) palloc(sizeof(LSEG));
2134 :
2135 6 : statlseg_construct(result, pt1, pt2);
2136 :
2137 6 : PG_RETURN_LSEG_P(result);
2138 : }
2139 :
2140 : /* like lseg_construct, but assume space already allocated */
2141 : static inline void
2142 1010922 : statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2)
2143 : {
2144 1010922 : lseg->p[0].x = pt1->x;
2145 1010922 : lseg->p[0].y = pt1->y;
2146 1010922 : lseg->p[1].x = pt2->x;
2147 1010922 : lseg->p[1].y = pt2->y;
2148 1010922 : }
2149 :
2150 :
2151 : /*
2152 : * Return slope of the line segment
2153 : */
2154 : static inline float8
2155 3848070 : lseg_sl(LSEG *lseg)
2156 : {
2157 3848070 : return point_sl(&lseg->p[0], &lseg->p[1]);
2158 : }
2159 :
2160 :
2161 : /*
2162 : * Return inverse slope of the line segment
2163 : */
2164 : static inline float8
2165 384 : lseg_invsl(LSEG *lseg)
2166 : {
2167 384 : return point_invsl(&lseg->p[0], &lseg->p[1]);
2168 : }
2169 :
2170 :
2171 : Datum
2172 48 : lseg_length(PG_FUNCTION_ARGS)
2173 : {
2174 48 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2175 :
2176 48 : PG_RETURN_FLOAT8(point_dt(&lseg->p[0], &lseg->p[1]));
2177 : }
2178 :
2179 : /*----------------------------------------------------------
2180 : * Relative position routines.
2181 : *---------------------------------------------------------*/
2182 :
2183 : /*
2184 : ** find intersection of the two lines, and see if it falls on
2185 : ** both segments.
2186 : */
2187 : Datum
2188 25368 : lseg_intersect(PG_FUNCTION_ARGS)
2189 : {
2190 25368 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2191 25368 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2192 :
2193 25368 : PG_RETURN_BOOL(lseg_interpt_lseg(NULL, l1, l2));
2194 : }
2195 :
2196 :
2197 : Datum
2198 384 : lseg_parallel(PG_FUNCTION_ARGS)
2199 : {
2200 384 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2201 384 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2202 :
2203 384 : PG_RETURN_BOOL(FPeq(lseg_sl(l1), lseg_sl(l2)));
2204 : }
2205 :
2206 : /*
2207 : * Determine if two line segments are perpendicular.
2208 : */
2209 : Datum
2210 384 : lseg_perp(PG_FUNCTION_ARGS)
2211 : {
2212 384 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2213 384 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2214 :
2215 384 : PG_RETURN_BOOL(FPeq(lseg_sl(l1), lseg_invsl(l2)));
2216 : }
2217 :
2218 : Datum
2219 48 : lseg_vertical(PG_FUNCTION_ARGS)
2220 : {
2221 48 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2222 :
2223 48 : PG_RETURN_BOOL(FPeq(lseg->p[0].x, lseg->p[1].x));
2224 : }
2225 :
2226 : Datum
2227 48 : lseg_horizontal(PG_FUNCTION_ARGS)
2228 : {
2229 48 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2230 :
2231 48 : PG_RETURN_BOOL(FPeq(lseg->p[0].y, lseg->p[1].y));
2232 : }
2233 :
2234 :
2235 : Datum
2236 386 : lseg_eq(PG_FUNCTION_ARGS)
2237 : {
2238 386 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2239 386 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2240 :
2241 386 : PG_RETURN_BOOL(point_eq_point(&l1->p[0], &l2->p[0]) &&
2242 : point_eq_point(&l1->p[1], &l2->p[1]));
2243 : }
2244 :
2245 : Datum
2246 384 : lseg_ne(PG_FUNCTION_ARGS)
2247 : {
2248 384 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2249 384 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2250 :
2251 384 : PG_RETURN_BOOL(!point_eq_point(&l1->p[0], &l2->p[0]) ||
2252 : !point_eq_point(&l1->p[1], &l2->p[1]));
2253 : }
2254 :
2255 : Datum
2256 384 : lseg_lt(PG_FUNCTION_ARGS)
2257 : {
2258 384 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2259 384 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2260 :
2261 384 : PG_RETURN_BOOL(FPlt(point_dt(&l1->p[0], &l1->p[1]),
2262 : point_dt(&l2->p[0], &l2->p[1])));
2263 : }
2264 :
2265 : Datum
2266 384 : lseg_le(PG_FUNCTION_ARGS)
2267 : {
2268 384 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2269 384 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2270 :
2271 384 : PG_RETURN_BOOL(FPle(point_dt(&l1->p[0], &l1->p[1]),
2272 : point_dt(&l2->p[0], &l2->p[1])));
2273 : }
2274 :
2275 : Datum
2276 384 : lseg_gt(PG_FUNCTION_ARGS)
2277 : {
2278 384 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2279 384 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2280 :
2281 384 : PG_RETURN_BOOL(FPgt(point_dt(&l1->p[0], &l1->p[1]),
2282 : point_dt(&l2->p[0], &l2->p[1])));
2283 : }
2284 :
2285 : Datum
2286 384 : lseg_ge(PG_FUNCTION_ARGS)
2287 : {
2288 384 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2289 384 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2290 :
2291 384 : PG_RETURN_BOOL(FPge(point_dt(&l1->p[0], &l1->p[1]),
2292 : point_dt(&l2->p[0], &l2->p[1])));
2293 : }
2294 :
2295 :
2296 : /*----------------------------------------------------------
2297 : * Line arithmetic routines.
2298 : *---------------------------------------------------------*/
2299 :
2300 : /* lseg_distance -
2301 : * If two segments don't intersect, then the closest
2302 : * point will be from one of the endpoints to the other
2303 : * segment.
2304 : */
2305 : Datum
2306 384 : lseg_distance(PG_FUNCTION_ARGS)
2307 : {
2308 384 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2309 384 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2310 :
2311 384 : PG_RETURN_FLOAT8(lseg_closept_lseg(NULL, l1, l2));
2312 : }
2313 :
2314 :
2315 : Datum
2316 96 : lseg_center(PG_FUNCTION_ARGS)
2317 : {
2318 96 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2319 : Point *result;
2320 :
2321 96 : result = (Point *) palloc(sizeof(Point));
2322 :
2323 96 : result->x = float8_div(float8_pl(lseg->p[0].x, lseg->p[1].x), 2.0);
2324 96 : result->y = float8_div(float8_pl(lseg->p[0].y, lseg->p[1].y), 2.0);
2325 :
2326 96 : PG_RETURN_POINT_P(result);
2327 : }
2328 :
2329 :
2330 : /*
2331 : * Return whether the two segments intersect. If *result is not NULL,
2332 : * it is set to the intersection point.
2333 : *
2334 : * This function is almost perfectly symmetric, even though it doesn't look
2335 : * like it. See lseg_interpt_line() for the other half of it.
2336 : */
2337 : static bool
2338 1468350 : lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2)
2339 : {
2340 : Point interpt;
2341 : LINE tmp;
2342 :
2343 1468350 : line_construct(&tmp, &l2->p[0], lseg_sl(l2));
2344 1468350 : if (!lseg_interpt_line(&interpt, l1, &tmp))
2345 1385856 : return false;
2346 :
2347 : /*
2348 : * If the line intersection point isn't within l2, there is no valid
2349 : * segment intersection point at all.
2350 : */
2351 82494 : if (!lseg_contain_point(l2, &interpt))
2352 61782 : return false;
2353 :
2354 20712 : if (result != NULL)
2355 6714 : *result = interpt;
2356 :
2357 20712 : return true;
2358 : }
2359 :
2360 : Datum
2361 5748 : lseg_interpt(PG_FUNCTION_ARGS)
2362 : {
2363 5748 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2364 5748 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2365 : Point *result;
2366 :
2367 5748 : result = (Point *) palloc(sizeof(Point));
2368 :
2369 5748 : if (!lseg_interpt_lseg(result, l1, l2))
2370 384 : PG_RETURN_NULL();
2371 5364 : PG_RETURN_POINT_P(result);
2372 : }
2373 :
2374 : /***********************************************************************
2375 : **
2376 : ** Routines for position comparisons of differently-typed
2377 : ** 2D objects.
2378 : **
2379 : ***********************************************************************/
2380 :
2381 : /*---------------------------------------------------------------------
2382 : * dist_
2383 : * Minimum distance from one object to another.
2384 : *-------------------------------------------------------------------*/
2385 :
2386 : /*
2387 : * Distance from a point to a line
2388 : */
2389 : Datum
2390 600 : dist_pl(PG_FUNCTION_ARGS)
2391 : {
2392 600 : Point *pt = PG_GETARG_POINT_P(0);
2393 600 : LINE *line = PG_GETARG_LINE_P(1);
2394 :
2395 600 : PG_RETURN_FLOAT8(line_closept_point(NULL, line, pt));
2396 : }
2397 :
2398 : /*
2399 : * Distance from a line to a point
2400 : */
2401 : Datum
2402 600 : dist_lp(PG_FUNCTION_ARGS)
2403 : {
2404 600 : LINE *line = PG_GETARG_LINE_P(0);
2405 600 : Point *pt = PG_GETARG_POINT_P(1);
2406 :
2407 600 : PG_RETURN_FLOAT8(line_closept_point(NULL, line, pt));
2408 : }
2409 :
2410 : /*
2411 : * Distance from a point to a lseg
2412 : */
2413 : Datum
2414 480 : dist_ps(PG_FUNCTION_ARGS)
2415 : {
2416 480 : Point *pt = PG_GETARG_POINT_P(0);
2417 480 : LSEG *lseg = PG_GETARG_LSEG_P(1);
2418 :
2419 480 : PG_RETURN_FLOAT8(lseg_closept_point(NULL, lseg, pt));
2420 : }
2421 :
2422 : /*
2423 : * Distance from a lseg to a point
2424 : */
2425 : Datum
2426 480 : dist_sp(PG_FUNCTION_ARGS)
2427 : {
2428 480 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2429 480 : Point *pt = PG_GETARG_POINT_P(1);
2430 :
2431 480 : PG_RETURN_FLOAT8(lseg_closept_point(NULL, lseg, pt));
2432 : }
2433 :
2434 : static float8
2435 1080 : dist_ppath_internal(Point *pt, PATH *path)
2436 : {
2437 1080 : float8 result = 0.0; /* keep compiler quiet */
2438 1080 : bool have_min = false;
2439 : float8 tmp;
2440 : int i;
2441 : LSEG lseg;
2442 :
2443 : Assert(path->npts > 0);
2444 :
2445 : /*
2446 : * The distance from a point to a path is the smallest distance from the
2447 : * point to any of its constituent segments.
2448 : */
2449 3360 : for (i = 0; i < path->npts; i++)
2450 : {
2451 : int iprev;
2452 :
2453 2280 : if (i > 0)
2454 1200 : iprev = i - 1;
2455 : else
2456 : {
2457 1080 : if (!path->closed)
2458 480 : continue;
2459 600 : iprev = path->npts - 1; /* Include the closure segment */
2460 : }
2461 :
2462 1800 : statlseg_construct(&lseg, &path->p[iprev], &path->p[i]);
2463 1800 : tmp = lseg_closept_point(NULL, &lseg, pt);
2464 1800 : if (!have_min || float8_lt(tmp, result))
2465 : {
2466 1128 : result = tmp;
2467 1128 : have_min = true;
2468 : }
2469 : }
2470 :
2471 1080 : return result;
2472 : }
2473 :
2474 : /*
2475 : * Distance from a point to a path
2476 : */
2477 : Datum
2478 540 : dist_ppath(PG_FUNCTION_ARGS)
2479 : {
2480 540 : Point *pt = PG_GETARG_POINT_P(0);
2481 540 : PATH *path = PG_GETARG_PATH_P(1);
2482 :
2483 540 : PG_RETURN_FLOAT8(dist_ppath_internal(pt, path));
2484 : }
2485 :
2486 : /*
2487 : * Distance from a path to a point
2488 : */
2489 : Datum
2490 540 : dist_pathp(PG_FUNCTION_ARGS)
2491 : {
2492 540 : PATH *path = PG_GETARG_PATH_P(0);
2493 540 : Point *pt = PG_GETARG_POINT_P(1);
2494 :
2495 540 : PG_RETURN_FLOAT8(dist_ppath_internal(pt, path));
2496 : }
2497 :
2498 : /*
2499 : * Distance from a point to a box
2500 : */
2501 : Datum
2502 426 : dist_pb(PG_FUNCTION_ARGS)
2503 : {
2504 426 : Point *pt = PG_GETARG_POINT_P(0);
2505 426 : BOX *box = PG_GETARG_BOX_P(1);
2506 :
2507 426 : PG_RETURN_FLOAT8(box_closept_point(NULL, box, pt));
2508 : }
2509 :
2510 : /*
2511 : * Distance from a box to a point
2512 : */
2513 : Datum
2514 155262 : dist_bp(PG_FUNCTION_ARGS)
2515 : {
2516 155262 : BOX *box = PG_GETARG_BOX_P(0);
2517 155262 : Point *pt = PG_GETARG_POINT_P(1);
2518 :
2519 155262 : PG_RETURN_FLOAT8(box_closept_point(NULL, box, pt));
2520 : }
2521 :
2522 : /*
2523 : * Distance from a lseg to a line
2524 : */
2525 : Datum
2526 480 : dist_sl(PG_FUNCTION_ARGS)
2527 : {
2528 480 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2529 480 : LINE *line = PG_GETARG_LINE_P(1);
2530 :
2531 480 : PG_RETURN_FLOAT8(lseg_closept_line(NULL, lseg, line));
2532 : }
2533 :
2534 : /*
2535 : * Distance from a line to a lseg
2536 : */
2537 : Datum
2538 480 : dist_ls(PG_FUNCTION_ARGS)
2539 : {
2540 480 : LINE *line = PG_GETARG_LINE_P(0);
2541 480 : LSEG *lseg = PG_GETARG_LSEG_P(1);
2542 :
2543 480 : PG_RETURN_FLOAT8(lseg_closept_line(NULL, lseg, line));
2544 : }
2545 :
2546 : /*
2547 : * Distance from a lseg to a box
2548 : */
2549 : Datum
2550 240 : dist_sb(PG_FUNCTION_ARGS)
2551 : {
2552 240 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2553 240 : BOX *box = PG_GETARG_BOX_P(1);
2554 :
2555 240 : PG_RETURN_FLOAT8(box_closept_lseg(NULL, box, lseg));
2556 : }
2557 :
2558 : /*
2559 : * Distance from a box to a lseg
2560 : */
2561 : Datum
2562 240 : dist_bs(PG_FUNCTION_ARGS)
2563 : {
2564 240 : BOX *box = PG_GETARG_BOX_P(0);
2565 240 : LSEG *lseg = PG_GETARG_LSEG_P(1);
2566 :
2567 240 : PG_RETURN_FLOAT8(box_closept_lseg(NULL, box, lseg));
2568 : }
2569 :
2570 : static float8
2571 336 : dist_cpoly_internal(CIRCLE *circle, POLYGON *poly)
2572 : {
2573 : float8 result;
2574 :
2575 : /* calculate distance to center, and subtract radius */
2576 336 : result = float8_mi(dist_ppoly_internal(&circle->center, poly),
2577 : circle->radius);
2578 336 : if (result < 0.0)
2579 180 : result = 0.0;
2580 :
2581 336 : return result;
2582 : }
2583 :
2584 : /*
2585 : * Distance from a circle to a polygon
2586 : */
2587 : Datum
2588 336 : dist_cpoly(PG_FUNCTION_ARGS)
2589 : {
2590 336 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
2591 336 : POLYGON *poly = PG_GETARG_POLYGON_P(1);
2592 :
2593 336 : PG_RETURN_FLOAT8(dist_cpoly_internal(circle, poly));
2594 : }
2595 :
2596 : /*
2597 : * Distance from a polygon to a circle
2598 : */
2599 : Datum
2600 0 : dist_polyc(PG_FUNCTION_ARGS)
2601 : {
2602 0 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
2603 0 : CIRCLE *circle = PG_GETARG_CIRCLE_P(1);
2604 :
2605 0 : PG_RETURN_FLOAT8(dist_cpoly_internal(circle, poly));
2606 : }
2607 :
2608 : /*
2609 : * Distance from a point to a polygon
2610 : */
2611 : Datum
2612 420 : dist_ppoly(PG_FUNCTION_ARGS)
2613 : {
2614 420 : Point *point = PG_GETARG_POINT_P(0);
2615 420 : POLYGON *poly = PG_GETARG_POLYGON_P(1);
2616 :
2617 420 : PG_RETURN_FLOAT8(dist_ppoly_internal(point, poly));
2618 : }
2619 :
2620 : Datum
2621 34308 : dist_polyp(PG_FUNCTION_ARGS)
2622 : {
2623 34308 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
2624 34308 : Point *point = PG_GETARG_POINT_P(1);
2625 :
2626 34308 : PG_RETURN_FLOAT8(dist_ppoly_internal(point, poly));
2627 : }
2628 :
2629 : static float8
2630 35064 : dist_ppoly_internal(Point *pt, POLYGON *poly)
2631 : {
2632 : float8 result;
2633 : float8 d;
2634 : int i;
2635 : LSEG seg;
2636 :
2637 35064 : if (point_inside(pt, poly->npts, poly->p) != 0)
2638 180 : return 0.0;
2639 :
2640 : /* initialize distance with segment between first and last points */
2641 34884 : seg.p[0].x = poly->p[0].x;
2642 34884 : seg.p[0].y = poly->p[0].y;
2643 34884 : seg.p[1].x = poly->p[poly->npts - 1].x;
2644 34884 : seg.p[1].y = poly->p[poly->npts - 1].y;
2645 34884 : result = lseg_closept_point(NULL, &seg, pt);
2646 :
2647 : /* check distances for other segments */
2648 258012 : for (i = 0; i < poly->npts - 1; i++)
2649 : {
2650 223128 : seg.p[0].x = poly->p[i].x;
2651 223128 : seg.p[0].y = poly->p[i].y;
2652 223128 : seg.p[1].x = poly->p[i + 1].x;
2653 223128 : seg.p[1].y = poly->p[i + 1].y;
2654 223128 : d = lseg_closept_point(NULL, &seg, pt);
2655 223128 : if (float8_lt(d, result))
2656 6588 : result = d;
2657 : }
2658 :
2659 34884 : return result;
2660 : }
2661 :
2662 :
2663 : /*---------------------------------------------------------------------
2664 : * interpt_
2665 : * Intersection point of objects.
2666 : * We choose to ignore the "point" of intersection between
2667 : * lines and boxes, since there are typically two.
2668 : *-------------------------------------------------------------------*/
2669 :
2670 : /*
2671 : * Return whether the line segment intersect with the line. If *result is not
2672 : * NULL, it is set to the intersection point.
2673 : */
2674 : static bool
2675 2377290 : lseg_interpt_line(Point *result, LSEG *lseg, LINE *line)
2676 : {
2677 : Point interpt;
2678 : LINE tmp;
2679 :
2680 : /*
2681 : * First, we promote the line segment to a line, because we know how to
2682 : * find the intersection point of two lines. If they don't have an
2683 : * intersection point, we are done.
2684 : */
2685 2377290 : line_construct(&tmp, &lseg->p[0], lseg_sl(lseg));
2686 2377290 : if (!line_interpt_line(&interpt, &tmp, line))
2687 12162 : return false;
2688 :
2689 : /*
2690 : * Then, we check whether the intersection point is actually on the line
2691 : * segment.
2692 : */
2693 2365128 : if (!lseg_contain_point(lseg, &interpt))
2694 2270652 : return false;
2695 94476 : if (result != NULL)
2696 : {
2697 : /*
2698 : * If there is an intersection, then check explicitly for matching
2699 : * endpoints since there may be rounding effects with annoying LSB
2700 : * residue.
2701 : */
2702 94092 : if (point_eq_point(&lseg->p[0], &interpt))
2703 6612 : *result = lseg->p[0];
2704 87480 : else if (point_eq_point(&lseg->p[1], &interpt))
2705 13254 : *result = lseg->p[1];
2706 : else
2707 74226 : *result = interpt;
2708 : }
2709 :
2710 94476 : return true;
2711 : }
2712 :
2713 : /*---------------------------------------------------------------------
2714 : * close_
2715 : * Point of closest proximity between objects.
2716 : *-------------------------------------------------------------------*/
2717 :
2718 : /*
2719 : * If *result is not NULL, it is set to the intersection point of a
2720 : * perpendicular of the line through the point. Returns the distance
2721 : * of those two points.
2722 : */
2723 : static float8
2724 1793160 : line_closept_point(Point *result, LINE *line, Point *point)
2725 : {
2726 : Point closept;
2727 : LINE tmp;
2728 :
2729 : /*
2730 : * We drop a perpendicular to find the intersection point. Ordinarily we
2731 : * should always find it, but that can fail in the presence of NaN
2732 : * coordinates, and perhaps even from simple roundoff issues.
2733 : */
2734 1793160 : line_construct(&tmp, point, line_invsl(line));
2735 1793160 : if (!line_interpt_line(&closept, &tmp, line))
2736 : {
2737 0 : if (result != NULL)
2738 0 : *result = *point;
2739 :
2740 0 : return get_float8_nan();
2741 : }
2742 :
2743 1793160 : if (result != NULL)
2744 600 : *result = closept;
2745 :
2746 1793160 : return point_dt(&closept, point);
2747 : }
2748 :
2749 : Datum
2750 600 : close_pl(PG_FUNCTION_ARGS)
2751 : {
2752 600 : Point *pt = PG_GETARG_POINT_P(0);
2753 600 : LINE *line = PG_GETARG_LINE_P(1);
2754 : Point *result;
2755 :
2756 600 : result = (Point *) palloc(sizeof(Point));
2757 :
2758 600 : if (isnan(line_closept_point(result, line, pt)))
2759 216 : PG_RETURN_NULL();
2760 :
2761 384 : PG_RETURN_POINT_P(result);
2762 : }
2763 :
2764 :
2765 : /*
2766 : * Closest point on line segment to specified point.
2767 : *
2768 : * If *result is not NULL, set it to the closest point on the line segment
2769 : * to the point. Returns the distance of the two points.
2770 : */
2771 : static float8
2772 906096 : lseg_closept_point(Point *result, LSEG *lseg, Point *pt)
2773 : {
2774 : Point closept;
2775 : LINE tmp;
2776 :
2777 : /*
2778 : * To find the closest point, we draw a perpendicular line from the point
2779 : * to the line segment.
2780 : */
2781 906096 : line_construct(&tmp, pt, point_invsl(&lseg->p[0], &lseg->p[1]));
2782 906096 : lseg_closept_line(&closept, lseg, &tmp);
2783 :
2784 906096 : if (result != NULL)
2785 476166 : *result = closept;
2786 :
2787 906096 : return point_dt(&closept, pt);
2788 : }
2789 :
2790 : Datum
2791 480 : close_ps(PG_FUNCTION_ARGS)
2792 : {
2793 480 : Point *pt = PG_GETARG_POINT_P(0);
2794 480 : LSEG *lseg = PG_GETARG_LSEG_P(1);
2795 : Point *result;
2796 :
2797 480 : result = (Point *) palloc(sizeof(Point));
2798 :
2799 480 : if (isnan(lseg_closept_point(result, lseg, pt)))
2800 96 : PG_RETURN_NULL();
2801 :
2802 384 : PG_RETURN_POINT_P(result);
2803 : }
2804 :
2805 :
2806 : /*
2807 : * Closest point on line segment to line segment
2808 : */
2809 : static float8
2810 5268 : lseg_closept_lseg(Point *result, LSEG *on_lseg, LSEG *to_lseg)
2811 : {
2812 : Point point;
2813 : float8 dist,
2814 : d;
2815 :
2816 : /* First, we handle the case when the line segments are intersecting. */
2817 5268 : if (lseg_interpt_lseg(result, on_lseg, to_lseg))
2818 24 : return 0.0;
2819 :
2820 : /*
2821 : * Then, we find the closest points from the endpoints of the second line
2822 : * segment, and keep the closest one.
2823 : */
2824 5244 : dist = lseg_closept_point(result, on_lseg, &to_lseg->p[0]);
2825 5244 : d = lseg_closept_point(&point, on_lseg, &to_lseg->p[1]);
2826 5244 : if (float8_lt(d, dist))
2827 : {
2828 1746 : dist = d;
2829 1746 : if (result != NULL)
2830 816 : *result = point;
2831 : }
2832 :
2833 : /* The closest point can still be one of the endpoints, so we test them. */
2834 5244 : d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[0]);
2835 5244 : if (float8_lt(d, dist))
2836 : {
2837 1152 : dist = d;
2838 1152 : if (result != NULL)
2839 744 : *result = on_lseg->p[0];
2840 : }
2841 5244 : d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[1]);
2842 5244 : if (float8_lt(d, dist))
2843 : {
2844 444 : dist = d;
2845 444 : if (result != NULL)
2846 252 : *result = on_lseg->p[1];
2847 : }
2848 :
2849 5244 : return dist;
2850 : }
2851 :
2852 : Datum
2853 384 : close_lseg(PG_FUNCTION_ARGS)
2854 : {
2855 384 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2856 384 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2857 : Point *result;
2858 :
2859 384 : if (lseg_sl(l1) == lseg_sl(l2))
2860 78 : PG_RETURN_NULL();
2861 :
2862 306 : result = (Point *) palloc(sizeof(Point));
2863 :
2864 306 : if (isnan(lseg_closept_lseg(result, l2, l1)))
2865 90 : PG_RETURN_NULL();
2866 :
2867 216 : PG_RETURN_POINT_P(result);
2868 : }
2869 :
2870 :
2871 : /*
2872 : * Closest point on or in box to specified point.
2873 : *
2874 : * If *result is not NULL, set it to the closest point on the box to the
2875 : * given point, and return the distance of the two points.
2876 : */
2877 : static float8
2878 155988 : box_closept_point(Point *result, BOX *box, Point *pt)
2879 : {
2880 : float8 dist,
2881 : d;
2882 : Point point,
2883 : closept;
2884 : LSEG lseg;
2885 :
2886 155988 : if (box_contain_point(box, pt))
2887 : {
2888 42 : if (result != NULL)
2889 6 : *result = *pt;
2890 :
2891 42 : return 0.0;
2892 : }
2893 :
2894 : /* pairwise check lseg distances */
2895 155946 : point.x = box->low.x;
2896 155946 : point.y = box->high.y;
2897 155946 : statlseg_construct(&lseg, &box->low, &point);
2898 155946 : dist = lseg_closept_point(result, &lseg, pt);
2899 :
2900 155946 : statlseg_construct(&lseg, &box->high, &point);
2901 155946 : d = lseg_closept_point(&closept, &lseg, pt);
2902 155946 : if (float8_lt(d, dist))
2903 : {
2904 7434 : dist = d;
2905 7434 : if (result != NULL)
2906 54 : *result = closept;
2907 : }
2908 :
2909 155946 : point.x = box->high.x;
2910 155946 : point.y = box->low.y;
2911 155946 : statlseg_construct(&lseg, &box->low, &point);
2912 155946 : d = lseg_closept_point(&closept, &lseg, pt);
2913 155946 : if (float8_lt(d, dist))
2914 : {
2915 7938 : dist = d;
2916 7938 : if (result != NULL)
2917 6 : *result = closept;
2918 : }
2919 :
2920 155946 : statlseg_construct(&lseg, &box->high, &point);
2921 155946 : d = lseg_closept_point(&closept, &lseg, pt);
2922 155946 : if (float8_lt(d, dist))
2923 : {
2924 36 : dist = d;
2925 36 : if (result != NULL)
2926 12 : *result = closept;
2927 : }
2928 :
2929 155946 : return dist;
2930 : }
2931 :
2932 : Datum
2933 300 : close_pb(PG_FUNCTION_ARGS)
2934 : {
2935 300 : Point *pt = PG_GETARG_POINT_P(0);
2936 300 : BOX *box = PG_GETARG_BOX_P(1);
2937 : Point *result;
2938 :
2939 300 : result = (Point *) palloc(sizeof(Point));
2940 :
2941 300 : if (isnan(box_closept_point(result, box, pt)))
2942 30 : PG_RETURN_NULL();
2943 :
2944 270 : PG_RETURN_POINT_P(result);
2945 : }
2946 :
2947 : /*
2948 : * Closest point on line segment to line.
2949 : *
2950 : * Return the distance between the line and the closest point of the line
2951 : * segment to the line. If *result is not NULL, set it to that point.
2952 : *
2953 : * NOTE: When the lines are parallel, endpoints of one of the line segment
2954 : * are FPeq(), in presence of NaN or Infinite coordinates, or perhaps =
2955 : * even because of simple roundoff issues, there may not be a single closest
2956 : * point. We are likely to set the result to the second endpoint in these
2957 : * cases.
2958 : */
2959 : static float8
2960 907482 : lseg_closept_line(Point *result, LSEG *lseg, LINE *line)
2961 : {
2962 : float8 dist1,
2963 : dist2;
2964 :
2965 907482 : if (lseg_interpt_line(result, lseg, line))
2966 11802 : return 0.0;
2967 :
2968 895680 : dist1 = line_closept_point(NULL, line, &lseg->p[0]);
2969 895680 : dist2 = line_closept_point(NULL, line, &lseg->p[1]);
2970 :
2971 895680 : if (dist1 < dist2)
2972 : {
2973 475710 : if (result != NULL)
2974 475506 : *result = lseg->p[0];
2975 :
2976 475710 : return dist1;
2977 : }
2978 : else
2979 : {
2980 419970 : if (result != NULL)
2981 419418 : *result = lseg->p[1];
2982 :
2983 419970 : return dist2;
2984 : }
2985 : }
2986 :
2987 : Datum
2988 480 : close_ls(PG_FUNCTION_ARGS)
2989 : {
2990 480 : LINE *line = PG_GETARG_LINE_P(0);
2991 480 : LSEG *lseg = PG_GETARG_LSEG_P(1);
2992 : Point *result;
2993 :
2994 480 : if (lseg_sl(lseg) == line_sl(line))
2995 54 : PG_RETURN_NULL();
2996 :
2997 426 : result = (Point *) palloc(sizeof(Point));
2998 :
2999 426 : if (isnan(lseg_closept_line(result, lseg, line)))
3000 144 : PG_RETURN_NULL();
3001 :
3002 282 : PG_RETURN_POINT_P(result);
3003 : }
3004 :
3005 :
3006 : /*
3007 : * Closest point on or in box to line segment.
3008 : *
3009 : * Returns the distance between the closest point on or in the box to
3010 : * the line segment. If *result is not NULL, it is set to that point.
3011 : */
3012 : static float8
3013 720 : box_closept_lseg(Point *result, BOX *box, LSEG *lseg)
3014 : {
3015 : float8 dist,
3016 : d;
3017 : Point point,
3018 : closept;
3019 : LSEG bseg;
3020 :
3021 720 : if (box_interpt_lseg(result, box, lseg))
3022 144 : return 0.0;
3023 :
3024 : /* pairwise check lseg distances */
3025 576 : point.x = box->low.x;
3026 576 : point.y = box->high.y;
3027 576 : statlseg_construct(&bseg, &box->low, &point);
3028 576 : dist = lseg_closept_lseg(result, &bseg, lseg);
3029 :
3030 576 : statlseg_construct(&bseg, &box->high, &point);
3031 576 : d = lseg_closept_lseg(&closept, &bseg, lseg);
3032 576 : if (float8_lt(d, dist))
3033 : {
3034 144 : dist = d;
3035 144 : if (result != NULL)
3036 48 : *result = closept;
3037 : }
3038 :
3039 576 : point.x = box->high.x;
3040 576 : point.y = box->low.y;
3041 576 : statlseg_construct(&bseg, &box->low, &point);
3042 576 : d = lseg_closept_lseg(&closept, &bseg, lseg);
3043 576 : if (float8_lt(d, dist))
3044 : {
3045 18 : dist = d;
3046 18 : if (result != NULL)
3047 6 : *result = closept;
3048 : }
3049 :
3050 576 : statlseg_construct(&bseg, &box->high, &point);
3051 576 : d = lseg_closept_lseg(&closept, &bseg, lseg);
3052 576 : if (float8_lt(d, dist))
3053 : {
3054 18 : dist = d;
3055 18 : if (result != NULL)
3056 6 : *result = closept;
3057 : }
3058 :
3059 576 : return dist;
3060 : }
3061 :
3062 : Datum
3063 240 : close_sb(PG_FUNCTION_ARGS)
3064 : {
3065 240 : LSEG *lseg = PG_GETARG_LSEG_P(0);
3066 240 : BOX *box = PG_GETARG_BOX_P(1);
3067 : Point *result;
3068 :
3069 240 : result = (Point *) palloc(sizeof(Point));
3070 :
3071 240 : if (isnan(box_closept_lseg(result, box, lseg)))
3072 30 : PG_RETURN_NULL();
3073 :
3074 210 : PG_RETURN_POINT_P(result);
3075 : }
3076 :
3077 :
3078 : /*---------------------------------------------------------------------
3079 : * on_
3080 : * Whether one object lies completely within another.
3081 : *-------------------------------------------------------------------*/
3082 :
3083 : /*
3084 : * Does the point satisfy the equation?
3085 : */
3086 : static bool
3087 1104 : line_contain_point(LINE *line, Point *point)
3088 : {
3089 1104 : return FPzero(float8_pl(float8_pl(float8_mul(line->A, point->x),
3090 : float8_mul(line->B, point->y)),
3091 : line->C));
3092 : }
3093 :
3094 : Datum
3095 600 : on_pl(PG_FUNCTION_ARGS)
3096 : {
3097 600 : Point *pt = PG_GETARG_POINT_P(0);
3098 600 : LINE *line = PG_GETARG_LINE_P(1);
3099 :
3100 600 : PG_RETURN_BOOL(line_contain_point(line, pt));
3101 : }
3102 :
3103 :
3104 : /*
3105 : * Determine colinearity by detecting a triangle inequality.
3106 : * This algorithm seems to behave nicely even with lsb residues - tgl 1997-07-09
3107 : */
3108 : static bool
3109 4014858 : lseg_contain_point(LSEG *lseg, Point *pt)
3110 : {
3111 8029716 : return FPeq(point_dt(pt, &lseg->p[0]) +
3112 4014858 : point_dt(pt, &lseg->p[1]),
3113 : point_dt(&lseg->p[0], &lseg->p[1]));
3114 : }
3115 :
3116 : Datum
3117 480 : on_ps(PG_FUNCTION_ARGS)
3118 : {
3119 480 : Point *pt = PG_GETARG_POINT_P(0);
3120 480 : LSEG *lseg = PG_GETARG_LSEG_P(1);
3121 :
3122 480 : PG_RETURN_BOOL(lseg_contain_point(lseg, pt));
3123 : }
3124 :
3125 :
3126 : /*
3127 : * Check whether the point is in the box or on its border
3128 : */
3129 : static bool
3130 437784 : box_contain_point(BOX *box, Point *point)
3131 : {
3132 253782 : return box->high.x >= point->x && box->low.x <= point->x &&
3133 691566 : box->high.y >= point->y && box->low.y <= point->y;
3134 : }
3135 :
3136 : Datum
3137 138252 : on_pb(PG_FUNCTION_ARGS)
3138 : {
3139 138252 : Point *pt = PG_GETARG_POINT_P(0);
3140 138252 : BOX *box = PG_GETARG_BOX_P(1);
3141 :
3142 138252 : PG_RETURN_BOOL(box_contain_point(box, pt));
3143 : }
3144 :
3145 : Datum
3146 142686 : box_contain_pt(PG_FUNCTION_ARGS)
3147 : {
3148 142686 : BOX *box = PG_GETARG_BOX_P(0);
3149 142686 : Point *pt = PG_GETARG_POINT_P(1);
3150 :
3151 142686 : PG_RETURN_BOOL(box_contain_point(box, pt));
3152 : }
3153 :
3154 : /* on_ppath -
3155 : * Whether a point lies within (on) a polyline.
3156 : * If open, we have to (groan) check each segment.
3157 : * (uses same algorithm as for point intersecting segment - tgl 1997-07-09)
3158 : * If closed, we use the old O(n) ray method for point-in-polygon.
3159 : * The ray is horizontal, from pt out to the right.
3160 : * Each segment that crosses the ray counts as an
3161 : * intersection; note that an endpoint or edge may touch
3162 : * but not cross.
3163 : * (we can do p-in-p in lg(n), but it takes preprocessing)
3164 : */
3165 : Datum
3166 600 : on_ppath(PG_FUNCTION_ARGS)
3167 : {
3168 600 : Point *pt = PG_GETARG_POINT_P(0);
3169 600 : PATH *path = PG_GETARG_PATH_P(1);
3170 : int i,
3171 : n;
3172 : float8 a,
3173 : b;
3174 :
3175 : /*-- OPEN --*/
3176 600 : if (!path->closed)
3177 : {
3178 300 : n = path->npts - 1;
3179 300 : a = point_dt(pt, &path->p[0]);
3180 708 : for (i = 0; i < n; i++)
3181 : {
3182 438 : b = point_dt(pt, &path->p[i + 1]);
3183 438 : if (FPeq(float8_pl(a, b), point_dt(&path->p[i], &path->p[i + 1])))
3184 30 : PG_RETURN_BOOL(true);
3185 408 : a = b;
3186 : }
3187 270 : PG_RETURN_BOOL(false);
3188 : }
3189 :
3190 : /*-- CLOSED --*/
3191 300 : PG_RETURN_BOOL(point_inside(pt, path->npts, path->p) != 0);
3192 : }
3193 :
3194 :
3195 : /*
3196 : * Check whether the line segment is on the line or close enough
3197 : *
3198 : * It is, if both of its points are on the line or close enough.
3199 : */
3200 : Datum
3201 480 : on_sl(PG_FUNCTION_ARGS)
3202 : {
3203 480 : LSEG *lseg = PG_GETARG_LSEG_P(0);
3204 480 : LINE *line = PG_GETARG_LINE_P(1);
3205 :
3206 480 : PG_RETURN_BOOL(line_contain_point(line, &lseg->p[0]) &&
3207 : line_contain_point(line, &lseg->p[1]));
3208 : }
3209 :
3210 :
3211 : /*
3212 : * Check whether the line segment is in the box or on its border
3213 : *
3214 : * It is, if both of its points are in the box or on its border.
3215 : */
3216 : static bool
3217 240 : box_contain_lseg(BOX *box, LSEG *lseg)
3218 : {
3219 258 : return box_contain_point(box, &lseg->p[0]) &&
3220 18 : box_contain_point(box, &lseg->p[1]);
3221 : }
3222 :
3223 : Datum
3224 240 : on_sb(PG_FUNCTION_ARGS)
3225 : {
3226 240 : LSEG *lseg = PG_GETARG_LSEG_P(0);
3227 240 : BOX *box = PG_GETARG_BOX_P(1);
3228 :
3229 240 : PG_RETURN_BOOL(box_contain_lseg(box, lseg));
3230 : }
3231 :
3232 : /*---------------------------------------------------------------------
3233 : * inter_
3234 : * Whether one object intersects another.
3235 : *-------------------------------------------------------------------*/
3236 :
3237 : Datum
3238 480 : inter_sl(PG_FUNCTION_ARGS)
3239 : {
3240 480 : LSEG *lseg = PG_GETARG_LSEG_P(0);
3241 480 : LINE *line = PG_GETARG_LINE_P(1);
3242 :
3243 480 : PG_RETURN_BOOL(lseg_interpt_line(NULL, lseg, line));
3244 : }
3245 :
3246 :
3247 : /*
3248 : * Do line segment and box intersect?
3249 : *
3250 : * Segment completely inside box counts as intersection.
3251 : * If you want only segments crossing box boundaries,
3252 : * try converting box to path first.
3253 : *
3254 : * This function also sets the *result to the closest point on the line
3255 : * segment to the center of the box when they overlap and the result is
3256 : * not NULL. It is somewhat arbitrary, but maybe the best we can do as
3257 : * there are typically two points they intersect.
3258 : *
3259 : * Optimize for non-intersection by checking for box intersection first.
3260 : * - thomas 1998-01-30
3261 : */
3262 : static bool
3263 960 : box_interpt_lseg(Point *result, BOX *box, LSEG *lseg)
3264 : {
3265 : BOX lbox;
3266 : LSEG bseg;
3267 : Point point;
3268 :
3269 960 : lbox.low.x = float8_min(lseg->p[0].x, lseg->p[1].x);
3270 960 : lbox.low.y = float8_min(lseg->p[0].y, lseg->p[1].y);
3271 960 : lbox.high.x = float8_max(lseg->p[0].x, lseg->p[1].x);
3272 960 : lbox.high.y = float8_max(lseg->p[0].y, lseg->p[1].y);
3273 :
3274 : /* nothing close to overlap? then not going to intersect */
3275 960 : if (!box_ov(&lbox, box))
3276 624 : return false;
3277 :
3278 336 : if (result != NULL)
3279 : {
3280 84 : box_cn(&point, box);
3281 84 : lseg_closept_point(result, lseg, &point);
3282 : }
3283 :
3284 : /* an endpoint of segment is inside box? then clearly intersects */
3285 600 : if (box_contain_point(box, &lseg->p[0]) ||
3286 264 : box_contain_point(box, &lseg->p[1]))
3287 96 : return true;
3288 :
3289 : /* pairwise check lseg intersections */
3290 240 : point.x = box->low.x;
3291 240 : point.y = box->high.y;
3292 240 : statlseg_construct(&bseg, &box->low, &point);
3293 240 : if (lseg_interpt_lseg(NULL, &bseg, lseg))
3294 96 : return true;
3295 :
3296 144 : statlseg_construct(&bseg, &box->high, &point);
3297 144 : if (lseg_interpt_lseg(NULL, &bseg, lseg))
3298 0 : return true;
3299 :
3300 144 : point.x = box->high.x;
3301 144 : point.y = box->low.y;
3302 144 : statlseg_construct(&bseg, &box->low, &point);
3303 144 : if (lseg_interpt_lseg(NULL, &bseg, lseg))
3304 0 : return true;
3305 :
3306 144 : statlseg_construct(&bseg, &box->high, &point);
3307 144 : if (lseg_interpt_lseg(NULL, &bseg, lseg))
3308 0 : return true;
3309 :
3310 : /* if we dropped through, no two segs intersected */
3311 144 : return false;
3312 : }
3313 :
3314 : Datum
3315 240 : inter_sb(PG_FUNCTION_ARGS)
3316 : {
3317 240 : LSEG *lseg = PG_GETARG_LSEG_P(0);
3318 240 : BOX *box = PG_GETARG_BOX_P(1);
3319 :
3320 240 : PG_RETURN_BOOL(box_interpt_lseg(NULL, box, lseg));
3321 : }
3322 :
3323 :
3324 : /* inter_lb()
3325 : * Do line and box intersect?
3326 : */
3327 : Datum
3328 300 : inter_lb(PG_FUNCTION_ARGS)
3329 : {
3330 300 : LINE *line = PG_GETARG_LINE_P(0);
3331 300 : BOX *box = PG_GETARG_BOX_P(1);
3332 : LSEG bseg;
3333 : Point p1,
3334 : p2;
3335 :
3336 : /* pairwise check lseg intersections */
3337 300 : p1.x = box->low.x;
3338 300 : p1.y = box->low.y;
3339 300 : p2.x = box->low.x;
3340 300 : p2.y = box->high.y;
3341 300 : statlseg_construct(&bseg, &p1, &p2);
3342 300 : if (lseg_interpt_line(NULL, &bseg, line))
3343 66 : PG_RETURN_BOOL(true);
3344 234 : p1.x = box->high.x;
3345 234 : p1.y = box->high.y;
3346 234 : statlseg_construct(&bseg, &p1, &p2);
3347 234 : if (lseg_interpt_line(NULL, &bseg, line))
3348 12 : PG_RETURN_BOOL(true);
3349 222 : p2.x = box->high.x;
3350 222 : p2.y = box->low.y;
3351 222 : statlseg_construct(&bseg, &p1, &p2);
3352 222 : if (lseg_interpt_line(NULL, &bseg, line))
3353 0 : PG_RETURN_BOOL(true);
3354 222 : p1.x = box->low.x;
3355 222 : p1.y = box->low.y;
3356 222 : statlseg_construct(&bseg, &p1, &p2);
3357 222 : if (lseg_interpt_line(NULL, &bseg, line))
3358 0 : PG_RETURN_BOOL(true);
3359 :
3360 : /* if we dropped through, no intersection */
3361 222 : PG_RETURN_BOOL(false);
3362 : }
3363 :
3364 : /*------------------------------------------------------------------
3365 : * The following routines define a data type and operator class for
3366 : * POLYGONS .... Part of which (the polygon's bounding box) is built on
3367 : * top of the BOX data type.
3368 : *
3369 : * make_bound_box - create the bounding box for the input polygon
3370 : *------------------------------------------------------------------*/
3371 :
3372 : /*---------------------------------------------------------------------
3373 : * Make the smallest bounding box for the given polygon.
3374 : *---------------------------------------------------------------------*/
3375 : static void
3376 60510 : make_bound_box(POLYGON *poly)
3377 : {
3378 : int i;
3379 : float8 x1,
3380 : y1,
3381 : x2,
3382 : y2;
3383 :
3384 : Assert(poly->npts > 0);
3385 :
3386 60510 : x1 = x2 = poly->p[0].x;
3387 60510 : y2 = y1 = poly->p[0].y;
3388 722078 : for (i = 1; i < poly->npts; i++)
3389 : {
3390 661568 : if (float8_lt(poly->p[i].x, x1))
3391 66 : x1 = poly->p[i].x;
3392 661568 : if (float8_gt(poly->p[i].x, x2))
3393 361066 : x2 = poly->p[i].x;
3394 661568 : if (float8_lt(poly->p[i].y, y1))
3395 180402 : y1 = poly->p[i].y;
3396 661568 : if (float8_gt(poly->p[i].y, y2))
3397 180610 : y2 = poly->p[i].y;
3398 : }
3399 :
3400 60510 : poly->boundbox.low.x = x1;
3401 60510 : poly->boundbox.high.x = x2;
3402 60510 : poly->boundbox.low.y = y1;
3403 60510 : poly->boundbox.high.y = y2;
3404 60510 : }
3405 :
3406 : /*------------------------------------------------------------------
3407 : * poly_in - read in the polygon from a string specification
3408 : *
3409 : * External format:
3410 : * "((x0,y0),...,(xn,yn))"
3411 : * "x0,y0,...,xn,yn"
3412 : * also supports the older style "(x1,...,xn,y1,...yn)"
3413 : *------------------------------------------------------------------*/
3414 : Datum
3415 406 : poly_in(PG_FUNCTION_ARGS)
3416 : {
3417 406 : char *str = PG_GETARG_CSTRING(0);
3418 406 : Node *escontext = fcinfo->context;
3419 : POLYGON *poly;
3420 : int npts;
3421 : int size;
3422 : int base_size;
3423 : bool isopen;
3424 :
3425 406 : if ((npts = pair_count(str, ',')) <= 0)
3426 36 : ereturn(escontext, (Datum) 0,
3427 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
3428 : errmsg("invalid input syntax for type %s: \"%s\"",
3429 : "polygon", str)));
3430 :
3431 370 : base_size = sizeof(poly->p[0]) * npts;
3432 370 : size = offsetof(POLYGON, p) + base_size;
3433 :
3434 : /* Check for integer overflow */
3435 370 : if (base_size / npts != sizeof(poly->p[0]) || size <= base_size)
3436 0 : ereturn(escontext, (Datum) 0,
3437 : (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
3438 : errmsg("too many points requested")));
3439 :
3440 370 : poly = (POLYGON *) palloc0(size); /* zero any holes */
3441 :
3442 370 : SET_VARSIZE(poly, size);
3443 370 : poly->npts = npts;
3444 :
3445 370 : if (!path_decode(str, false, npts, &(poly->p[0]), &isopen, NULL, "polygon",
3446 : str, escontext))
3447 12 : PG_RETURN_NULL();
3448 :
3449 352 : make_bound_box(poly);
3450 :
3451 352 : PG_RETURN_POLYGON_P(poly);
3452 : }
3453 :
3454 : /*---------------------------------------------------------------
3455 : * poly_out - convert internal POLYGON representation to the
3456 : * character string format "((f8,f8),...,(f8,f8))"
3457 : *---------------------------------------------------------------*/
3458 : Datum
3459 93666 : poly_out(PG_FUNCTION_ARGS)
3460 : {
3461 93666 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
3462 :
3463 93666 : PG_RETURN_CSTRING(path_encode(PATH_CLOSED, poly->npts, poly->p));
3464 : }
3465 :
3466 : /*
3467 : * poly_recv - converts external binary format to polygon
3468 : *
3469 : * External representation is int32 number of points, and the points.
3470 : * We recompute the bounding box on read, instead of trusting it to
3471 : * be valid. (Checking it would take just as long, so may as well
3472 : * omit it from external representation.)
3473 : */
3474 : Datum
3475 0 : poly_recv(PG_FUNCTION_ARGS)
3476 : {
3477 0 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
3478 : POLYGON *poly;
3479 : int32 npts;
3480 : int32 i;
3481 : int size;
3482 :
3483 0 : npts = pq_getmsgint(buf, sizeof(int32));
3484 0 : if (npts <= 0 || npts >= (int32) ((INT_MAX - offsetof(POLYGON, p)) / sizeof(Point)))
3485 0 : ereport(ERROR,
3486 : (errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
3487 : errmsg("invalid number of points in external \"polygon\" value")));
3488 :
3489 0 : size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * npts;
3490 0 : poly = (POLYGON *) palloc0(size); /* zero any holes */
3491 :
3492 0 : SET_VARSIZE(poly, size);
3493 0 : poly->npts = npts;
3494 :
3495 0 : for (i = 0; i < npts; i++)
3496 : {
3497 0 : poly->p[i].x = pq_getmsgfloat8(buf);
3498 0 : poly->p[i].y = pq_getmsgfloat8(buf);
3499 : }
3500 :
3501 0 : make_bound_box(poly);
3502 :
3503 0 : PG_RETURN_POLYGON_P(poly);
3504 : }
3505 :
3506 : /*
3507 : * poly_send - converts polygon to binary format
3508 : */
3509 : Datum
3510 0 : poly_send(PG_FUNCTION_ARGS)
3511 : {
3512 0 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
3513 : StringInfoData buf;
3514 : int32 i;
3515 :
3516 0 : pq_begintypsend(&buf);
3517 0 : pq_sendint32(&buf, poly->npts);
3518 0 : for (i = 0; i < poly->npts; i++)
3519 : {
3520 0 : pq_sendfloat8(&buf, poly->p[i].x);
3521 0 : pq_sendfloat8(&buf, poly->p[i].y);
3522 : }
3523 0 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
3524 : }
3525 :
3526 :
3527 : /*-------------------------------------------------------
3528 : * Is polygon A strictly left of polygon B? i.e. is
3529 : * the right most point of A left of the left most point
3530 : * of B?
3531 : *-------------------------------------------------------*/
3532 : Datum
3533 294 : poly_left(PG_FUNCTION_ARGS)
3534 : {
3535 294 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3536 294 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3537 : bool result;
3538 :
3539 294 : result = polya->boundbox.high.x < polyb->boundbox.low.x;
3540 :
3541 : /*
3542 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3543 : */
3544 294 : PG_FREE_IF_COPY(polya, 0);
3545 294 : PG_FREE_IF_COPY(polyb, 1);
3546 :
3547 294 : PG_RETURN_BOOL(result);
3548 : }
3549 :
3550 : /*-------------------------------------------------------
3551 : * Is polygon A overlapping or left of polygon B? i.e. is
3552 : * the right most point of A at or left of the right most point
3553 : * of B?
3554 : *-------------------------------------------------------*/
3555 : Datum
3556 294 : poly_overleft(PG_FUNCTION_ARGS)
3557 : {
3558 294 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3559 294 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3560 : bool result;
3561 :
3562 294 : result = polya->boundbox.high.x <= polyb->boundbox.high.x;
3563 :
3564 : /*
3565 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3566 : */
3567 294 : PG_FREE_IF_COPY(polya, 0);
3568 294 : PG_FREE_IF_COPY(polyb, 1);
3569 :
3570 294 : PG_RETURN_BOOL(result);
3571 : }
3572 :
3573 : /*-------------------------------------------------------
3574 : * Is polygon A strictly right of polygon B? i.e. is
3575 : * the left most point of A right of the right most point
3576 : * of B?
3577 : *-------------------------------------------------------*/
3578 : Datum
3579 294 : poly_right(PG_FUNCTION_ARGS)
3580 : {
3581 294 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3582 294 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3583 : bool result;
3584 :
3585 294 : result = polya->boundbox.low.x > polyb->boundbox.high.x;
3586 :
3587 : /*
3588 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3589 : */
3590 294 : PG_FREE_IF_COPY(polya, 0);
3591 294 : PG_FREE_IF_COPY(polyb, 1);
3592 :
3593 294 : PG_RETURN_BOOL(result);
3594 : }
3595 :
3596 : /*-------------------------------------------------------
3597 : * Is polygon A overlapping or right of polygon B? i.e. is
3598 : * the left most point of A at or right of the left most point
3599 : * of B?
3600 : *-------------------------------------------------------*/
3601 : Datum
3602 294 : poly_overright(PG_FUNCTION_ARGS)
3603 : {
3604 294 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3605 294 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3606 : bool result;
3607 :
3608 294 : result = polya->boundbox.low.x >= polyb->boundbox.low.x;
3609 :
3610 : /*
3611 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3612 : */
3613 294 : PG_FREE_IF_COPY(polya, 0);
3614 294 : PG_FREE_IF_COPY(polyb, 1);
3615 :
3616 294 : PG_RETURN_BOOL(result);
3617 : }
3618 :
3619 : /*-------------------------------------------------------
3620 : * Is polygon A strictly below polygon B? i.e. is
3621 : * the upper most point of A below the lower most point
3622 : * of B?
3623 : *-------------------------------------------------------*/
3624 : Datum
3625 294 : poly_below(PG_FUNCTION_ARGS)
3626 : {
3627 294 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3628 294 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3629 : bool result;
3630 :
3631 294 : result = polya->boundbox.high.y < polyb->boundbox.low.y;
3632 :
3633 : /*
3634 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3635 : */
3636 294 : PG_FREE_IF_COPY(polya, 0);
3637 294 : PG_FREE_IF_COPY(polyb, 1);
3638 :
3639 294 : PG_RETURN_BOOL(result);
3640 : }
3641 :
3642 : /*-------------------------------------------------------
3643 : * Is polygon A overlapping or below polygon B? i.e. is
3644 : * the upper most point of A at or below the upper most point
3645 : * of B?
3646 : *-------------------------------------------------------*/
3647 : Datum
3648 294 : poly_overbelow(PG_FUNCTION_ARGS)
3649 : {
3650 294 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3651 294 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3652 : bool result;
3653 :
3654 294 : result = polya->boundbox.high.y <= polyb->boundbox.high.y;
3655 :
3656 : /*
3657 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3658 : */
3659 294 : PG_FREE_IF_COPY(polya, 0);
3660 294 : PG_FREE_IF_COPY(polyb, 1);
3661 :
3662 294 : PG_RETURN_BOOL(result);
3663 : }
3664 :
3665 : /*-------------------------------------------------------
3666 : * Is polygon A strictly above polygon B? i.e. is
3667 : * the lower most point of A above the upper most point
3668 : * of B?
3669 : *-------------------------------------------------------*/
3670 : Datum
3671 294 : poly_above(PG_FUNCTION_ARGS)
3672 : {
3673 294 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3674 294 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3675 : bool result;
3676 :
3677 294 : result = polya->boundbox.low.y > polyb->boundbox.high.y;
3678 :
3679 : /*
3680 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3681 : */
3682 294 : PG_FREE_IF_COPY(polya, 0);
3683 294 : PG_FREE_IF_COPY(polyb, 1);
3684 :
3685 294 : PG_RETURN_BOOL(result);
3686 : }
3687 :
3688 : /*-------------------------------------------------------
3689 : * Is polygon A overlapping or above polygon B? i.e. is
3690 : * the lower most point of A at or above the lower most point
3691 : * of B?
3692 : *-------------------------------------------------------*/
3693 : Datum
3694 294 : poly_overabove(PG_FUNCTION_ARGS)
3695 : {
3696 294 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3697 294 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3698 : bool result;
3699 :
3700 294 : result = polya->boundbox.low.y >= polyb->boundbox.low.y;
3701 :
3702 : /*
3703 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3704 : */
3705 294 : PG_FREE_IF_COPY(polya, 0);
3706 294 : PG_FREE_IF_COPY(polyb, 1);
3707 :
3708 294 : PG_RETURN_BOOL(result);
3709 : }
3710 :
3711 :
3712 : /*-------------------------------------------------------
3713 : * Is polygon A the same as polygon B? i.e. are all the
3714 : * points the same?
3715 : * Check all points for matches in both forward and reverse
3716 : * direction since polygons are non-directional and are
3717 : * closed shapes.
3718 : *-------------------------------------------------------*/
3719 : Datum
3720 6296 : poly_same(PG_FUNCTION_ARGS)
3721 : {
3722 6296 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3723 6296 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3724 : bool result;
3725 :
3726 6296 : if (polya->npts != polyb->npts)
3727 204 : result = false;
3728 : else
3729 6092 : result = plist_same(polya->npts, polya->p, polyb->p);
3730 :
3731 : /*
3732 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3733 : */
3734 6296 : PG_FREE_IF_COPY(polya, 0);
3735 6296 : PG_FREE_IF_COPY(polyb, 1);
3736 :
3737 6296 : PG_RETURN_BOOL(result);
3738 : }
3739 :
3740 : /*-----------------------------------------------------------------
3741 : * Determine if polygon A overlaps polygon B
3742 : *-----------------------------------------------------------------*/
3743 : static bool
3744 29418 : poly_overlap_internal(POLYGON *polya, POLYGON *polyb)
3745 : {
3746 : bool result;
3747 :
3748 : Assert(polya->npts > 0 && polyb->npts > 0);
3749 :
3750 : /* Quick check by bounding box */
3751 29418 : result = box_ov(&polya->boundbox, &polyb->boundbox);
3752 :
3753 : /*
3754 : * Brute-force algorithm - try to find intersected edges, if so then
3755 : * polygons are overlapped else check is one polygon inside other or not
3756 : * by testing single point of them.
3757 : */
3758 29418 : if (result)
3759 : {
3760 : int ia,
3761 : ib;
3762 : LSEG sa,
3763 : sb;
3764 :
3765 : /* Init first of polya's edge with last point */
3766 10614 : sa.p[0] = polya->p[polya->npts - 1];
3767 10614 : result = false;
3768 :
3769 126546 : for (ia = 0; ia < polya->npts && !result; ia++)
3770 : {
3771 : /* Second point of polya's edge is a current one */
3772 115932 : sa.p[1] = polya->p[ia];
3773 :
3774 : /* Init first of polyb's edge with last point */
3775 115932 : sb.p[0] = polyb->p[polyb->npts - 1];
3776 :
3777 577014 : for (ib = 0; ib < polyb->npts && !result; ib++)
3778 : {
3779 461082 : sb.p[1] = polyb->p[ib];
3780 461082 : result = lseg_interpt_lseg(NULL, &sa, &sb);
3781 461082 : sb.p[0] = sb.p[1];
3782 : }
3783 :
3784 : /*
3785 : * move current endpoint to the first point of next edge
3786 : */
3787 115932 : sa.p[0] = sa.p[1];
3788 : }
3789 :
3790 10614 : if (!result)
3791 : {
3792 13902 : result = (point_inside(polya->p, polyb->npts, polyb->p) ||
3793 4428 : point_inside(polyb->p, polya->npts, polya->p));
3794 : }
3795 : }
3796 :
3797 29418 : return result;
3798 : }
3799 :
3800 : Datum
3801 29124 : poly_overlap(PG_FUNCTION_ARGS)
3802 : {
3803 29124 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3804 29124 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3805 : bool result;
3806 :
3807 29124 : result = poly_overlap_internal(polya, polyb);
3808 :
3809 : /*
3810 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3811 : */
3812 29124 : PG_FREE_IF_COPY(polya, 0);
3813 29124 : PG_FREE_IF_COPY(polyb, 1);
3814 :
3815 29124 : PG_RETURN_BOOL(result);
3816 : }
3817 :
3818 : /*
3819 : * Tests special kind of segment for in/out of polygon.
3820 : * Special kind means:
3821 : * - point a should be on segment s
3822 : * - segment (a,b) should not be contained by s
3823 : * Returns true if:
3824 : * - segment (a,b) is collinear to s and (a,b) is in polygon
3825 : * - segment (a,b) s not collinear to s. Note: that doesn't
3826 : * mean that segment is in polygon!
3827 : */
3828 :
3829 : static bool
3830 606 : touched_lseg_inside_poly(Point *a, Point *b, LSEG *s, POLYGON *poly, int start)
3831 : {
3832 : /* point a is on s, b is not */
3833 : LSEG t;
3834 :
3835 606 : t.p[0] = *a;
3836 606 : t.p[1] = *b;
3837 :
3838 606 : if (point_eq_point(a, s->p))
3839 : {
3840 72 : if (lseg_contain_point(&t, s->p + 1))
3841 0 : return lseg_inside_poly(b, s->p + 1, poly, start);
3842 : }
3843 534 : else if (point_eq_point(a, s->p + 1))
3844 : {
3845 156 : if (lseg_contain_point(&t, s->p))
3846 0 : return lseg_inside_poly(b, s->p, poly, start);
3847 : }
3848 378 : else if (lseg_contain_point(&t, s->p))
3849 : {
3850 0 : return lseg_inside_poly(b, s->p, poly, start);
3851 : }
3852 378 : else if (lseg_contain_point(&t, s->p + 1))
3853 : {
3854 0 : return lseg_inside_poly(b, s->p + 1, poly, start);
3855 : }
3856 :
3857 606 : return true; /* may be not true, but that will check later */
3858 : }
3859 :
3860 : /*
3861 : * Returns true if segment (a,b) is in polygon, option
3862 : * start is used for optimization - function checks
3863 : * polygon's edges starting from start
3864 : */
3865 : static bool
3866 198276 : lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start)
3867 : {
3868 : LSEG s,
3869 : t;
3870 : int i;
3871 198276 : bool res = true,
3872 198276 : intersection = false;
3873 :
3874 : /* since this function recurses, it could be driven to stack overflow */
3875 198276 : check_stack_depth();
3876 :
3877 198276 : t.p[0] = *a;
3878 198276 : t.p[1] = *b;
3879 198276 : s.p[0] = poly->p[(start == 0) ? (poly->npts - 1) : (start - 1)];
3880 :
3881 980694 : for (i = start; i < poly->npts && res; i++)
3882 : {
3883 : Point interpt;
3884 :
3885 782886 : CHECK_FOR_INTERRUPTS();
3886 :
3887 782886 : s.p[1] = poly->p[i];
3888 :
3889 782886 : if (lseg_contain_point(&s, t.p))
3890 : {
3891 786 : if (lseg_contain_point(&s, t.p + 1))
3892 468 : return true; /* t is contained by s */
3893 :
3894 : /* Y-cross */
3895 318 : res = touched_lseg_inside_poly(t.p, t.p + 1, &s, poly, i + 1);
3896 : }
3897 782100 : else if (lseg_contain_point(&s, t.p + 1))
3898 : {
3899 : /* Y-cross */
3900 288 : res = touched_lseg_inside_poly(t.p + 1, t.p, &s, poly, i + 1);
3901 : }
3902 781812 : else if (lseg_interpt_lseg(&interpt, &t, &s))
3903 : {
3904 : /*
3905 : * segments are X-crossing, go to check each subsegment
3906 : */
3907 :
3908 1350 : intersection = true;
3909 1350 : res = lseg_inside_poly(t.p, &interpt, poly, i + 1);
3910 1350 : if (res)
3911 1158 : res = lseg_inside_poly(t.p + 1, &interpt, poly, i + 1);
3912 : }
3913 :
3914 782418 : s.p[0] = s.p[1];
3915 : }
3916 :
3917 197808 : if (res && !intersection)
3918 : {
3919 : Point p;
3920 :
3921 : /*
3922 : * if X-intersection wasn't found, then check central point of tested
3923 : * segment. In opposite case we already check all subsegments
3924 : */
3925 196458 : p.x = float8_div(float8_pl(t.p[0].x, t.p[1].x), 2.0);
3926 196458 : p.y = float8_div(float8_pl(t.p[0].y, t.p[1].y), 2.0);
3927 :
3928 196458 : res = point_inside(&p, poly->npts, poly->p);
3929 : }
3930 :
3931 197808 : return res;
3932 : }
3933 :
3934 : /*
3935 : * Check whether the first polygon contains the second
3936 : */
3937 : static bool
3938 84930 : poly_contain_poly(POLYGON *contains_poly, POLYGON *contained_poly)
3939 : {
3940 : int i;
3941 : LSEG s;
3942 :
3943 : Assert(contains_poly->npts > 0 && contained_poly->npts > 0);
3944 :
3945 : /*
3946 : * Quick check to see if contained's bounding box is contained in
3947 : * contains' bb.
3948 : */
3949 84930 : if (!box_contain_box(&contains_poly->boundbox, &contained_poly->boundbox))
3950 57342 : return false;
3951 :
3952 27588 : s.p[0] = contained_poly->p[contained_poly->npts - 1];
3953 :
3954 210888 : for (i = 0; i < contained_poly->npts; i++)
3955 : {
3956 195768 : s.p[1] = contained_poly->p[i];
3957 195768 : if (!lseg_inside_poly(s.p, s.p + 1, contains_poly, 0))
3958 12468 : return false;
3959 183300 : s.p[0] = s.p[1];
3960 : }
3961 :
3962 15120 : return true;
3963 : }
3964 :
3965 : Datum
3966 384 : poly_contain(PG_FUNCTION_ARGS)
3967 : {
3968 384 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3969 384 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3970 : bool result;
3971 :
3972 384 : result = poly_contain_poly(polya, polyb);
3973 :
3974 : /*
3975 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3976 : */
3977 384 : PG_FREE_IF_COPY(polya, 0);
3978 384 : PG_FREE_IF_COPY(polyb, 1);
3979 :
3980 384 : PG_RETURN_BOOL(result);
3981 : }
3982 :
3983 :
3984 : /*-----------------------------------------------------------------
3985 : * Determine if polygon A is contained by polygon B
3986 : *-----------------------------------------------------------------*/
3987 : Datum
3988 84546 : poly_contained(PG_FUNCTION_ARGS)
3989 : {
3990 84546 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3991 84546 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3992 : bool result;
3993 :
3994 : /* Just switch the arguments and pass it off to poly_contain */
3995 84546 : result = poly_contain_poly(polyb, polya);
3996 :
3997 : /*
3998 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3999 : */
4000 84546 : PG_FREE_IF_COPY(polya, 0);
4001 84546 : PG_FREE_IF_COPY(polyb, 1);
4002 :
4003 84546 : PG_RETURN_BOOL(result);
4004 : }
4005 :
4006 :
4007 : Datum
4008 444 : poly_contain_pt(PG_FUNCTION_ARGS)
4009 : {
4010 444 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
4011 444 : Point *p = PG_GETARG_POINT_P(1);
4012 :
4013 444 : PG_RETURN_BOOL(point_inside(p, poly->npts, poly->p) != 0);
4014 : }
4015 :
4016 : Datum
4017 482 : pt_contained_poly(PG_FUNCTION_ARGS)
4018 : {
4019 482 : Point *p = PG_GETARG_POINT_P(0);
4020 482 : POLYGON *poly = PG_GETARG_POLYGON_P(1);
4021 :
4022 482 : PG_RETURN_BOOL(point_inside(p, poly->npts, poly->p) != 0);
4023 : }
4024 :
4025 :
4026 : Datum
4027 294 : poly_distance(PG_FUNCTION_ARGS)
4028 : {
4029 294 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
4030 294 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
4031 294 : float8 min = 0.0; /* initialize to keep compiler quiet */
4032 294 : bool have_min = false;
4033 : float8 tmp;
4034 : int i,
4035 : j;
4036 : LSEG seg1,
4037 : seg2;
4038 :
4039 : /*
4040 : * Distance is zero if polygons overlap. We must check this because the
4041 : * path distance will not give the right answer if one poly is entirely
4042 : * within the other.
4043 : */
4044 294 : if (poly_overlap_internal(polya, polyb))
4045 150 : PG_RETURN_FLOAT8(0.0);
4046 :
4047 : /*
4048 : * When they don't overlap, the distance calculation is identical to that
4049 : * for closed paths (i.e., we needn't care about the fact that polygons
4050 : * include their contained areas). See path_distance().
4051 : */
4052 528 : for (i = 0; i < polya->npts; i++)
4053 : {
4054 : int iprev;
4055 :
4056 384 : if (i > 0)
4057 240 : iprev = i - 1;
4058 : else
4059 144 : iprev = polya->npts - 1;
4060 :
4061 1308 : for (j = 0; j < polyb->npts; j++)
4062 : {
4063 : int jprev;
4064 :
4065 924 : if (j > 0)
4066 540 : jprev = j - 1;
4067 : else
4068 384 : jprev = polyb->npts - 1;
4069 :
4070 924 : statlseg_construct(&seg1, &polya->p[iprev], &polya->p[i]);
4071 924 : statlseg_construct(&seg2, &polyb->p[jprev], &polyb->p[j]);
4072 :
4073 924 : tmp = lseg_closept_lseg(NULL, &seg1, &seg2);
4074 924 : if (!have_min || float8_lt(tmp, min))
4075 : {
4076 192 : min = tmp;
4077 192 : have_min = true;
4078 : }
4079 : }
4080 : }
4081 :
4082 144 : if (!have_min)
4083 0 : PG_RETURN_NULL();
4084 :
4085 144 : PG_RETURN_FLOAT8(min);
4086 : }
4087 :
4088 :
4089 : /***********************************************************************
4090 : **
4091 : ** Routines for 2D points.
4092 : **
4093 : ***********************************************************************/
4094 :
4095 : Datum
4096 1053908 : construct_point(PG_FUNCTION_ARGS)
4097 : {
4098 1053908 : float8 x = PG_GETARG_FLOAT8(0);
4099 1053908 : float8 y = PG_GETARG_FLOAT8(1);
4100 : Point *result;
4101 :
4102 1053908 : result = (Point *) palloc(sizeof(Point));
4103 :
4104 1053908 : point_construct(result, x, y);
4105 :
4106 1053908 : PG_RETURN_POINT_P(result);
4107 : }
4108 :
4109 :
4110 : static inline void
4111 3072 : point_add_point(Point *result, Point *pt1, Point *pt2)
4112 : {
4113 3072 : point_construct(result,
4114 : float8_pl(pt1->x, pt2->x),
4115 : float8_pl(pt1->y, pt2->y));
4116 3072 : }
4117 :
4118 : Datum
4119 600 : point_add(PG_FUNCTION_ARGS)
4120 : {
4121 600 : Point *p1 = PG_GETARG_POINT_P(0);
4122 600 : Point *p2 = PG_GETARG_POINT_P(1);
4123 : Point *result;
4124 :
4125 600 : result = (Point *) palloc(sizeof(Point));
4126 :
4127 600 : point_add_point(result, p1, p2);
4128 :
4129 600 : PG_RETURN_POINT_P(result);
4130 : }
4131 :
4132 :
4133 : static inline void
4134 2820 : point_sub_point(Point *result, Point *pt1, Point *pt2)
4135 : {
4136 2820 : point_construct(result,
4137 : float8_mi(pt1->x, pt2->x),
4138 : float8_mi(pt1->y, pt2->y));
4139 2820 : }
4140 :
4141 : Datum
4142 600 : point_sub(PG_FUNCTION_ARGS)
4143 : {
4144 600 : Point *p1 = PG_GETARG_POINT_P(0);
4145 600 : Point *p2 = PG_GETARG_POINT_P(1);
4146 : Point *result;
4147 :
4148 600 : result = (Point *) palloc(sizeof(Point));
4149 :
4150 600 : point_sub_point(result, p1, p2);
4151 :
4152 600 : PG_RETURN_POINT_P(result);
4153 : }
4154 :
4155 :
4156 : static inline void
4157 2220 : point_mul_point(Point *result, Point *pt1, Point *pt2)
4158 : {
4159 2220 : point_construct(result,
4160 : float8_mi(float8_mul(pt1->x, pt2->x),
4161 : float8_mul(pt1->y, pt2->y)),
4162 : float8_pl(float8_mul(pt1->x, pt2->y),
4163 : float8_mul(pt1->y, pt2->x)));
4164 2214 : }
4165 :
4166 : Datum
4167 300 : point_mul(PG_FUNCTION_ARGS)
4168 : {
4169 300 : Point *p1 = PG_GETARG_POINT_P(0);
4170 300 : Point *p2 = PG_GETARG_POINT_P(1);
4171 : Point *result;
4172 :
4173 300 : result = (Point *) palloc(sizeof(Point));
4174 :
4175 300 : point_mul_point(result, p1, p2);
4176 :
4177 294 : PG_RETURN_POINT_P(result);
4178 : }
4179 :
4180 :
4181 : static inline void
4182 594 : point_div_point(Point *result, Point *pt1, Point *pt2)
4183 : {
4184 : float8 div;
4185 :
4186 594 : div = float8_pl(float8_mul(pt2->x, pt2->x), float8_mul(pt2->y, pt2->y));
4187 :
4188 582 : point_construct(result,
4189 : float8_div(float8_pl(float8_mul(pt1->x, pt2->x),
4190 : float8_mul(pt1->y, pt2->y)), div),
4191 : float8_div(float8_mi(float8_mul(pt1->y, pt2->x),
4192 : float8_mul(pt1->x, pt2->y)), div));
4193 564 : }
4194 :
4195 : Datum
4196 132 : point_div(PG_FUNCTION_ARGS)
4197 : {
4198 132 : Point *p1 = PG_GETARG_POINT_P(0);
4199 132 : Point *p2 = PG_GETARG_POINT_P(1);
4200 : Point *result;
4201 :
4202 132 : result = (Point *) palloc(sizeof(Point));
4203 :
4204 132 : point_div_point(result, p1, p2);
4205 :
4206 120 : PG_RETURN_POINT_P(result);
4207 : }
4208 :
4209 :
4210 : /***********************************************************************
4211 : **
4212 : ** Routines for 2D boxes.
4213 : **
4214 : ***********************************************************************/
4215 :
4216 : Datum
4217 241704 : points_box(PG_FUNCTION_ARGS)
4218 : {
4219 241704 : Point *p1 = PG_GETARG_POINT_P(0);
4220 241704 : Point *p2 = PG_GETARG_POINT_P(1);
4221 : BOX *result;
4222 :
4223 241704 : result = (BOX *) palloc(sizeof(BOX));
4224 :
4225 241704 : box_construct(result, p1, p2);
4226 :
4227 241704 : PG_RETURN_BOX_P(result);
4228 : }
4229 :
4230 : Datum
4231 300 : box_add(PG_FUNCTION_ARGS)
4232 : {
4233 300 : BOX *box = PG_GETARG_BOX_P(0);
4234 300 : Point *p = PG_GETARG_POINT_P(1);
4235 : BOX *result;
4236 :
4237 300 : result = (BOX *) palloc(sizeof(BOX));
4238 :
4239 300 : point_add_point(&result->high, &box->high, p);
4240 300 : point_add_point(&result->low, &box->low, p);
4241 :
4242 300 : PG_RETURN_BOX_P(result);
4243 : }
4244 :
4245 : Datum
4246 300 : box_sub(PG_FUNCTION_ARGS)
4247 : {
4248 300 : BOX *box = PG_GETARG_BOX_P(0);
4249 300 : Point *p = PG_GETARG_POINT_P(1);
4250 : BOX *result;
4251 :
4252 300 : result = (BOX *) palloc(sizeof(BOX));
4253 :
4254 300 : point_sub_point(&result->high, &box->high, p);
4255 300 : point_sub_point(&result->low, &box->low, p);
4256 :
4257 300 : PG_RETURN_BOX_P(result);
4258 : }
4259 :
4260 : Datum
4261 150 : box_mul(PG_FUNCTION_ARGS)
4262 : {
4263 150 : BOX *box = PG_GETARG_BOX_P(0);
4264 150 : Point *p = PG_GETARG_POINT_P(1);
4265 : BOX *result;
4266 : Point high,
4267 : low;
4268 :
4269 150 : result = (BOX *) palloc(sizeof(BOX));
4270 :
4271 150 : point_mul_point(&high, &box->high, p);
4272 150 : point_mul_point(&low, &box->low, p);
4273 :
4274 150 : box_construct(result, &high, &low);
4275 :
4276 150 : PG_RETURN_BOX_P(result);
4277 : }
4278 :
4279 : Datum
4280 60 : box_div(PG_FUNCTION_ARGS)
4281 : {
4282 60 : BOX *box = PG_GETARG_BOX_P(0);
4283 60 : Point *p = PG_GETARG_POINT_P(1);
4284 : BOX *result;
4285 : Point high,
4286 : low;
4287 :
4288 60 : result = (BOX *) palloc(sizeof(BOX));
4289 :
4290 60 : point_div_point(&high, &box->high, p);
4291 60 : point_div_point(&low, &box->low, p);
4292 :
4293 60 : box_construct(result, &high, &low);
4294 :
4295 60 : PG_RETURN_BOX_P(result);
4296 : }
4297 :
4298 : /*
4299 : * Convert point to empty box
4300 : */
4301 : Datum
4302 366 : point_box(PG_FUNCTION_ARGS)
4303 : {
4304 366 : Point *pt = PG_GETARG_POINT_P(0);
4305 : BOX *box;
4306 :
4307 366 : box = (BOX *) palloc(sizeof(BOX));
4308 :
4309 366 : box->high.x = pt->x;
4310 366 : box->low.x = pt->x;
4311 366 : box->high.y = pt->y;
4312 366 : box->low.y = pt->y;
4313 :
4314 366 : PG_RETURN_BOX_P(box);
4315 : }
4316 :
4317 : /*
4318 : * Smallest bounding box that includes both of the given boxes
4319 : */
4320 : Datum
4321 150 : boxes_bound_box(PG_FUNCTION_ARGS)
4322 : {
4323 150 : BOX *box1 = PG_GETARG_BOX_P(0),
4324 150 : *box2 = PG_GETARG_BOX_P(1),
4325 : *container;
4326 :
4327 150 : container = (BOX *) palloc(sizeof(BOX));
4328 :
4329 150 : container->high.x = float8_max(box1->high.x, box2->high.x);
4330 150 : container->low.x = float8_min(box1->low.x, box2->low.x);
4331 150 : container->high.y = float8_max(box1->high.y, box2->high.y);
4332 150 : container->low.y = float8_min(box1->low.y, box2->low.y);
4333 :
4334 150 : PG_RETURN_BOX_P(container);
4335 : }
4336 :
4337 :
4338 : /***********************************************************************
4339 : **
4340 : ** Routines for 2D paths.
4341 : **
4342 : ***********************************************************************/
4343 :
4344 : /* path_add()
4345 : * Concatenate two paths (only if they are both open).
4346 : */
4347 : Datum
4348 486 : path_add(PG_FUNCTION_ARGS)
4349 : {
4350 486 : PATH *p1 = PG_GETARG_PATH_P(0);
4351 486 : PATH *p2 = PG_GETARG_PATH_P(1);
4352 : PATH *result;
4353 : int size,
4354 : base_size;
4355 : int i;
4356 :
4357 486 : if (p1->closed || p2->closed)
4358 390 : PG_RETURN_NULL();
4359 :
4360 96 : base_size = sizeof(p1->p[0]) * (p1->npts + p2->npts);
4361 96 : size = offsetof(PATH, p) + base_size;
4362 :
4363 : /* Check for integer overflow */
4364 96 : if (base_size / sizeof(p1->p[0]) != (p1->npts + p2->npts) ||
4365 : size <= base_size)
4366 0 : ereport(ERROR,
4367 : (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
4368 : errmsg("too many points requested")));
4369 :
4370 96 : result = (PATH *) palloc(size);
4371 :
4372 96 : SET_VARSIZE(result, size);
4373 96 : result->npts = (p1->npts + p2->npts);
4374 96 : result->closed = p1->closed;
4375 : /* prevent instability in unused pad bytes */
4376 96 : result->dummy = 0;
4377 :
4378 336 : for (i = 0; i < p1->npts; i++)
4379 : {
4380 240 : result->p[i].x = p1->p[i].x;
4381 240 : result->p[i].y = p1->p[i].y;
4382 : }
4383 336 : for (i = 0; i < p2->npts; i++)
4384 : {
4385 240 : result->p[i + p1->npts].x = p2->p[i].x;
4386 240 : result->p[i + p1->npts].y = p2->p[i].y;
4387 : }
4388 :
4389 96 : PG_RETURN_PATH_P(result);
4390 : }
4391 :
4392 : /* path_add_pt()
4393 : * Translation operators.
4394 : */
4395 : Datum
4396 540 : path_add_pt(PG_FUNCTION_ARGS)
4397 : {
4398 540 : PATH *path = PG_GETARG_PATH_P_COPY(0);
4399 540 : Point *point = PG_GETARG_POINT_P(1);
4400 : int i;
4401 :
4402 1680 : for (i = 0; i < path->npts; i++)
4403 1140 : point_add_point(&path->p[i], &path->p[i], point);
4404 :
4405 540 : PG_RETURN_PATH_P(path);
4406 : }
4407 :
4408 : Datum
4409 540 : path_sub_pt(PG_FUNCTION_ARGS)
4410 : {
4411 540 : PATH *path = PG_GETARG_PATH_P_COPY(0);
4412 540 : Point *point = PG_GETARG_POINT_P(1);
4413 : int i;
4414 :
4415 1680 : for (i = 0; i < path->npts; i++)
4416 1140 : point_sub_point(&path->p[i], &path->p[i], point);
4417 :
4418 540 : PG_RETURN_PATH_P(path);
4419 : }
4420 :
4421 : /* path_mul_pt()
4422 : * Rotation and scaling operators.
4423 : */
4424 : Datum
4425 540 : path_mul_pt(PG_FUNCTION_ARGS)
4426 : {
4427 540 : PATH *path = PG_GETARG_PATH_P_COPY(0);
4428 540 : Point *point = PG_GETARG_POINT_P(1);
4429 : int i;
4430 :
4431 1680 : for (i = 0; i < path->npts; i++)
4432 1140 : point_mul_point(&path->p[i], &path->p[i], point);
4433 :
4434 540 : PG_RETURN_PATH_P(path);
4435 : }
4436 :
4437 : Datum
4438 114 : path_div_pt(PG_FUNCTION_ARGS)
4439 : {
4440 114 : PATH *path = PG_GETARG_PATH_P_COPY(0);
4441 114 : Point *point = PG_GETARG_POINT_P(1);
4442 : int i;
4443 :
4444 342 : for (i = 0; i < path->npts; i++)
4445 234 : point_div_point(&path->p[i], &path->p[i], point);
4446 :
4447 108 : PG_RETURN_PATH_P(path);
4448 : }
4449 :
4450 :
4451 : Datum
4452 90 : path_poly(PG_FUNCTION_ARGS)
4453 : {
4454 90 : PATH *path = PG_GETARG_PATH_P(0);
4455 : POLYGON *poly;
4456 : int size;
4457 : int i;
4458 :
4459 : /* This is not very consistent --- other similar cases return NULL ... */
4460 90 : if (!path->closed)
4461 6 : ereport(ERROR,
4462 : (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
4463 : errmsg("open path cannot be converted to polygon")));
4464 :
4465 : /*
4466 : * Never overflows: the old size fit in MaxAllocSize, and the new size is
4467 : * just a small constant larger.
4468 : */
4469 84 : size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * path->npts;
4470 84 : poly = (POLYGON *) palloc(size);
4471 :
4472 84 : SET_VARSIZE(poly, size);
4473 84 : poly->npts = path->npts;
4474 :
4475 252 : for (i = 0; i < path->npts; i++)
4476 : {
4477 168 : poly->p[i].x = path->p[i].x;
4478 168 : poly->p[i].y = path->p[i].y;
4479 : }
4480 :
4481 84 : make_bound_box(poly);
4482 :
4483 84 : PG_RETURN_POLYGON_P(poly);
4484 : }
4485 :
4486 :
4487 : /***********************************************************************
4488 : **
4489 : ** Routines for 2D polygons.
4490 : **
4491 : ***********************************************************************/
4492 :
4493 : Datum
4494 126 : poly_npoints(PG_FUNCTION_ARGS)
4495 : {
4496 126 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
4497 :
4498 126 : PG_RETURN_INT32(poly->npts);
4499 : }
4500 :
4501 :
4502 : Datum
4503 42 : poly_center(PG_FUNCTION_ARGS)
4504 : {
4505 42 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
4506 : Point *result;
4507 : CIRCLE circle;
4508 :
4509 42 : result = (Point *) palloc(sizeof(Point));
4510 :
4511 42 : poly_to_circle(&circle, poly);
4512 42 : *result = circle.center;
4513 :
4514 42 : PG_RETURN_POINT_P(result);
4515 : }
4516 :
4517 :
4518 : Datum
4519 42 : poly_box(PG_FUNCTION_ARGS)
4520 : {
4521 42 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
4522 : BOX *box;
4523 :
4524 42 : box = (BOX *) palloc(sizeof(BOX));
4525 42 : *box = poly->boundbox;
4526 :
4527 42 : PG_RETURN_BOX_P(box);
4528 : }
4529 :
4530 :
4531 : /* box_poly()
4532 : * Convert a box to a polygon.
4533 : */
4534 : Datum
4535 18630 : box_poly(PG_FUNCTION_ARGS)
4536 : {
4537 18630 : BOX *box = PG_GETARG_BOX_P(0);
4538 : POLYGON *poly;
4539 : int size;
4540 :
4541 : /* map four corners of the box to a polygon */
4542 18630 : size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * 4;
4543 18630 : poly = (POLYGON *) palloc(size);
4544 :
4545 18630 : SET_VARSIZE(poly, size);
4546 18630 : poly->npts = 4;
4547 :
4548 18630 : poly->p[0].x = box->low.x;
4549 18630 : poly->p[0].y = box->low.y;
4550 18630 : poly->p[1].x = box->low.x;
4551 18630 : poly->p[1].y = box->high.y;
4552 18630 : poly->p[2].x = box->high.x;
4553 18630 : poly->p[2].y = box->high.y;
4554 18630 : poly->p[3].x = box->high.x;
4555 18630 : poly->p[3].y = box->low.y;
4556 :
4557 18630 : box_construct(&poly->boundbox, &box->high, &box->low);
4558 :
4559 18630 : PG_RETURN_POLYGON_P(poly);
4560 : }
4561 :
4562 :
4563 : Datum
4564 42 : poly_path(PG_FUNCTION_ARGS)
4565 : {
4566 42 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
4567 : PATH *path;
4568 : int size;
4569 : int i;
4570 :
4571 : /*
4572 : * Never overflows: the old size fit in MaxAllocSize, and the new size is
4573 : * smaller by a small constant.
4574 : */
4575 42 : size = offsetof(PATH, p) + sizeof(path->p[0]) * poly->npts;
4576 42 : path = (PATH *) palloc(size);
4577 :
4578 42 : SET_VARSIZE(path, size);
4579 42 : path->npts = poly->npts;
4580 42 : path->closed = true;
4581 : /* prevent instability in unused pad bytes */
4582 42 : path->dummy = 0;
4583 :
4584 168 : for (i = 0; i < poly->npts; i++)
4585 : {
4586 126 : path->p[i].x = poly->p[i].x;
4587 126 : path->p[i].y = poly->p[i].y;
4588 : }
4589 :
4590 42 : PG_RETURN_PATH_P(path);
4591 : }
4592 :
4593 :
4594 : /***********************************************************************
4595 : **
4596 : ** Routines for circles.
4597 : **
4598 : ***********************************************************************/
4599 :
4600 : /*----------------------------------------------------------
4601 : * Formatting and conversion routines.
4602 : *---------------------------------------------------------*/
4603 :
4604 : /* circle_in - convert a string to internal form.
4605 : *
4606 : * External format: (center and radius of circle)
4607 : * "<(f8,f8),f8>"
4608 : * also supports quick entry style "f8,f8,f8"
4609 : */
4610 : Datum
4611 402 : circle_in(PG_FUNCTION_ARGS)
4612 : {
4613 402 : char *str = PG_GETARG_CSTRING(0);
4614 402 : Node *escontext = fcinfo->context;
4615 402 : CIRCLE *circle = (CIRCLE *) palloc(sizeof(CIRCLE));
4616 : char *s,
4617 : *cp;
4618 402 : int depth = 0;
4619 :
4620 402 : s = str;
4621 426 : while (isspace((unsigned char) *s))
4622 24 : s++;
4623 402 : if (*s == LDELIM_C)
4624 324 : depth++, s++;
4625 78 : else if (*s == LDELIM)
4626 : {
4627 : /* If there are two left parens, consume the first one */
4628 54 : cp = (s + 1);
4629 66 : while (isspace((unsigned char) *cp))
4630 12 : cp++;
4631 54 : if (*cp == LDELIM)
4632 24 : depth++, s = cp;
4633 : }
4634 :
4635 : /* pair_decode will consume parens around the pair, if any */
4636 402 : if (!pair_decode(s, &circle->center.x, &circle->center.y, &s, "circle", str,
4637 : escontext))
4638 12 : PG_RETURN_NULL();
4639 :
4640 378 : if (*s == DELIM)
4641 378 : s++;
4642 :
4643 378 : if (!single_decode(s, &circle->radius, &s, "circle", str, escontext))
4644 0 : PG_RETURN_NULL();
4645 :
4646 : /* We have to accept NaN. */
4647 378 : if (circle->radius < 0.0)
4648 18 : ereturn(escontext, (Datum) 0,
4649 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
4650 : errmsg("invalid input syntax for type %s: \"%s\"",
4651 : "circle", str)));
4652 :
4653 696 : while (depth > 0)
4654 : {
4655 342 : if ((*s == RDELIM) || ((*s == RDELIM_C) && (depth == 1)))
4656 : {
4657 336 : depth--;
4658 336 : s++;
4659 354 : while (isspace((unsigned char) *s))
4660 18 : s++;
4661 : }
4662 : else
4663 6 : ereturn(escontext, (Datum) 0,
4664 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
4665 : errmsg("invalid input syntax for type %s: \"%s\"",
4666 : "circle", str)));
4667 : }
4668 :
4669 354 : if (*s != '\0')
4670 6 : ereturn(escontext, (Datum) 0,
4671 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
4672 : errmsg("invalid input syntax for type %s: \"%s\"",
4673 : "circle", str)));
4674 :
4675 348 : PG_RETURN_CIRCLE_P(circle);
4676 : }
4677 :
4678 : /* circle_out - convert a circle to external form.
4679 : */
4680 : Datum
4681 9176 : circle_out(PG_FUNCTION_ARGS)
4682 : {
4683 9176 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
4684 : StringInfoData str;
4685 :
4686 9176 : initStringInfo(&str);
4687 :
4688 9176 : appendStringInfoChar(&str, LDELIM_C);
4689 9176 : appendStringInfoChar(&str, LDELIM);
4690 9176 : pair_encode(circle->center.x, circle->center.y, &str);
4691 9176 : appendStringInfoChar(&str, RDELIM);
4692 9176 : appendStringInfoChar(&str, DELIM);
4693 9176 : single_encode(circle->radius, &str);
4694 9176 : appendStringInfoChar(&str, RDELIM_C);
4695 :
4696 9176 : PG_RETURN_CSTRING(str.data);
4697 : }
4698 :
4699 : /*
4700 : * circle_recv - converts external binary format to circle
4701 : */
4702 : Datum
4703 0 : circle_recv(PG_FUNCTION_ARGS)
4704 : {
4705 0 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
4706 : CIRCLE *circle;
4707 :
4708 0 : circle = (CIRCLE *) palloc(sizeof(CIRCLE));
4709 :
4710 0 : circle->center.x = pq_getmsgfloat8(buf);
4711 0 : circle->center.y = pq_getmsgfloat8(buf);
4712 0 : circle->radius = pq_getmsgfloat8(buf);
4713 :
4714 : /* We have to accept NaN. */
4715 0 : if (circle->radius < 0.0)
4716 0 : ereport(ERROR,
4717 : (errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
4718 : errmsg("invalid radius in external \"circle\" value")));
4719 :
4720 0 : PG_RETURN_CIRCLE_P(circle);
4721 : }
4722 :
4723 : /*
4724 : * circle_send - converts circle to binary format
4725 : */
4726 : Datum
4727 0 : circle_send(PG_FUNCTION_ARGS)
4728 : {
4729 0 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
4730 : StringInfoData buf;
4731 :
4732 0 : pq_begintypsend(&buf);
4733 0 : pq_sendfloat8(&buf, circle->center.x);
4734 0 : pq_sendfloat8(&buf, circle->center.y);
4735 0 : pq_sendfloat8(&buf, circle->radius);
4736 0 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
4737 : }
4738 :
4739 :
4740 : /*----------------------------------------------------------
4741 : * Relational operators for CIRCLEs.
4742 : * <, >, <=, >=, and == are based on circle area.
4743 : *---------------------------------------------------------*/
4744 :
4745 : /* circles identical?
4746 : *
4747 : * We consider NaNs values to be equal to each other to let those circles
4748 : * to be found.
4749 : */
4750 : Datum
4751 386 : circle_same(PG_FUNCTION_ARGS)
4752 : {
4753 386 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4754 386 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4755 :
4756 386 : PG_RETURN_BOOL(((isnan(circle1->radius) && isnan(circle2->radius)) ||
4757 : FPeq(circle1->radius, circle2->radius)) &&
4758 : point_eq_point(&circle1->center, &circle2->center));
4759 : }
4760 :
4761 : /* circle_overlap - does circle1 overlap circle2?
4762 : */
4763 : Datum
4764 19218 : circle_overlap(PG_FUNCTION_ARGS)
4765 : {
4766 19218 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4767 19218 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4768 :
4769 19218 : PG_RETURN_BOOL(FPle(point_dt(&circle1->center, &circle2->center),
4770 : float8_pl(circle1->radius, circle2->radius)));
4771 : }
4772 :
4773 : /* circle_overleft - is the right edge of circle1 at or left of
4774 : * the right edge of circle2?
4775 : */
4776 : Datum
4777 384 : circle_overleft(PG_FUNCTION_ARGS)
4778 : {
4779 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4780 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4781 :
4782 384 : PG_RETURN_BOOL(FPle(float8_pl(circle1->center.x, circle1->radius),
4783 : float8_pl(circle2->center.x, circle2->radius)));
4784 : }
4785 :
4786 : /* circle_left - is circle1 strictly left of circle2?
4787 : */
4788 : Datum
4789 384 : circle_left(PG_FUNCTION_ARGS)
4790 : {
4791 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4792 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4793 :
4794 384 : PG_RETURN_BOOL(FPlt(float8_pl(circle1->center.x, circle1->radius),
4795 : float8_mi(circle2->center.x, circle2->radius)));
4796 : }
4797 :
4798 : /* circle_right - is circle1 strictly right of circle2?
4799 : */
4800 : Datum
4801 384 : circle_right(PG_FUNCTION_ARGS)
4802 : {
4803 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4804 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4805 :
4806 384 : PG_RETURN_BOOL(FPgt(float8_mi(circle1->center.x, circle1->radius),
4807 : float8_pl(circle2->center.x, circle2->radius)));
4808 : }
4809 :
4810 : /* circle_overright - is the left edge of circle1 at or right of
4811 : * the left edge of circle2?
4812 : */
4813 : Datum
4814 384 : circle_overright(PG_FUNCTION_ARGS)
4815 : {
4816 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4817 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4818 :
4819 384 : PG_RETURN_BOOL(FPge(float8_mi(circle1->center.x, circle1->radius),
4820 : float8_mi(circle2->center.x, circle2->radius)));
4821 : }
4822 :
4823 : /* circle_contained - is circle1 contained by circle2?
4824 : */
4825 : Datum
4826 384 : circle_contained(PG_FUNCTION_ARGS)
4827 : {
4828 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4829 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4830 :
4831 384 : PG_RETURN_BOOL(FPle(point_dt(&circle1->center, &circle2->center),
4832 : float8_mi(circle2->radius, circle1->radius)));
4833 : }
4834 :
4835 : /* circle_contain - does circle1 contain circle2?
4836 : */
4837 : Datum
4838 396 : circle_contain(PG_FUNCTION_ARGS)
4839 : {
4840 396 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4841 396 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4842 :
4843 396 : PG_RETURN_BOOL(FPle(point_dt(&circle1->center, &circle2->center),
4844 : float8_mi(circle1->radius, circle2->radius)));
4845 : }
4846 :
4847 :
4848 : /* circle_below - is circle1 strictly below circle2?
4849 : */
4850 : Datum
4851 384 : circle_below(PG_FUNCTION_ARGS)
4852 : {
4853 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4854 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4855 :
4856 384 : PG_RETURN_BOOL(FPlt(float8_pl(circle1->center.y, circle1->radius),
4857 : float8_mi(circle2->center.y, circle2->radius)));
4858 : }
4859 :
4860 : /* circle_above - is circle1 strictly above circle2?
4861 : */
4862 : Datum
4863 384 : circle_above(PG_FUNCTION_ARGS)
4864 : {
4865 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4866 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4867 :
4868 384 : PG_RETURN_BOOL(FPgt(float8_mi(circle1->center.y, circle1->radius),
4869 : float8_pl(circle2->center.y, circle2->radius)));
4870 : }
4871 :
4872 : /* circle_overbelow - is the upper edge of circle1 at or below
4873 : * the upper edge of circle2?
4874 : */
4875 : Datum
4876 384 : circle_overbelow(PG_FUNCTION_ARGS)
4877 : {
4878 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4879 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4880 :
4881 384 : PG_RETURN_BOOL(FPle(float8_pl(circle1->center.y, circle1->radius),
4882 : float8_pl(circle2->center.y, circle2->radius)));
4883 : }
4884 :
4885 : /* circle_overabove - is the lower edge of circle1 at or above
4886 : * the lower edge of circle2?
4887 : */
4888 : Datum
4889 384 : circle_overabove(PG_FUNCTION_ARGS)
4890 : {
4891 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4892 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4893 :
4894 384 : PG_RETURN_BOOL(FPge(float8_mi(circle1->center.y, circle1->radius),
4895 : float8_mi(circle2->center.y, circle2->radius)));
4896 : }
4897 :
4898 :
4899 : /* circle_relop - is area(circle1) relop area(circle2), within
4900 : * our accuracy constraint?
4901 : */
4902 : Datum
4903 384 : circle_eq(PG_FUNCTION_ARGS)
4904 : {
4905 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4906 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4907 :
4908 384 : PG_RETURN_BOOL(FPeq(circle_ar(circle1), circle_ar(circle2)));
4909 : }
4910 :
4911 : Datum
4912 384 : circle_ne(PG_FUNCTION_ARGS)
4913 : {
4914 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4915 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4916 :
4917 384 : PG_RETURN_BOOL(FPne(circle_ar(circle1), circle_ar(circle2)));
4918 : }
4919 :
4920 : Datum
4921 1578 : circle_lt(PG_FUNCTION_ARGS)
4922 : {
4923 1578 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4924 1578 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4925 :
4926 1578 : PG_RETURN_BOOL(FPlt(circle_ar(circle1), circle_ar(circle2)));
4927 : }
4928 :
4929 : Datum
4930 384 : circle_gt(PG_FUNCTION_ARGS)
4931 : {
4932 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4933 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4934 :
4935 384 : PG_RETURN_BOOL(FPgt(circle_ar(circle1), circle_ar(circle2)));
4936 : }
4937 :
4938 : Datum
4939 384 : circle_le(PG_FUNCTION_ARGS)
4940 : {
4941 384 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4942 384 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4943 :
4944 384 : PG_RETURN_BOOL(FPle(circle_ar(circle1), circle_ar(circle2)));
4945 : }
4946 :
4947 : Datum
4948 486 : circle_ge(PG_FUNCTION_ARGS)
4949 : {
4950 486 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4951 486 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4952 :
4953 486 : PG_RETURN_BOOL(FPge(circle_ar(circle1), circle_ar(circle2)));
4954 : }
4955 :
4956 :
4957 : /*----------------------------------------------------------
4958 : * "Arithmetic" operators on circles.
4959 : *---------------------------------------------------------*/
4960 :
4961 : /* circle_add_pt()
4962 : * Translation operator.
4963 : */
4964 : Datum
4965 480 : circle_add_pt(PG_FUNCTION_ARGS)
4966 : {
4967 480 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
4968 480 : Point *point = PG_GETARG_POINT_P(1);
4969 : CIRCLE *result;
4970 :
4971 480 : result = (CIRCLE *) palloc(sizeof(CIRCLE));
4972 :
4973 480 : point_add_point(&result->center, &circle->center, point);
4974 480 : result->radius = circle->radius;
4975 :
4976 480 : PG_RETURN_CIRCLE_P(result);
4977 : }
4978 :
4979 : Datum
4980 480 : circle_sub_pt(PG_FUNCTION_ARGS)
4981 : {
4982 480 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
4983 480 : Point *point = PG_GETARG_POINT_P(1);
4984 : CIRCLE *result;
4985 :
4986 480 : result = (CIRCLE *) palloc(sizeof(CIRCLE));
4987 :
4988 480 : point_sub_point(&result->center, &circle->center, point);
4989 480 : result->radius = circle->radius;
4990 :
4991 480 : PG_RETURN_CIRCLE_P(result);
4992 : }
4993 :
4994 :
4995 : /* circle_mul_pt()
4996 : * Rotation and scaling operators.
4997 : */
4998 : Datum
4999 480 : circle_mul_pt(PG_FUNCTION_ARGS)
5000 : {
5001 480 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5002 480 : Point *point = PG_GETARG_POINT_P(1);
5003 : CIRCLE *result;
5004 :
5005 480 : result = (CIRCLE *) palloc(sizeof(CIRCLE));
5006 :
5007 480 : point_mul_point(&result->center, &circle->center, point);
5008 480 : result->radius = float8_mul(circle->radius, HYPOT(point->x, point->y));
5009 :
5010 480 : PG_RETURN_CIRCLE_P(result);
5011 : }
5012 :
5013 : Datum
5014 108 : circle_div_pt(PG_FUNCTION_ARGS)
5015 : {
5016 108 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5017 108 : Point *point = PG_GETARG_POINT_P(1);
5018 : CIRCLE *result;
5019 :
5020 108 : result = (CIRCLE *) palloc(sizeof(CIRCLE));
5021 :
5022 108 : point_div_point(&result->center, &circle->center, point);
5023 96 : result->radius = float8_div(circle->radius, HYPOT(point->x, point->y));
5024 :
5025 96 : PG_RETURN_CIRCLE_P(result);
5026 : }
5027 :
5028 :
5029 : /* circle_area - returns the area of the circle.
5030 : */
5031 : Datum
5032 510 : circle_area(PG_FUNCTION_ARGS)
5033 : {
5034 510 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5035 :
5036 510 : PG_RETURN_FLOAT8(circle_ar(circle));
5037 : }
5038 :
5039 :
5040 : /* circle_diameter - returns the diameter of the circle.
5041 : */
5042 : Datum
5043 96 : circle_diameter(PG_FUNCTION_ARGS)
5044 : {
5045 96 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5046 :
5047 96 : PG_RETURN_FLOAT8(float8_mul(circle->radius, 2.0));
5048 : }
5049 :
5050 :
5051 : /* circle_radius - returns the radius of the circle.
5052 : */
5053 : Datum
5054 18756 : circle_radius(PG_FUNCTION_ARGS)
5055 : {
5056 18756 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5057 :
5058 18756 : PG_RETURN_FLOAT8(circle->radius);
5059 : }
5060 :
5061 :
5062 : /* circle_distance - returns the distance between
5063 : * two circles.
5064 : */
5065 : Datum
5066 168 : circle_distance(PG_FUNCTION_ARGS)
5067 : {
5068 168 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
5069 168 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
5070 : float8 result;
5071 :
5072 168 : result = float8_mi(point_dt(&circle1->center, &circle2->center),
5073 : float8_pl(circle1->radius, circle2->radius));
5074 168 : if (result < 0.0)
5075 72 : result = 0.0;
5076 :
5077 168 : PG_RETURN_FLOAT8(result);
5078 : }
5079 :
5080 :
5081 : Datum
5082 24 : circle_contain_pt(PG_FUNCTION_ARGS)
5083 : {
5084 24 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5085 24 : Point *point = PG_GETARG_POINT_P(1);
5086 : float8 d;
5087 :
5088 24 : d = point_dt(&circle->center, point);
5089 24 : PG_RETURN_BOOL(d <= circle->radius);
5090 : }
5091 :
5092 :
5093 : Datum
5094 60 : pt_contained_circle(PG_FUNCTION_ARGS)
5095 : {
5096 60 : Point *point = PG_GETARG_POINT_P(0);
5097 60 : CIRCLE *circle = PG_GETARG_CIRCLE_P(1);
5098 : float8 d;
5099 :
5100 60 : d = point_dt(&circle->center, point);
5101 60 : PG_RETURN_BOOL(d <= circle->radius);
5102 : }
5103 :
5104 :
5105 : /* dist_pc - returns the distance between
5106 : * a point and a circle.
5107 : */
5108 : Datum
5109 846 : dist_pc(PG_FUNCTION_ARGS)
5110 : {
5111 846 : Point *point = PG_GETARG_POINT_P(0);
5112 846 : CIRCLE *circle = PG_GETARG_CIRCLE_P(1);
5113 : float8 result;
5114 :
5115 846 : result = float8_mi(point_dt(point, &circle->center),
5116 : circle->radius);
5117 846 : if (result < 0.0)
5118 114 : result = 0.0;
5119 :
5120 846 : PG_RETURN_FLOAT8(result);
5121 : }
5122 :
5123 : /*
5124 : * Distance from a circle to a point
5125 : */
5126 : Datum
5127 18726 : dist_cpoint(PG_FUNCTION_ARGS)
5128 : {
5129 18726 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5130 18726 : Point *point = PG_GETARG_POINT_P(1);
5131 : float8 result;
5132 :
5133 18726 : result = float8_mi(point_dt(point, &circle->center), circle->radius);
5134 18726 : if (result < 0.0)
5135 0 : result = 0.0;
5136 :
5137 18726 : PG_RETURN_FLOAT8(result);
5138 : }
5139 :
5140 : /* circle_center - returns the center point of the circle.
5141 : */
5142 : Datum
5143 18906 : circle_center(PG_FUNCTION_ARGS)
5144 : {
5145 18906 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5146 : Point *result;
5147 :
5148 18906 : result = (Point *) palloc(sizeof(Point));
5149 18906 : result->x = circle->center.x;
5150 18906 : result->y = circle->center.y;
5151 :
5152 18906 : PG_RETURN_POINT_P(result);
5153 : }
5154 :
5155 :
5156 : /* circle_ar - returns the area of the circle.
5157 : */
5158 : static float8
5159 7710 : circle_ar(CIRCLE *circle)
5160 : {
5161 7710 : return float8_mul(float8_mul(circle->radius, circle->radius), M_PI);
5162 : }
5163 :
5164 :
5165 : /*----------------------------------------------------------
5166 : * Conversion operators.
5167 : *---------------------------------------------------------*/
5168 :
5169 : Datum
5170 180158 : cr_circle(PG_FUNCTION_ARGS)
5171 : {
5172 180158 : Point *center = PG_GETARG_POINT_P(0);
5173 180158 : float8 radius = PG_GETARG_FLOAT8(1);
5174 : CIRCLE *result;
5175 :
5176 180158 : result = (CIRCLE *) palloc(sizeof(CIRCLE));
5177 :
5178 180158 : result->center.x = center->x;
5179 180158 : result->center.y = center->y;
5180 180158 : result->radius = radius;
5181 :
5182 180158 : PG_RETURN_CIRCLE_P(result);
5183 : }
5184 :
5185 : Datum
5186 48 : circle_box(PG_FUNCTION_ARGS)
5187 : {
5188 48 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5189 : BOX *box;
5190 : float8 delta;
5191 :
5192 48 : box = (BOX *) palloc(sizeof(BOX));
5193 :
5194 48 : delta = float8_div(circle->radius, sqrt(2.0));
5195 :
5196 48 : box->high.x = float8_pl(circle->center.x, delta);
5197 48 : box->low.x = float8_mi(circle->center.x, delta);
5198 48 : box->high.y = float8_pl(circle->center.y, delta);
5199 48 : box->low.y = float8_mi(circle->center.y, delta);
5200 :
5201 48 : PG_RETURN_BOX_P(box);
5202 : }
5203 :
5204 : /* box_circle()
5205 : * Convert a box to a circle.
5206 : */
5207 : Datum
5208 18630 : box_circle(PG_FUNCTION_ARGS)
5209 : {
5210 18630 : BOX *box = PG_GETARG_BOX_P(0);
5211 : CIRCLE *circle;
5212 :
5213 18630 : circle = (CIRCLE *) palloc(sizeof(CIRCLE));
5214 :
5215 18630 : circle->center.x = float8_div(float8_pl(box->high.x, box->low.x), 2.0);
5216 18630 : circle->center.y = float8_div(float8_pl(box->high.y, box->low.y), 2.0);
5217 :
5218 18630 : circle->radius = point_dt(&circle->center, &box->high);
5219 :
5220 18630 : PG_RETURN_CIRCLE_P(circle);
5221 : }
5222 :
5223 :
5224 : Datum
5225 60086 : circle_poly(PG_FUNCTION_ARGS)
5226 : {
5227 60086 : int32 npts = PG_GETARG_INT32(0);
5228 60086 : CIRCLE *circle = PG_GETARG_CIRCLE_P(1);
5229 : POLYGON *poly;
5230 : int base_size,
5231 : size;
5232 : int i;
5233 : float8 angle;
5234 : float8 anglestep;
5235 :
5236 60086 : if (FPzero(circle->radius))
5237 6 : ereport(ERROR,
5238 : (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
5239 : errmsg("cannot convert circle with radius zero to polygon")));
5240 :
5241 60080 : if (npts < 2)
5242 6 : ereport(ERROR,
5243 : (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
5244 : errmsg("must request at least 2 points")));
5245 :
5246 60074 : base_size = sizeof(poly->p[0]) * npts;
5247 60074 : size = offsetof(POLYGON, p) + base_size;
5248 :
5249 : /* Check for integer overflow */
5250 60074 : if (base_size / npts != sizeof(poly->p[0]) || size <= base_size)
5251 0 : ereport(ERROR,
5252 : (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
5253 : errmsg("too many points requested")));
5254 :
5255 60074 : poly = (POLYGON *) palloc0(size); /* zero any holes */
5256 60074 : SET_VARSIZE(poly, size);
5257 60074 : poly->npts = npts;
5258 :
5259 60074 : anglestep = float8_div(2.0 * M_PI, npts);
5260 :
5261 780818 : for (i = 0; i < npts; i++)
5262 : {
5263 720744 : angle = float8_mul(anglestep, i);
5264 :
5265 720744 : poly->p[i].x = float8_mi(circle->center.x,
5266 : float8_mul(circle->radius, cos(angle)));
5267 720744 : poly->p[i].y = float8_pl(circle->center.y,
5268 : float8_mul(circle->radius, sin(angle)));
5269 : }
5270 :
5271 60074 : make_bound_box(poly);
5272 :
5273 60074 : PG_RETURN_POLYGON_P(poly);
5274 : }
5275 :
5276 : /*
5277 : * Convert polygon to circle
5278 : *
5279 : * The result must be preallocated.
5280 : *
5281 : * XXX This algorithm should use weighted means of line segments
5282 : * rather than straight average values of points - tgl 97/01/21.
5283 : */
5284 : static void
5285 72 : poly_to_circle(CIRCLE *result, POLYGON *poly)
5286 : {
5287 : int i;
5288 :
5289 : Assert(poly->npts > 0);
5290 :
5291 72 : result->center.x = 0;
5292 72 : result->center.y = 0;
5293 72 : result->radius = 0;
5294 :
5295 324 : for (i = 0; i < poly->npts; i++)
5296 252 : point_add_point(&result->center, &result->center, &poly->p[i]);
5297 72 : result->center.x = float8_div(result->center.x, poly->npts);
5298 72 : result->center.y = float8_div(result->center.y, poly->npts);
5299 :
5300 324 : for (i = 0; i < poly->npts; i++)
5301 252 : result->radius = float8_pl(result->radius,
5302 : point_dt(&poly->p[i], &result->center));
5303 72 : result->radius = float8_div(result->radius, poly->npts);
5304 72 : }
5305 :
5306 : Datum
5307 30 : poly_circle(PG_FUNCTION_ARGS)
5308 : {
5309 30 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
5310 : CIRCLE *result;
5311 :
5312 30 : result = (CIRCLE *) palloc(sizeof(CIRCLE));
5313 :
5314 30 : poly_to_circle(result, poly);
5315 :
5316 30 : PG_RETURN_CIRCLE_P(result);
5317 : }
5318 :
5319 :
5320 : /***********************************************************************
5321 : **
5322 : ** Private routines for multiple types.
5323 : **
5324 : ***********************************************************************/
5325 :
5326 : /*
5327 : * Test to see if the point is inside the polygon, returns 1/0, or 2 if
5328 : * the point is on the polygon.
5329 : * Code adapted but not copied from integer-based routines in WN: A
5330 : * Server for the HTTP
5331 : * version 1.15.1, file wn/image.c
5332 : * http://hopf.math.northwestern.edu/index.html
5333 : * Description of algorithm: http://www.linuxjournal.com/article/2197
5334 : * http://www.linuxjournal.com/article/2029
5335 : */
5336 :
5337 : #define POINT_ON_POLYGON INT_MAX
5338 :
5339 : static int
5340 246650 : point_inside(Point *p, int npts, Point *plist)
5341 : {
5342 : float8 x0,
5343 : y0;
5344 : float8 prev_x,
5345 : prev_y;
5346 246650 : int i = 0;
5347 : float8 x,
5348 : y;
5349 : int cross,
5350 246650 : total_cross = 0;
5351 :
5352 : Assert(npts > 0);
5353 :
5354 : /* compute first polygon point relative to single point */
5355 246650 : x0 = float8_mi(plist[0].x, p->x);
5356 246650 : y0 = float8_mi(plist[0].y, p->y);
5357 :
5358 246650 : prev_x = x0;
5359 246650 : prev_y = y0;
5360 : /* loop over polygon points and aggregate total_cross */
5361 1137948 : for (i = 1; i < npts; i++)
5362 : {
5363 : /* compute next polygon point relative to single point */
5364 891430 : x = float8_mi(plist[i].x, p->x);
5365 891430 : y = float8_mi(plist[i].y, p->y);
5366 :
5367 : /* compute previous to current point crossing */
5368 891430 : if ((cross = lseg_crossing(x, y, prev_x, prev_y)) == POINT_ON_POLYGON)
5369 132 : return 2;
5370 891298 : total_cross += cross;
5371 :
5372 891298 : prev_x = x;
5373 891298 : prev_y = y;
5374 : }
5375 :
5376 : /* now do the first point */
5377 246518 : if ((cross = lseg_crossing(x0, y0, prev_x, prev_y)) == POINT_ON_POLYGON)
5378 108 : return 2;
5379 246410 : total_cross += cross;
5380 :
5381 246410 : if (total_cross != 0)
5382 189194 : return 1;
5383 57216 : return 0;
5384 : }
5385 :
5386 :
5387 : /* lseg_crossing()
5388 : * Returns +/-2 if line segment crosses the positive X-axis in a +/- direction.
5389 : * Returns +/-1 if one point is on the positive X-axis.
5390 : * Returns 0 if both points are on the positive X-axis, or there is no crossing.
5391 : * Returns POINT_ON_POLYGON if the segment contains (0,0).
5392 : * Wow, that is one confusing API, but it is used above, and when summed,
5393 : * can tell is if a point is in a polygon.
5394 : */
5395 :
5396 : static int
5397 1137948 : lseg_crossing(float8 x, float8 y, float8 prev_x, float8 prev_y)
5398 : {
5399 : float8 z;
5400 : int y_sign;
5401 :
5402 1137948 : if (FPzero(y))
5403 : { /* y == 0, on X axis */
5404 1744 : if (FPzero(x)) /* (x,y) is (0,0)? */
5405 228 : return POINT_ON_POLYGON;
5406 1516 : else if (FPgt(x, 0))
5407 : { /* x > 0 */
5408 1010 : if (FPzero(prev_y)) /* y and prev_y are zero */
5409 : /* prev_x > 0? */
5410 60 : return FPgt(prev_x, 0.0) ? 0 : POINT_ON_POLYGON;
5411 950 : return FPlt(prev_y, 0.0) ? 1 : -1;
5412 : }
5413 : else
5414 : { /* x < 0, x not on positive X axis */
5415 506 : if (FPzero(prev_y))
5416 : /* prev_x < 0? */
5417 24 : return FPlt(prev_x, 0.0) ? 0 : POINT_ON_POLYGON;
5418 482 : return 0;
5419 : }
5420 : }
5421 : else
5422 : { /* y != 0 */
5423 : /* compute y crossing direction from previous point */
5424 1136204 : y_sign = FPgt(y, 0.0) ? 1 : -1;
5425 :
5426 1136204 : if (FPzero(prev_y))
5427 : /* previous point was on X axis, so new point is either off or on */
5428 1528 : return FPlt(prev_x, 0.0) ? 0 : y_sign;
5429 1134676 : else if ((y_sign < 0 && FPlt(prev_y, 0.0)) ||
5430 580058 : (y_sign > 0 && FPgt(prev_y, 0.0)))
5431 : /* both above or below X axis */
5432 722500 : return 0; /* same sign */
5433 : else
5434 : { /* y and prev_y cross X-axis */
5435 412176 : if (FPge(x, 0.0) && FPgt(prev_x, 0.0))
5436 : /* both non-negative so cross positive X-axis */
5437 149886 : return 2 * y_sign;
5438 262290 : if (FPlt(x, 0.0) && FPle(prev_x, 0.0))
5439 : /* both non-positive so do not cross positive X-axis */
5440 132444 : return 0;
5441 :
5442 : /* x and y cross axes, see URL above point_inside() */
5443 129846 : z = float8_mi(float8_mul(float8_mi(x, prev_x), y),
5444 : float8_mul(float8_mi(y, prev_y), x));
5445 129846 : if (FPzero(z))
5446 12 : return POINT_ON_POLYGON;
5447 129834 : if ((y_sign < 0 && FPlt(z, 0.0)) ||
5448 74496 : (y_sign > 0 && FPgt(z, 0.0)))
5449 72684 : return 0;
5450 57150 : return 2 * y_sign;
5451 : }
5452 : }
5453 : }
5454 :
5455 :
5456 : static bool
5457 6092 : plist_same(int npts, Point *p1, Point *p2)
5458 : {
5459 : int i,
5460 : ii,
5461 : j;
5462 :
5463 : /* find match for first point */
5464 6260 : for (i = 0; i < npts; i++)
5465 : {
5466 6224 : if (point_eq_point(&p2[i], &p1[0]))
5467 : {
5468 :
5469 : /* match found? then look forward through remaining points */
5470 18184 : for (ii = 1, j = i + 1; ii < npts; ii++, j++)
5471 : {
5472 12140 : if (j >= npts)
5473 18 : j = 0;
5474 12140 : if (!point_eq_point(&p2[j], &p1[ii]))
5475 36 : break;
5476 : }
5477 6080 : if (ii == npts)
5478 6044 : return true;
5479 :
5480 : /* match not found forwards? then look backwards */
5481 84 : for (ii = 1, j = i - 1; ii < npts; ii++, j--)
5482 : {
5483 72 : if (j < 0)
5484 12 : j = (npts - 1);
5485 72 : if (!point_eq_point(&p2[j], &p1[ii]))
5486 24 : break;
5487 : }
5488 36 : if (ii == npts)
5489 12 : return true;
5490 : }
5491 : }
5492 :
5493 36 : return false;
5494 : }
5495 :
5496 :
5497 : /*-------------------------------------------------------------------------
5498 : * Determine the hypotenuse.
5499 : *
5500 : * If required, x and y are swapped to make x the larger number. The
5501 : * traditional formula of x^2+y^2 is rearranged to factor x outside the
5502 : * sqrt. This allows computation of the hypotenuse for significantly
5503 : * larger values, and with a higher precision than when using the naive
5504 : * formula. In particular, this cannot overflow unless the final result
5505 : * would be out-of-range.
5506 : *
5507 : * sqrt( x^2 + y^2 ) = sqrt( x^2( 1 + y^2/x^2) )
5508 : * = x * sqrt( 1 + y^2/x^2 )
5509 : * = x * sqrt( 1 + y/x * y/x )
5510 : *
5511 : * It is expected that this routine will eventually be replaced with the
5512 : * C99 hypot() function.
5513 : *
5514 : * This implementation conforms to IEEE Std 1003.1 and GLIBC, in that the
5515 : * case of hypot(inf,nan) results in INF, and not NAN.
5516 : *-----------------------------------------------------------------------
5517 : */
5518 : float8
5519 15654194 : pg_hypot(float8 x, float8 y)
5520 : {
5521 : float8 yx,
5522 : result;
5523 :
5524 : /* Handle INF and NaN properly */
5525 15654194 : if (isinf(x) || isinf(y))
5526 7152 : return get_float8_infinity();
5527 :
5528 15647042 : if (isnan(x) || isnan(y))
5529 21522 : return get_float8_nan();
5530 :
5531 : /* Else, drop any minus signs */
5532 15625520 : x = fabs(x);
5533 15625520 : y = fabs(y);
5534 :
5535 : /* Swap x and y if needed to make x the larger one */
5536 15625520 : if (x < y)
5537 : {
5538 7639828 : float8 temp = x;
5539 :
5540 7639828 : x = y;
5541 7639828 : y = temp;
5542 : }
5543 :
5544 : /*
5545 : * If y is zero, the hypotenuse is x. This test saves a few cycles in
5546 : * such cases, but more importantly it also protects against
5547 : * divide-by-zero errors, since now x >= y.
5548 : */
5549 15625520 : if (y == 0.0)
5550 4001926 : return x;
5551 :
5552 : /* Determine the hypotenuse */
5553 11623594 : yx = y / x;
5554 11623594 : result = x * sqrt(1.0 + (yx * yx));
5555 :
5556 11623594 : if (unlikely(isinf(result)))
5557 0 : float_overflow_error();
5558 11623594 : if (unlikely(result == 0.0))
5559 0 : float_underflow_error();
5560 :
5561 11623594 : return result;
5562 : }
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