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) 1996-2026, 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 182218 : single_decode(char *num, float8 *x, char **endptr_p,
195 : const char *type_name, const char *orig_string,
196 : Node *escontext)
197 : {
198 182218 : *x = float8in_internal(num, endptr_p, type_name, orig_string, escontext);
199 182182 : return (!SOFT_ERROR_OCCURRED(escontext));
200 : } /* single_decode() */
201 :
202 : static void
203 6104 : single_encode(float8 x, StringInfo str)
204 : {
205 6104 : char *xstr = float8out_internal(x);
206 :
207 6104 : appendStringInfoString(str, xstr);
208 6104 : pfree(xstr);
209 6104 : } /* single_encode() */
210 :
211 : static bool
212 90888 : 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 90954 : while (isspace((unsigned char) *str))
219 66 : str++;
220 90888 : if ((has_delim = (*str == LDELIM)))
221 64956 : str++;
222 :
223 90888 : if (!single_decode(str, x, &str, type_name, orig_string, escontext))
224 0 : return false;
225 :
226 90864 : if (*str++ != DELIM)
227 36 : goto fail;
228 :
229 90828 : if (!single_decode(str, y, &str, type_name, orig_string, escontext))
230 36 : return false;
231 :
232 90784 : if (has_delim)
233 : {
234 64904 : if (*str++ != RDELIM)
235 12 : goto fail;
236 64934 : while (isspace((unsigned char) *str))
237 42 : str++;
238 : }
239 :
240 : /* report stopping point if wanted, else complain if not end of string */
241 90772 : if (endptr_p)
242 73437 : *endptr_p = str;
243 17335 : else if (*str != '\0')
244 4 : goto fail;
245 90768 : return true;
246 :
247 52 : fail:
248 52 : 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 909275 : pair_encode(float8 x, float8 y, StringInfo str)
256 : {
257 909275 : char *xstr = float8out_internal(x);
258 909275 : char *ystr = float8out_internal(y);
259 :
260 909275 : appendStringInfo(str, "%s,%s", xstr, ystr);
261 909275 : pfree(xstr);
262 909275 : pfree(ystr);
263 909275 : }
264 :
265 : static bool
266 34191 : 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 34191 : int depth = 0;
272 : char *cp;
273 : int i;
274 :
275 34195 : while (isspace((unsigned char) *str))
276 4 : str++;
277 34191 : if ((*isopen = (*str == LDELIM_EP)))
278 : {
279 : /* no open delimiter allowed? */
280 20273 : if (!opentype)
281 4 : goto fail;
282 20269 : depth++;
283 20269 : str++;
284 : }
285 13918 : else if (*str == LDELIM)
286 : {
287 13814 : cp = (str + 1);
288 13824 : while (isspace((unsigned char) *cp))
289 10 : cp++;
290 13814 : if (*cp == LDELIM)
291 : {
292 818 : depth++;
293 818 : str = cp;
294 : }
295 12996 : else if (strrchr(str, LDELIM) == str)
296 : {
297 12706 : depth++;
298 12706 : str = cp;
299 : }
300 : }
301 :
302 107370 : for (i = 0; i < npts; i++)
303 : {
304 73259 : if (!pair_decode(str, &(p->x), &(p->y), &str, type_name, orig_string,
305 : escontext))
306 48 : return false;
307 73183 : if (*str == DELIM)
308 39048 : str++;
309 73183 : p++;
310 : }
311 :
312 67820 : while (depth > 0)
313 : {
314 33737 : if (*str == RDELIM || (*str == RDELIM_EP && *isopen && depth == 1))
315 : {
316 33709 : depth--;
317 33709 : str++;
318 33721 : while (isspace((unsigned char) *str))
319 12 : str++;
320 : }
321 : else
322 28 : goto fail;
323 : }
324 :
325 : /* report stopping point if wanted, else complain if not end of string */
326 34083 : if (endptr_p)
327 20585 : *endptr_p = str;
328 13498 : else if (*str != '\0')
329 4 : goto fail;
330 34079 : return true;
331 :
332 36 : fail:
333 36 : 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 307863 : path_encode(enum path_delim path_delim, int npts, Point *pt)
341 : {
342 : StringInfoData str;
343 : int i;
344 :
345 307863 : initStringInfo(&str);
346 :
347 307863 : switch (path_delim)
348 : {
349 52090 : case PATH_CLOSED:
350 52090 : appendStringInfoChar(&str, LDELIM);
351 52090 : break;
352 32407 : case PATH_OPEN:
353 32407 : appendStringInfoChar(&str, LDELIM_EP);
354 32407 : break;
355 223366 : case PATH_NONE:
356 223366 : break;
357 : }
358 :
359 1211034 : for (i = 0; i < npts; i++)
360 : {
361 903171 : if (i > 0)
362 595308 : appendStringInfoChar(&str, DELIM);
363 903171 : appendStringInfoChar(&str, LDELIM);
364 903171 : pair_encode(pt->x, pt->y, &str);
365 903171 : appendStringInfoChar(&str, RDELIM);
366 903171 : pt++;
367 : }
368 :
369 307863 : switch (path_delim)
370 : {
371 52090 : case PATH_CLOSED:
372 52090 : appendStringInfoChar(&str, RDELIM);
373 52090 : break;
374 32407 : case PATH_OPEN:
375 32407 : appendStringInfoChar(&str, RDELIM_EP);
376 32407 : break;
377 223366 : case PATH_NONE:
378 223366 : break;
379 : }
380 :
381 307863 : 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 20882 : pair_count(char *s, char delim)
393 : {
394 20882 : int ndelim = 0;
395 :
396 93326 : while ((s = strchr(s, delim)) != NULL)
397 : {
398 72444 : ndelim++;
399 72444 : s++;
400 : }
401 20882 : 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 13228 : box_in(PG_FUNCTION_ARGS)
423 : {
424 13228 : char *str = PG_GETARG_CSTRING(0);
425 13228 : Node *escontext = fcinfo->context;
426 13228 : BOX *box = palloc_object(BOX);
427 : bool isopen;
428 : float8 x,
429 : y;
430 :
431 13228 : if (!path_decode(str, false, 2, &(box->high), &isopen, NULL, "box", str,
432 : escontext))
433 16 : PG_RETURN_NULL();
434 :
435 : /* reorder corners if necessary... */
436 13192 : if (float8_lt(box->high.x, box->low.x))
437 : {
438 596 : x = box->high.x;
439 596 : box->high.x = box->low.x;
440 596 : box->low.x = x;
441 : }
442 13192 : if (float8_lt(box->high.y, box->low.y))
443 : {
444 604 : y = box->high.y;
445 604 : box->high.y = box->low.y;
446 604 : box->low.y = y;
447 : }
448 :
449 13192 : PG_RETURN_BOX_P(box);
450 : }
451 :
452 : /* box_out - convert a box to external form.
453 : */
454 : Datum
455 89728 : box_out(PG_FUNCTION_ARGS)
456 : {
457 89728 : BOX *box = PG_GETARG_BOX_P(0);
458 :
459 89728 : 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 = palloc_object(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 173684 : box_construct(BOX *result, Point *pt1, Point *pt2)
519 : {
520 173684 : if (float8_gt(pt1->x, pt2->x))
521 : {
522 12372 : result->high.x = pt1->x;
523 12372 : result->low.x = pt2->x;
524 : }
525 : else
526 : {
527 161312 : result->high.x = pt2->x;
528 161312 : result->low.x = pt1->x;
529 : }
530 173684 : if (float8_gt(pt1->y, pt2->y))
531 : {
532 12386 : result->high.y = pt1->y;
533 12386 : result->low.y = pt2->y;
534 : }
535 : else
536 : {
537 161298 : result->high.y = pt2->y;
538 161298 : result->low.y = pt1->y;
539 : }
540 173684 : }
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 9173 : box_same(PG_FUNCTION_ARGS)
552 : {
553 9173 : BOX *box1 = PG_GETARG_BOX_P(0);
554 9173 : BOX *box2 = PG_GETARG_BOX_P(1);
555 :
556 9173 : 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 43156 : box_overlap(PG_FUNCTION_ARGS)
564 : {
565 43156 : BOX *box1 = PG_GETARG_BOX_P(0);
566 43156 : BOX *box2 = PG_GETARG_BOX_P(1);
567 :
568 43156 : PG_RETURN_BOOL(box_ov(box1, box2));
569 : }
570 :
571 : static bool
572 984120 : box_ov(BOX *box1, BOX *box2)
573 : {
574 1486696 : return (FPle(box1->low.x, box2->high.x) &&
575 584524 : FPle(box2->low.x, box1->high.x) &&
576 1568644 : FPle(box1->low.y, box2->high.y) &&
577 65648 : FPle(box2->low.y, box1->high.y));
578 : }
579 :
580 : /* box_left - is box1 strictly left of box2?
581 : */
582 : Datum
583 33348 : box_left(PG_FUNCTION_ARGS)
584 : {
585 33348 : BOX *box1 = PG_GETARG_BOX_P(0);
586 33348 : BOX *box2 = PG_GETARG_BOX_P(1);
587 :
588 33348 : 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 66472 : box_overleft(PG_FUNCTION_ARGS)
599 : {
600 66472 : BOX *box1 = PG_GETARG_BOX_P(0);
601 66472 : BOX *box2 = PG_GETARG_BOX_P(1);
602 :
603 66472 : 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 87828 : box_right(PG_FUNCTION_ARGS)
610 : {
611 87828 : BOX *box1 = PG_GETARG_BOX_P(0);
612 87828 : BOX *box2 = PG_GETARG_BOX_P(1);
613 :
614 87828 : 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 74932 : box_overright(PG_FUNCTION_ARGS)
625 : {
626 74932 : BOX *box1 = PG_GETARG_BOX_P(0);
627 74932 : BOX *box2 = PG_GETARG_BOX_P(1);
628 :
629 74932 : PG_RETURN_BOOL(FPge(box1->low.x, box2->low.x));
630 : }
631 :
632 : /* box_below - is box1 strictly below box2?
633 : */
634 : Datum
635 18452 : box_below(PG_FUNCTION_ARGS)
636 : {
637 18452 : BOX *box1 = PG_GETARG_BOX_P(0);
638 18452 : BOX *box2 = PG_GETARG_BOX_P(1);
639 :
640 18452 : 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 53624 : box_overbelow(PG_FUNCTION_ARGS)
648 : {
649 53624 : BOX *box1 = PG_GETARG_BOX_P(0);
650 53624 : BOX *box2 = PG_GETARG_BOX_P(1);
651 :
652 53624 : PG_RETURN_BOOL(FPle(box1->high.y, box2->high.y));
653 : }
654 :
655 : /* box_above - is box1 strictly above box2?
656 : */
657 : Datum
658 38480 : box_above(PG_FUNCTION_ARGS)
659 : {
660 38480 : BOX *box1 = PG_GETARG_BOX_P(0);
661 38480 : BOX *box2 = PG_GETARG_BOX_P(1);
662 :
663 38480 : 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 74100 : box_overabove(PG_FUNCTION_ARGS)
671 : {
672 74100 : BOX *box1 = PG_GETARG_BOX_P(0);
673 74100 : BOX *box2 = PG_GETARG_BOX_P(1);
674 :
675 74100 : PG_RETURN_BOOL(FPge(box1->low.y, box2->low.y));
676 : }
677 :
678 : /* box_contained - is box1 contained by box2?
679 : */
680 : Datum
681 105528 : box_contained(PG_FUNCTION_ARGS)
682 : {
683 105528 : BOX *box1 = PG_GETARG_BOX_P(0);
684 105528 : BOX *box2 = PG_GETARG_BOX_P(1);
685 :
686 105528 : PG_RETURN_BOOL(box_contain_box(box2, box1));
687 : }
688 :
689 : /* box_contain - does box1 contain box2?
690 : */
691 : Datum
692 8168 : box_contain(PG_FUNCTION_ARGS)
693 : {
694 8168 : BOX *box1 = PG_GETARG_BOX_P(0);
695 8168 : BOX *box2 = PG_GETARG_BOX_P(1);
696 :
697 8168 : 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 170316 : box_contain_box(BOX *contains_box, BOX *contained_box)
705 : {
706 278368 : return FPge(contains_box->high.x, contained_box->high.x) &&
707 185236 : FPle(contains_box->low.x, contained_box->low.x) &&
708 355552 : FPge(contains_box->high.y, contained_box->high.y) &&
709 64996 : 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
722 100 : box_below_eq(PG_FUNCTION_ARGS)
723 : {
724 100 : BOX *box1 = PG_GETARG_BOX_P(0);
725 100 : BOX *box2 = PG_GETARG_BOX_P(1);
726 :
727 100 : PG_RETURN_BOOL(FPle(box1->high.y, box2->low.y));
728 : }
729 :
730 : Datum
731 100 : box_above_eq(PG_FUNCTION_ARGS)
732 : {
733 100 : BOX *box1 = PG_GETARG_BOX_P(0);
734 100 : BOX *box2 = PG_GETARG_BOX_P(1);
735 :
736 100 : 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 20 : box_lt(PG_FUNCTION_ARGS)
745 : {
746 20 : BOX *box1 = PG_GETARG_BOX_P(0);
747 20 : BOX *box2 = PG_GETARG_BOX_P(1);
748 :
749 20 : PG_RETURN_BOOL(FPlt(box_ar(box1), box_ar(box2)));
750 : }
751 :
752 : Datum
753 20 : box_gt(PG_FUNCTION_ARGS)
754 : {
755 20 : BOX *box1 = PG_GETARG_BOX_P(0);
756 20 : BOX *box2 = PG_GETARG_BOX_P(1);
757 :
758 20 : PG_RETURN_BOOL(FPgt(box_ar(box1), box_ar(box2)));
759 : }
760 :
761 : Datum
762 20 : box_eq(PG_FUNCTION_ARGS)
763 : {
764 20 : BOX *box1 = PG_GETARG_BOX_P(0);
765 20 : BOX *box2 = PG_GETARG_BOX_P(1);
766 :
767 20 : PG_RETURN_BOOL(FPeq(box_ar(box1), box_ar(box2)));
768 : }
769 :
770 : Datum
771 20 : box_le(PG_FUNCTION_ARGS)
772 : {
773 20 : BOX *box1 = PG_GETARG_BOX_P(0);
774 20 : BOX *box2 = PG_GETARG_BOX_P(1);
775 :
776 20 : PG_RETURN_BOOL(FPle(box_ar(box1), box_ar(box2)));
777 : }
778 :
779 : Datum
780 20 : box_ge(PG_FUNCTION_ARGS)
781 : {
782 20 : BOX *box1 = PG_GETARG_BOX_P(0);
783 20 : BOX *box2 = PG_GETARG_BOX_P(1);
784 :
785 20 : 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 20 : box_area(PG_FUNCTION_ARGS)
797 : {
798 20 : BOX *box = PG_GETARG_BOX_P(0);
799 :
800 20 : 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 20 : box_width(PG_FUNCTION_ARGS)
809 : {
810 20 : BOX *box = PG_GETARG_BOX_P(0);
811 :
812 20 : 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 20 : box_height(PG_FUNCTION_ARGS)
821 : {
822 20 : BOX *box = PG_GETARG_BOX_P(0);
823 :
824 20 : 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
832 100 : box_distance(PG_FUNCTION_ARGS)
833 : {
834 100 : BOX *box1 = PG_GETARG_BOX_P(0);
835 100 : BOX *box2 = PG_GETARG_BOX_P(1);
836 : Point a,
837 : b;
838 :
839 100 : box_cn(&a, box1);
840 100 : box_cn(&b, box2);
841 :
842 100 : PG_RETURN_FLOAT8(point_dt(&a, &b));
843 : }
844 :
845 :
846 : /* box_center - returns the center point of the box.
847 : */
848 : Datum
849 60 : box_center(PG_FUNCTION_ARGS)
850 : {
851 60 : BOX *box = PG_GETARG_BOX_P(0);
852 60 : Point *result = palloc_object(Point);
853 :
854 60 : box_cn(result, box);
855 :
856 60 : PG_RETURN_POINT_P(result);
857 : }
858 :
859 :
860 : /* box_ar - returns the area of the box.
861 : */
862 : static float8
863 220 : box_ar(BOX *box)
864 : {
865 220 : 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
872 316 : box_cn(Point *center, BOX *box)
873 : {
874 316 : center->x = float8_div(float8_pl(box->high.x, box->low.x), 2.0);
875 316 : center->y = float8_div(float8_pl(box->high.y, box->low.y), 2.0);
876 316 : }
877 :
878 :
879 : /* box_wd - returns the width (length) of the box
880 : * (horizontal magnitude).
881 : */
882 : static float8
883 240 : box_wd(BOX *box)
884 : {
885 240 : 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
893 240 : box_ht(BOX *box)
894 : {
895 240 : 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
908 100 : box_intersect(PG_FUNCTION_ARGS)
909 : {
910 100 : BOX *box1 = PG_GETARG_BOX_P(0);
911 100 : BOX *box2 = PG_GETARG_BOX_P(1);
912 : BOX *result;
913 :
914 100 : if (!box_ov(box1, box2))
915 56 : PG_RETURN_NULL();
916 :
917 44 : result = palloc_object(BOX);
918 :
919 44 : result->high.x = float8_min(box1->high.x, box2->high.x);
920 44 : result->low.x = float8_max(box1->low.x, box2->low.x);
921 44 : result->high.y = float8_min(box1->high.y, box2->high.y);
922 44 : result->low.y = float8_max(box1->low.y, box2->low.y);
923 :
924 44 : 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 20 : box_diagonal(PG_FUNCTION_ARGS)
934 : {
935 20 : BOX *box = PG_GETARG_BOX_P(0);
936 20 : LSEG *result = palloc_object(LSEG);
937 :
938 20 : statlseg_construct(result, &box->high, &box->low);
939 :
940 20 : PG_RETURN_LSEG_P(result);
941 : }
942 :
943 : /***********************************************************************
944 : **
945 : ** Routines for 2D lines.
946 : **
947 : ***********************************************************************/
948 :
949 : static bool
950 92 : line_decode(char *s, const char *str, LINE *line, Node *escontext)
951 : {
952 : /* s was already advanced over leading '{' */
953 92 : if (!single_decode(s, &line->A, &s, "line", str, escontext))
954 0 : return false;
955 88 : if (*s++ != DELIM)
956 4 : goto fail;
957 84 : if (!single_decode(s, &line->B, &s, "line", str, escontext))
958 0 : return false;
959 84 : if (*s++ != DELIM)
960 12 : goto fail;
961 72 : if (!single_decode(s, &line->C, &s, "line", str, escontext))
962 16 : return false;
963 56 : if (*s++ != RDELIM_L)
964 4 : goto fail;
965 56 : while (isspace((unsigned char) *s))
966 4 : s++;
967 52 : if (*s != '\0')
968 4 : goto fail;
969 48 : return true;
970 :
971 24 : fail:
972 24 : 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
979 140 : line_in(PG_FUNCTION_ARGS)
980 : {
981 140 : char *str = PG_GETARG_CSTRING(0);
982 140 : Node *escontext = fcinfo->context;
983 140 : LINE *line = palloc_object(LINE);
984 : LSEG lseg;
985 : bool isopen;
986 : char *s;
987 :
988 140 : s = str;
989 144 : while (isspace((unsigned char) *s))
990 4 : s++;
991 140 : if (*s == LDELIM_L)
992 : {
993 92 : if (!line_decode(s + 1, str, line, escontext))
994 24 : PG_RETURN_NULL();
995 48 : if (FPzero(line->A) && FPzero(line->B))
996 12 : 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 48 : if (!path_decode(s, true, 2, &lseg.p[0], &isopen, NULL, "line", str,
1003 : escontext))
1004 8 : PG_RETURN_NULL();
1005 24 : if (point_eq_point(&lseg.p[0], &lseg.p[1]))
1006 4 : 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 20 : line_construct(line, &lseg.p[0], lseg_sl(&lseg));
1016 : }
1017 :
1018 56 : PG_RETURN_LINE_P(line);
1019 : }
1020 :
1021 :
1022 : Datum
1023 4628 : line_out(PG_FUNCTION_ARGS)
1024 : {
1025 4628 : LINE *line = PG_GETARG_LINE_P(0);
1026 4628 : char *astr = float8out_internal(line->A);
1027 4628 : char *bstr = float8out_internal(line->B);
1028 4628 : char *cstr = float8out_internal(line->C);
1029 :
1030 4628 : 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 = palloc_object(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 4363641 : line_construct(LINE *result, Point *pt, float8 m)
1084 : {
1085 4363641 : if (isinf(m))
1086 : {
1087 : /* vertical - use "x = C" */
1088 996465 : result->A = -1.0;
1089 996465 : result->B = 0.0;
1090 996465 : result->C = pt->x;
1091 : }
1092 3367176 : else if (m == 0)
1093 : {
1094 : /* horizontal - use "y = C" */
1095 985612 : result->A = 0.0;
1096 985612 : result->B = -1.0;
1097 985612 : result->C = pt->y;
1098 : }
1099 : else
1100 : {
1101 : /* use "mx - y + yinter = 0" */
1102 2381564 : result->A = m;
1103 2381564 : result->B = -1.0;
1104 2381564 : result->C = float8_mi(pt->y, float8_mul(m, pt->x));
1105 : /* on some platforms, the preceding expression tends to produce -0 */
1106 2381564 : if (result->C == 0.0)
1107 3240 : result->C = 0.0;
1108 : }
1109 4363641 : }
1110 :
1111 : /* line_construct_pp()
1112 : * two points
1113 : */
1114 : Datum
1115 361 : line_construct_pp(PG_FUNCTION_ARGS)
1116 : {
1117 361 : Point *pt1 = PG_GETARG_POINT_P(0);
1118 361 : Point *pt2 = PG_GETARG_POINT_P(1);
1119 361 : LINE *result = palloc_object(LINE);
1120 :
1121 361 : if (point_eq_point(pt1, pt2))
1122 4 : ereport(ERROR,
1123 : (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
1124 : errmsg("invalid line specification: must be two distinct points")));
1125 :
1126 357 : line_construct(result, pt1, point_sl(pt1, pt2));
1127 :
1128 357 : PG_RETURN_LINE_P(result);
1129 : }
1130 :
1131 :
1132 : /*----------------------------------------------------------
1133 : * Relative position routines.
1134 : *---------------------------------------------------------*/
1135 :
1136 : Datum
1137 400 : line_intersect(PG_FUNCTION_ARGS)
1138 : {
1139 400 : LINE *l1 = PG_GETARG_LINE_P(0);
1140 400 : LINE *l2 = PG_GETARG_LINE_P(1);
1141 :
1142 400 : PG_RETURN_BOOL(line_interpt_line(NULL, l1, l2));
1143 : }
1144 :
1145 : Datum
1146 400 : line_parallel(PG_FUNCTION_ARGS)
1147 : {
1148 400 : LINE *l1 = PG_GETARG_LINE_P(0);
1149 400 : LINE *l2 = PG_GETARG_LINE_P(1);
1150 :
1151 400 : PG_RETURN_BOOL(!line_interpt_line(NULL, l1, l2));
1152 : }
1153 :
1154 : Datum
1155 400 : line_perp(PG_FUNCTION_ARGS)
1156 : {
1157 400 : LINE *l1 = PG_GETARG_LINE_P(0);
1158 400 : LINE *l2 = PG_GETARG_LINE_P(1);
1159 :
1160 400 : if (FPzero(l1->A))
1161 120 : PG_RETURN_BOOL(FPzero(l2->B));
1162 280 : if (FPzero(l2->A))
1163 84 : PG_RETURN_BOOL(FPzero(l1->B));
1164 196 : if (FPzero(l1->B))
1165 56 : PG_RETURN_BOOL(FPzero(l2->A));
1166 140 : if (FPzero(l2->B))
1167 40 : PG_RETURN_BOOL(FPzero(l1->A));
1168 :
1169 100 : 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 40 : line_vertical(PG_FUNCTION_ARGS)
1175 : {
1176 40 : LINE *line = PG_GETARG_LINE_P(0);
1177 :
1178 40 : PG_RETURN_BOOL(FPzero(line->B));
1179 : }
1180 :
1181 : Datum
1182 40 : line_horizontal(PG_FUNCTION_ARGS)
1183 : {
1184 40 : LINE *line = PG_GETARG_LINE_P(0);
1185 :
1186 40 : PG_RETURN_BOOL(FPzero(line->A));
1187 : }
1188 :
1189 :
1190 : /*
1191 : * Check whether the two lines are the same
1192 : */
1193 : Datum
1194 410 : line_eq(PG_FUNCTION_ARGS)
1195 : {
1196 410 : LINE *l1 = PG_GETARG_LINE_P(0);
1197 410 : LINE *l2 = PG_GETARG_LINE_P(1);
1198 : float8 ratio;
1199 :
1200 : /* If any NaNs are involved, insist on exact equality */
1201 410 : if (unlikely(isnan(l1->A) || isnan(l1->B) || isnan(l1->C) ||
1202 : isnan(l2->A) || isnan(l2->B) || isnan(l2->C)))
1203 : {
1204 154 : 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 256 : if (!FPzero(l2->A))
1211 160 : ratio = float8_div(l1->A, l2->A);
1212 96 : else if (!FPzero(l2->B))
1213 96 : 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 256 : 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 320 : line_sl(LINE *line)
1234 : {
1235 320 : if (FPzero(line->A))
1236 96 : return 0.0;
1237 224 : if (FPzero(line->B))
1238 64 : return get_float8_infinity();
1239 160 : return float8_div(line->A, -line->B);
1240 : }
1241 :
1242 :
1243 : /*
1244 : * Return inverse slope of the line
1245 : */
1246 : static inline float8
1247 1195440 : line_invsl(LINE *line)
1248 : {
1249 1195440 : if (FPzero(line->A))
1250 476880 : return get_float8_infinity();
1251 718560 : if (FPzero(line->B))
1252 463736 : return 0.0;
1253 254824 : return float8_div(line->B, line->A);
1254 : }
1255 :
1256 :
1257 : /* line_distance()
1258 : * Distance between two lines.
1259 : */
1260 : Datum
1261 400 : line_distance(PG_FUNCTION_ARGS)
1262 : {
1263 400 : LINE *l1 = PG_GETARG_LINE_P(0);
1264 400 : LINE *l2 = PG_GETARG_LINE_P(1);
1265 : float8 ratio;
1266 :
1267 400 : if (line_interpt_line(NULL, l1, l2)) /* intersecting? */
1268 336 : PG_RETURN_FLOAT8(0.0);
1269 :
1270 64 : if (!FPzero(l1->A) && !isnan(l1->A) && !FPzero(l2->A) && !isnan(l2->A))
1271 28 : ratio = float8_div(l1->A, l2->A);
1272 36 : else if (!FPzero(l1->B) && !isnan(l1->B) && !FPzero(l2->B) && !isnan(l2->B))
1273 36 : ratio = float8_div(l1->B, l2->B);
1274 : else
1275 0 : ratio = 1.0;
1276 :
1277 64 : 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 400 : line_interpt(PG_FUNCTION_ARGS)
1287 : {
1288 400 : LINE *l1 = PG_GETARG_LINE_P(0);
1289 400 : LINE *l2 = PG_GETARG_LINE_P(1);
1290 : Point *result;
1291 :
1292 400 : result = palloc_object(Point);
1293 :
1294 400 : if (!line_interpt_line(result, l1, l2))
1295 64 : PG_RETURN_NULL();
1296 336 : 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 2781900 : line_interpt_line(Point *result, LINE *l1, LINE *l2)
1315 : {
1316 : float8 x,
1317 : y;
1318 :
1319 2781900 : if (!FPzero(l1->B))
1320 : {
1321 2024300 : if (FPeq(l2->A, float8_mul(l1->A, float8_div(l2->B, l1->B))))
1322 6392 : return false;
1323 :
1324 2017908 : 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 2017908 : y = float8_div(-float8_pl(float8_mul(l1->A, x), l1->C), l1->B);
1329 : }
1330 757600 : else if (!FPzero(l2->B))
1331 : {
1332 755628 : if (FPeq(l1->A, float8_mul(l2->A, float8_div(l1->B, l2->B))))
1333 0 : return false;
1334 :
1335 755628 : 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 755628 : y = float8_div(-float8_pl(float8_mul(l2->A, x), l2->C), l2->B);
1340 : }
1341 : else
1342 1972 : return false;
1343 :
1344 : /* On some platforms, the preceding expressions tend to produce -0. */
1345 2773536 : if (x == 0.0)
1346 81140 : x = 0.0;
1347 2773536 : if (y == 0.0)
1348 79952 : y = 0.0;
1349 :
1350 2773536 : if (result != NULL)
1351 2772528 : point_construct(result, x, y);
1352 :
1353 2773536 : 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 36 : path_area(PG_FUNCTION_ARGS)
1381 : {
1382 36 : PATH *path = PG_GETARG_PATH_P(0);
1383 36 : float8 area = 0.0;
1384 : int i,
1385 : j;
1386 :
1387 36 : if (!path->closed)
1388 16 : PG_RETURN_NULL();
1389 :
1390 56 : for (i = 0; i < path->npts; i++)
1391 : {
1392 36 : j = (i + 1) % path->npts;
1393 36 : area = float8_pl(area, float8_mul(path->p[i].x, path->p[j].y));
1394 36 : area = float8_mi(area, float8_mul(path->p[i].y, path->p[j].x));
1395 : }
1396 :
1397 20 : PG_RETURN_FLOAT8(float8_div(fabs(area), 2.0));
1398 : }
1399 :
1400 :
1401 : Datum
1402 20613 : path_in(PG_FUNCTION_ARGS)
1403 : {
1404 20613 : char *str = PG_GETARG_CSTRING(0);
1405 20613 : Node *escontext = fcinfo->context;
1406 : PATH *path;
1407 : bool isopen;
1408 : char *s;
1409 : int npts;
1410 : int size;
1411 : int base_size;
1412 20613 : int depth = 0;
1413 :
1414 20613 : if ((npts = pair_count(str, ',')) <= 0)
1415 12 : ereturn(escontext, (Datum) 0,
1416 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
1417 : errmsg("invalid input syntax for type %s: \"%s\"",
1418 : "path", str)));
1419 :
1420 20601 : s = str;
1421 20609 : while (isspace((unsigned char) *s))
1422 8 : s++;
1423 :
1424 : /* skip single leading paren */
1425 20601 : if ((*s == LDELIM) && (strrchr(s, LDELIM) == s))
1426 : {
1427 16 : s++;
1428 16 : depth++;
1429 : }
1430 :
1431 20601 : base_size = sizeof(path->p[0]) * npts;
1432 20601 : size = offsetof(PATH, p) + base_size;
1433 :
1434 : /* Check for integer overflow */
1435 20601 : 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 20601 : path = (PATH *) palloc(size);
1441 :
1442 20601 : SET_VARSIZE(path, size);
1443 20601 : path->npts = npts;
1444 :
1445 20601 : if (!path_decode(s, true, npts, &(path->p[0]), &isopen, &s, "path", str,
1446 : escontext))
1447 8 : PG_RETURN_NULL();
1448 :
1449 20585 : if (depth >= 1)
1450 : {
1451 16 : if (*s++ != RDELIM)
1452 4 : ereturn(escontext, (Datum) 0,
1453 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
1454 : errmsg("invalid input syntax for type %s: \"%s\"",
1455 : "path", str)));
1456 16 : while (isspace((unsigned char) *s))
1457 4 : s++;
1458 : }
1459 20581 : if (*s != '\0')
1460 4 : ereturn(escontext, (Datum) 0,
1461 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
1462 : errmsg("invalid input syntax for type %s: \"%s\"",
1463 : "path", str)));
1464 :
1465 20577 : path->closed = (!isopen);
1466 : /* prevent instability in unused pad bytes */
1467 20577 : path->dummy = 0;
1468 :
1469 20577 : PG_RETURN_PATH_P(path);
1470 : }
1471 :
1472 :
1473 : Datum
1474 31871 : path_out(PG_FUNCTION_ARGS)
1475 : {
1476 31871 : PATH *path = PG_GETARG_PATH_P(0);
1477 :
1478 31871 : 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 324 : path_n_lt(PG_FUNCTION_ARGS)
1554 : {
1555 324 : PATH *p1 = PG_GETARG_PATH_P(0);
1556 324 : PATH *p2 = PG_GETARG_PATH_P(1);
1557 :
1558 324 : PG_RETURN_BOOL(p1->npts < p2->npts);
1559 : }
1560 :
1561 : Datum
1562 324 : path_n_gt(PG_FUNCTION_ARGS)
1563 : {
1564 324 : PATH *p1 = PG_GETARG_PATH_P(0);
1565 324 : PATH *p2 = PG_GETARG_PATH_P(1);
1566 :
1567 324 : PG_RETURN_BOOL(p1->npts > p2->npts);
1568 : }
1569 :
1570 : Datum
1571 325 : path_n_eq(PG_FUNCTION_ARGS)
1572 : {
1573 325 : PATH *p1 = PG_GETARG_PATH_P(0);
1574 325 : PATH *p2 = PG_GETARG_PATH_P(1);
1575 :
1576 325 : PG_RETURN_BOOL(p1->npts == p2->npts);
1577 : }
1578 :
1579 : Datum
1580 324 : path_n_le(PG_FUNCTION_ARGS)
1581 : {
1582 324 : PATH *p1 = PG_GETARG_PATH_P(0);
1583 324 : PATH *p2 = PG_GETARG_PATH_P(1);
1584 :
1585 324 : PG_RETURN_BOOL(p1->npts <= p2->npts);
1586 : }
1587 :
1588 : Datum
1589 324 : path_n_ge(PG_FUNCTION_ARGS)
1590 : {
1591 324 : PATH *p1 = PG_GETARG_PATH_P(0);
1592 324 : PATH *p2 = PG_GETARG_PATH_P(1);
1593 :
1594 324 : PG_RETURN_BOOL(p1->npts >= p2->npts);
1595 : }
1596 :
1597 : /*----------------------------------------------------------
1598 : * Conversion operators.
1599 : *---------------------------------------------------------*/
1600 :
1601 : Datum
1602 108 : path_isclosed(PG_FUNCTION_ARGS)
1603 : {
1604 108 : PATH *path = PG_GETARG_PATH_P(0);
1605 :
1606 108 : PG_RETURN_BOOL(path->closed);
1607 : }
1608 :
1609 : Datum
1610 76 : path_isopen(PG_FUNCTION_ARGS)
1611 : {
1612 76 : PATH *path = PG_GETARG_PATH_P(0);
1613 :
1614 76 : PG_RETURN_BOOL(!path->closed);
1615 : }
1616 :
1617 : Datum
1618 3620 : path_npoints(PG_FUNCTION_ARGS)
1619 : {
1620 3620 : PATH *path = PG_GETARG_PATH_P(0);
1621 :
1622 3620 : PG_RETURN_INT32(path->npts);
1623 : }
1624 :
1625 :
1626 : Datum
1627 52 : path_close(PG_FUNCTION_ARGS)
1628 : {
1629 52 : PATH *path = PG_GETARG_PATH_P_COPY(0);
1630 :
1631 52 : path->closed = true;
1632 :
1633 52 : PG_RETURN_PATH_P(path);
1634 : }
1635 :
1636 : Datum
1637 36 : path_open(PG_FUNCTION_ARGS)
1638 : {
1639 36 : PATH *path = PG_GETARG_PATH_P_COPY(0);
1640 :
1641 36 : path->closed = false;
1642 :
1643 36 : 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 920612 : path_inter(PG_FUNCTION_ARGS)
1654 : {
1655 920612 : PATH *p1 = PG_GETARG_PATH_P(0);
1656 920612 : 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 920612 : b1.high.x = b1.low.x = p1->p[0].x;
1667 920612 : b1.high.y = b1.low.y = p1->p[0].y;
1668 3501400 : for (i = 1; i < p1->npts; i++)
1669 : {
1670 2580788 : b1.high.x = float8_max(p1->p[i].x, b1.high.x);
1671 2580788 : b1.high.y = float8_max(p1->p[i].y, b1.high.y);
1672 2580788 : b1.low.x = float8_min(p1->p[i].x, b1.low.x);
1673 2580788 : b1.low.y = float8_min(p1->p[i].y, b1.low.y);
1674 : }
1675 920612 : b2.high.x = b2.low.x = p2->p[0].x;
1676 920612 : b2.high.y = b2.low.y = p2->p[0].y;
1677 2634216 : for (i = 1; i < p2->npts; i++)
1678 : {
1679 1713604 : b2.high.x = float8_max(p2->p[i].x, b2.high.x);
1680 1713604 : b2.high.y = float8_max(p2->p[i].y, b2.high.y);
1681 1713604 : b2.low.x = float8_min(p2->p[i].x, b2.low.x);
1682 1713604 : b2.low.y = float8_min(p2->p[i].y, b2.low.y);
1683 : }
1684 920612 : if (!box_ov(&b1, &b2))
1685 898280 : PG_RETURN_BOOL(false);
1686 :
1687 : /* pairwise check lseg intersections */
1688 110008 : for (i = 0; i < p1->npts; i++)
1689 : {
1690 : int iprev;
1691 :
1692 92592 : if (i > 0)
1693 70260 : iprev = i - 1;
1694 : else
1695 : {
1696 22332 : if (!p1->closed)
1697 5324 : continue;
1698 17008 : iprev = p1->npts - 1; /* include the closure segment */
1699 : }
1700 :
1701 290444 : for (j = 0; j < p2->npts; j++)
1702 : {
1703 : int jprev;
1704 :
1705 208092 : if (j > 0)
1706 120824 : jprev = j - 1;
1707 : else
1708 : {
1709 87268 : if (!p2->closed)
1710 82492 : continue;
1711 4776 : jprev = p2->npts - 1; /* include the closure segment */
1712 : }
1713 :
1714 125600 : statlseg_construct(&seg1, &p1->p[iprev], &p1->p[i]);
1715 125600 : statlseg_construct(&seg2, &p2->p[jprev], &p2->p[j]);
1716 125600 : if (lseg_interpt_lseg(NULL, &seg1, &seg2))
1717 4916 : PG_RETURN_BOOL(true);
1718 : }
1719 : }
1720 :
1721 : /* if we dropped through, no two segs intersected */
1722 17416 : 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 324 : path_distance(PG_FUNCTION_ARGS)
1731 : {
1732 324 : PATH *p1 = PG_GETARG_PATH_P(0);
1733 324 : PATH *p2 = PG_GETARG_PATH_P(1);
1734 324 : float8 min = 0.0; /* initialize to keep compiler quiet */
1735 324 : bool have_min = false;
1736 : float8 tmp;
1737 : int i,
1738 : j;
1739 : LSEG seg1,
1740 : seg2;
1741 :
1742 1008 : for (i = 0; i < p1->npts; i++)
1743 : {
1744 : int iprev;
1745 :
1746 684 : if (i > 0)
1747 360 : iprev = i - 1;
1748 : else
1749 : {
1750 324 : if (!p1->closed)
1751 144 : continue;
1752 180 : iprev = p1->npts - 1; /* include the closure segment */
1753 : }
1754 :
1755 1680 : for (j = 0; j < p2->npts; j++)
1756 : {
1757 : int jprev;
1758 :
1759 1140 : if (j > 0)
1760 600 : jprev = j - 1;
1761 : else
1762 : {
1763 540 : if (!p2->closed)
1764 240 : continue;
1765 300 : jprev = p2->npts - 1; /* include the closure segment */
1766 : }
1767 :
1768 900 : statlseg_construct(&seg1, &p1->p[iprev], &p1->p[i]);
1769 900 : statlseg_construct(&seg2, &p2->p[jprev], &p2->p[j]);
1770 :
1771 900 : tmp = lseg_closept_lseg(NULL, &seg1, &seg2);
1772 900 : if (!have_min || float8_lt(tmp, min))
1773 : {
1774 388 : min = tmp;
1775 388 : have_min = true;
1776 : }
1777 : }
1778 : }
1779 :
1780 324 : if (!have_min)
1781 0 : PG_RETURN_NULL();
1782 :
1783 324 : PG_RETURN_FLOAT8(min);
1784 : }
1785 :
1786 :
1787 : /*----------------------------------------------------------
1788 : * "Arithmetic" operations.
1789 : *---------------------------------------------------------*/
1790 :
1791 : Datum
1792 36 : path_length(PG_FUNCTION_ARGS)
1793 : {
1794 36 : PATH *path = PG_GETARG_PATH_P(0);
1795 36 : float8 result = 0.0;
1796 : int i;
1797 :
1798 112 : for (i = 0; i < path->npts; i++)
1799 : {
1800 : int iprev;
1801 :
1802 76 : if (i > 0)
1803 40 : iprev = i - 1;
1804 : else
1805 : {
1806 36 : if (!path->closed)
1807 16 : continue;
1808 20 : iprev = path->npts - 1; /* include the closure segment */
1809 : }
1810 :
1811 60 : result = float8_pl(result, point_dt(&path->p[iprev], &path->p[i]));
1812 : }
1813 :
1814 36 : 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 17359 : point_in(PG_FUNCTION_ARGS)
1832 : {
1833 17359 : char *str = PG_GETARG_CSTRING(0);
1834 17359 : Point *point = palloc_object(Point);
1835 :
1836 : /* Ignore failure from pair_decode, since our return value won't matter */
1837 17359 : pair_decode(str, &point->x, &point->y, NULL, "point", str, fcinfo->context);
1838 17339 : PG_RETURN_POINT_P(point);
1839 : }
1840 :
1841 : Datum
1842 133638 : point_out(PG_FUNCTION_ARGS)
1843 : {
1844 133638 : Point *pt = PG_GETARG_POINT_P(0);
1845 :
1846 133638 : 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 12 : point_recv(PG_FUNCTION_ARGS)
1854 : {
1855 12 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
1856 : Point *point;
1857 :
1858 12 : point = palloc_object(Point);
1859 12 : point->x = pq_getmsgfloat8(buf);
1860 12 : point->y = pq_getmsgfloat8(buf);
1861 12 : PG_RETURN_POINT_P(point);
1862 : }
1863 :
1864 : /*
1865 : * point_send - converts point to binary format
1866 : */
1867 : Datum
1868 12 : point_send(PG_FUNCTION_ARGS)
1869 : {
1870 12 : Point *pt = PG_GETARG_POINT_P(0);
1871 : StringInfoData buf;
1872 :
1873 12 : pq_begintypsend(&buf);
1874 12 : pq_sendfloat8(&buf, pt->x);
1875 12 : pq_sendfloat8(&buf, pt->y);
1876 12 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
1877 : }
1878 :
1879 :
1880 : /*
1881 : * Initialize a point
1882 : */
1883 : static inline void
1884 3466983 : point_construct(Point *result, float8 x, float8 y)
1885 : {
1886 3466983 : result->x = x;
1887 3466983 : result->y = y;
1888 3466983 : }
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 471821 : point_left(PG_FUNCTION_ARGS)
1902 : {
1903 471821 : Point *pt1 = PG_GETARG_POINT_P(0);
1904 471821 : Point *pt2 = PG_GETARG_POINT_P(1);
1905 :
1906 471821 : PG_RETURN_BOOL(FPlt(pt1->x, pt2->x));
1907 : }
1908 :
1909 : Datum
1910 11222195 : point_right(PG_FUNCTION_ARGS)
1911 : {
1912 11222195 : Point *pt1 = PG_GETARG_POINT_P(0);
1913 11222195 : Point *pt2 = PG_GETARG_POINT_P(1);
1914 :
1915 11222195 : PG_RETURN_BOOL(FPgt(pt1->x, pt2->x));
1916 : }
1917 :
1918 : Datum
1919 11380785 : point_above(PG_FUNCTION_ARGS)
1920 : {
1921 11380785 : Point *pt1 = PG_GETARG_POINT_P(0);
1922 11380785 : Point *pt2 = PG_GETARG_POINT_P(1);
1923 :
1924 11380785 : PG_RETURN_BOOL(FPgt(pt1->y, pt2->y));
1925 : }
1926 :
1927 : Datum
1928 834661 : point_below(PG_FUNCTION_ARGS)
1929 : {
1930 834661 : Point *pt1 = PG_GETARG_POINT_P(0);
1931 834661 : Point *pt2 = PG_GETARG_POINT_P(1);
1932 :
1933 834661 : PG_RETURN_BOOL(FPlt(pt1->y, pt2->y));
1934 : }
1935 :
1936 : Datum
1937 331936 : point_vert(PG_FUNCTION_ARGS)
1938 : {
1939 331936 : Point *pt1 = PG_GETARG_POINT_P(0);
1940 331936 : Point *pt2 = PG_GETARG_POINT_P(1);
1941 :
1942 331936 : PG_RETURN_BOOL(FPeq(pt1->x, pt2->x));
1943 : }
1944 :
1945 : Datum
1946 354979 : point_horiz(PG_FUNCTION_ARGS)
1947 : {
1948 354979 : Point *pt1 = PG_GETARG_POINT_P(0);
1949 354979 : Point *pt2 = PG_GETARG_POINT_P(1);
1950 :
1951 354979 : PG_RETURN_BOOL(FPeq(pt1->y, pt2->y));
1952 : }
1953 :
1954 : Datum
1955 53469 : point_eq(PG_FUNCTION_ARGS)
1956 : {
1957 53469 : Point *pt1 = PG_GETARG_POINT_P(0);
1958 53469 : Point *pt2 = PG_GETARG_POINT_P(1);
1959 :
1960 53469 : PG_RETURN_BOOL(point_eq_point(pt1, pt2));
1961 : }
1962 :
1963 : Datum
1964 468 : point_ne(PG_FUNCTION_ARGS)
1965 : {
1966 468 : Point *pt1 = PG_GETARG_POINT_P(0);
1967 468 : Point *pt2 = PG_GETARG_POINT_P(1);
1968 :
1969 468 : 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 202261 : point_eq_point(Point *pt1, Point *pt2)
1978 : {
1979 : /* If any NaNs are involved, insist on exact equality */
1980 202261 : if (unlikely(isnan(pt1->x) || isnan(pt1->y) ||
1981 : isnan(pt2->x) || isnan(pt2->y)))
1982 284 : return (float8_eq(pt1->x, pt2->x) && float8_eq(pt1->y, pt2->y));
1983 :
1984 201977 : 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 492719 : point_distance(PG_FUNCTION_ARGS)
1994 : {
1995 492719 : Point *pt1 = PG_GETARG_POINT_P(0);
1996 492719 : Point *pt2 = PG_GETARG_POINT_P(1);
1997 :
1998 492719 : PG_RETURN_FLOAT8(point_dt(pt1, pt2));
1999 : }
2000 :
2001 : static inline float8
2002 10364099 : point_dt(Point *pt1, Point *pt2)
2003 : {
2004 10364099 : return hypot(float8_mi(pt1->x, pt2->x), float8_mi(pt1->y, pt2->y));
2005 : }
2006 :
2007 : Datum
2008 400 : point_slope(PG_FUNCTION_ARGS)
2009 : {
2010 400 : Point *pt1 = PG_GETARG_POINT_P(0);
2011 400 : Point *pt2 = PG_GETARG_POINT_P(1);
2012 :
2013 400 : 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 2566137 : point_sl(Point *pt1, Point *pt2)
2024 : {
2025 2566137 : if (FPeq(pt1->x, pt2->x))
2026 285669 : return get_float8_infinity();
2027 2280468 : if (FPeq(pt1->y, pt2->y))
2028 282996 : return 0.0;
2029 1997472 : 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 604320 : point_invsl(Point *pt1, Point *pt2)
2040 : {
2041 604320 : if (FPeq(pt1->x, pt2->x))
2042 239072 : return 0.0;
2043 365248 : if (FPeq(pt1->y, pt2->y))
2044 234136 : return get_float8_infinity();
2045 131112 : 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 69 : lseg_in(PG_FUNCTION_ARGS)
2066 : {
2067 69 : char *str = PG_GETARG_CSTRING(0);
2068 69 : Node *escontext = fcinfo->context;
2069 69 : LSEG *lseg = palloc_object(LSEG);
2070 : bool isopen;
2071 :
2072 69 : if (!path_decode(str, true, 2, &lseg->p[0], &isopen, NULL, "lseg", str,
2073 : escontext))
2074 8 : PG_RETURN_NULL();
2075 :
2076 45 : PG_RETURN_LSEG_P(lseg);
2077 : }
2078 :
2079 :
2080 : Datum
2081 4871 : lseg_out(PG_FUNCTION_ARGS)
2082 : {
2083 4871 : LSEG *ls = PG_GETARG_LSEG_P(0);
2084 :
2085 4871 : 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 = palloc_object(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 5 : lseg_construct(PG_FUNCTION_ARGS)
2130 : {
2131 5 : Point *pt1 = PG_GETARG_POINT_P(0);
2132 5 : Point *pt2 = PG_GETARG_POINT_P(1);
2133 5 : LSEG *result = palloc_object(LSEG);
2134 :
2135 5 : statlseg_construct(result, pt1, pt2);
2136 :
2137 5 : PG_RETURN_LSEG_P(result);
2138 : }
2139 :
2140 : /* like lseg_construct, but assume space already allocated */
2141 : static inline void
2142 673949 : statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2)
2143 : {
2144 673949 : lseg->p[0].x = pt1->x;
2145 673949 : lseg->p[0].y = pt1->y;
2146 673949 : lseg->p[1].x = pt2->x;
2147 673949 : lseg->p[1].y = pt2->y;
2148 673949 : }
2149 :
2150 :
2151 : /*
2152 : * Return slope of the line segment
2153 : */
2154 : static inline float8
2155 2565380 : lseg_sl(LSEG *lseg)
2156 : {
2157 2565380 : 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 256 : lseg_invsl(LSEG *lseg)
2166 : {
2167 256 : return point_invsl(&lseg->p[0], &lseg->p[1]);
2168 : }
2169 :
2170 :
2171 : Datum
2172 32 : lseg_length(PG_FUNCTION_ARGS)
2173 : {
2174 32 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2175 :
2176 32 : 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 16912 : lseg_intersect(PG_FUNCTION_ARGS)
2189 : {
2190 16912 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2191 16912 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2192 :
2193 16912 : PG_RETURN_BOOL(lseg_interpt_lseg(NULL, l1, l2));
2194 : }
2195 :
2196 :
2197 : Datum
2198 256 : lseg_parallel(PG_FUNCTION_ARGS)
2199 : {
2200 256 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2201 256 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2202 :
2203 256 : 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 256 : lseg_perp(PG_FUNCTION_ARGS)
2211 : {
2212 256 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2213 256 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2214 :
2215 256 : PG_RETURN_BOOL(FPeq(lseg_sl(l1), lseg_invsl(l2)));
2216 : }
2217 :
2218 : Datum
2219 32 : lseg_vertical(PG_FUNCTION_ARGS)
2220 : {
2221 32 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2222 :
2223 32 : PG_RETURN_BOOL(FPeq(lseg->p[0].x, lseg->p[1].x));
2224 : }
2225 :
2226 : Datum
2227 32 : lseg_horizontal(PG_FUNCTION_ARGS)
2228 : {
2229 32 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2230 :
2231 32 : PG_RETURN_BOOL(FPeq(lseg->p[0].y, lseg->p[1].y));
2232 : }
2233 :
2234 :
2235 : Datum
2236 257 : lseg_eq(PG_FUNCTION_ARGS)
2237 : {
2238 257 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2239 257 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2240 :
2241 257 : 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 256 : lseg_ne(PG_FUNCTION_ARGS)
2247 : {
2248 256 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2249 256 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2250 :
2251 256 : 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 256 : lseg_lt(PG_FUNCTION_ARGS)
2257 : {
2258 256 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2259 256 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2260 :
2261 256 : 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 256 : lseg_le(PG_FUNCTION_ARGS)
2267 : {
2268 256 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2269 256 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2270 :
2271 256 : 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 256 : lseg_gt(PG_FUNCTION_ARGS)
2277 : {
2278 256 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2279 256 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2280 :
2281 256 : 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 256 : lseg_ge(PG_FUNCTION_ARGS)
2287 : {
2288 256 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2289 256 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2290 :
2291 256 : 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 256 : lseg_distance(PG_FUNCTION_ARGS)
2307 : {
2308 256 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2309 256 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2310 :
2311 256 : PG_RETURN_FLOAT8(lseg_closept_lseg(NULL, l1, l2));
2312 : }
2313 :
2314 :
2315 : Datum
2316 64 : lseg_center(PG_FUNCTION_ARGS)
2317 : {
2318 64 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2319 : Point *result;
2320 :
2321 64 : result = palloc_object(Point);
2322 :
2323 64 : result->x = float8_div(float8_pl(lseg->p[0].x, lseg->p[1].x), 2.0);
2324 64 : result->y = float8_div(float8_pl(lseg->p[0].y, lseg->p[1].y), 2.0);
2325 :
2326 64 : 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 978900 : lseg_interpt_lseg(Point *result, LSEG *l1, LSEG *l2)
2339 : {
2340 : Point interpt;
2341 : LINE tmp;
2342 :
2343 978900 : line_construct(&tmp, &l2->p[0], lseg_sl(l2));
2344 978900 : if (!lseg_interpt_line(&interpt, l1, &tmp))
2345 923904 : 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 54996 : if (!lseg_contain_point(l2, &interpt))
2352 41188 : return false;
2353 :
2354 13808 : if (result != NULL)
2355 4476 : *result = interpt;
2356 :
2357 13808 : return true;
2358 : }
2359 :
2360 : Datum
2361 3832 : lseg_interpt(PG_FUNCTION_ARGS)
2362 : {
2363 3832 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2364 3832 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2365 : Point *result;
2366 :
2367 3832 : result = palloc_object(Point);
2368 :
2369 3832 : if (!lseg_interpt_lseg(result, l1, l2))
2370 256 : PG_RETURN_NULL();
2371 3576 : 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 400 : dist_pl(PG_FUNCTION_ARGS)
2391 : {
2392 400 : Point *pt = PG_GETARG_POINT_P(0);
2393 400 : LINE *line = PG_GETARG_LINE_P(1);
2394 :
2395 400 : PG_RETURN_FLOAT8(line_closept_point(NULL, line, pt));
2396 : }
2397 :
2398 : /*
2399 : * Distance from a line to a point
2400 : */
2401 : Datum
2402 400 : dist_lp(PG_FUNCTION_ARGS)
2403 : {
2404 400 : LINE *line = PG_GETARG_LINE_P(0);
2405 400 : Point *pt = PG_GETARG_POINT_P(1);
2406 :
2407 400 : PG_RETURN_FLOAT8(line_closept_point(NULL, line, pt));
2408 : }
2409 :
2410 : /*
2411 : * Distance from a point to a lseg
2412 : */
2413 : Datum
2414 320 : dist_ps(PG_FUNCTION_ARGS)
2415 : {
2416 320 : Point *pt = PG_GETARG_POINT_P(0);
2417 320 : LSEG *lseg = PG_GETARG_LSEG_P(1);
2418 :
2419 320 : PG_RETURN_FLOAT8(lseg_closept_point(NULL, lseg, pt));
2420 : }
2421 :
2422 : /*
2423 : * Distance from a lseg to a point
2424 : */
2425 : Datum
2426 320 : dist_sp(PG_FUNCTION_ARGS)
2427 : {
2428 320 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2429 320 : Point *pt = PG_GETARG_POINT_P(1);
2430 :
2431 320 : PG_RETURN_FLOAT8(lseg_closept_point(NULL, lseg, pt));
2432 : }
2433 :
2434 : static float8
2435 720 : dist_ppath_internal(Point *pt, PATH *path)
2436 : {
2437 720 : float8 result = 0.0; /* keep compiler quiet */
2438 720 : 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 2240 : for (i = 0; i < path->npts; i++)
2450 : {
2451 : int iprev;
2452 :
2453 1520 : if (i > 0)
2454 800 : iprev = i - 1;
2455 : else
2456 : {
2457 720 : if (!path->closed)
2458 320 : continue;
2459 400 : iprev = path->npts - 1; /* Include the closure segment */
2460 : }
2461 :
2462 1200 : statlseg_construct(&lseg, &path->p[iprev], &path->p[i]);
2463 1200 : tmp = lseg_closept_point(NULL, &lseg, pt);
2464 1200 : if (!have_min || float8_lt(tmp, result))
2465 : {
2466 752 : result = tmp;
2467 752 : have_min = true;
2468 : }
2469 : }
2470 :
2471 720 : return result;
2472 : }
2473 :
2474 : /*
2475 : * Distance from a point to a path
2476 : */
2477 : Datum
2478 360 : dist_ppath(PG_FUNCTION_ARGS)
2479 : {
2480 360 : Point *pt = PG_GETARG_POINT_P(0);
2481 360 : PATH *path = PG_GETARG_PATH_P(1);
2482 :
2483 360 : PG_RETURN_FLOAT8(dist_ppath_internal(pt, path));
2484 : }
2485 :
2486 : /*
2487 : * Distance from a path to a point
2488 : */
2489 : Datum
2490 360 : dist_pathp(PG_FUNCTION_ARGS)
2491 : {
2492 360 : PATH *path = PG_GETARG_PATH_P(0);
2493 360 : Point *pt = PG_GETARG_POINT_P(1);
2494 :
2495 360 : PG_RETURN_FLOAT8(dist_ppath_internal(pt, path));
2496 : }
2497 :
2498 : /*
2499 : * Distance from a point to a box
2500 : */
2501 : Datum
2502 284 : dist_pb(PG_FUNCTION_ARGS)
2503 : {
2504 284 : Point *pt = PG_GETARG_POINT_P(0);
2505 284 : BOX *box = PG_GETARG_BOX_P(1);
2506 :
2507 284 : PG_RETURN_FLOAT8(box_closept_point(NULL, box, pt));
2508 : }
2509 :
2510 : /*
2511 : * Distance from a box to a point
2512 : */
2513 : Datum
2514 103508 : dist_bp(PG_FUNCTION_ARGS)
2515 : {
2516 103508 : BOX *box = PG_GETARG_BOX_P(0);
2517 103508 : Point *pt = PG_GETARG_POINT_P(1);
2518 :
2519 103508 : PG_RETURN_FLOAT8(box_closept_point(NULL, box, pt));
2520 : }
2521 :
2522 : /*
2523 : * Distance from a lseg to a line
2524 : */
2525 : Datum
2526 320 : dist_sl(PG_FUNCTION_ARGS)
2527 : {
2528 320 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2529 320 : LINE *line = PG_GETARG_LINE_P(1);
2530 :
2531 320 : PG_RETURN_FLOAT8(lseg_closept_line(NULL, lseg, line));
2532 : }
2533 :
2534 : /*
2535 : * Distance from a line to a lseg
2536 : */
2537 : Datum
2538 320 : dist_ls(PG_FUNCTION_ARGS)
2539 : {
2540 320 : LINE *line = PG_GETARG_LINE_P(0);
2541 320 : LSEG *lseg = PG_GETARG_LSEG_P(1);
2542 :
2543 320 : PG_RETURN_FLOAT8(lseg_closept_line(NULL, lseg, line));
2544 : }
2545 :
2546 : /*
2547 : * Distance from a lseg to a box
2548 : */
2549 : Datum
2550 160 : dist_sb(PG_FUNCTION_ARGS)
2551 : {
2552 160 : LSEG *lseg = PG_GETARG_LSEG_P(0);
2553 160 : BOX *box = PG_GETARG_BOX_P(1);
2554 :
2555 160 : PG_RETURN_FLOAT8(box_closept_lseg(NULL, box, lseg));
2556 : }
2557 :
2558 : /*
2559 : * Distance from a box to a lseg
2560 : */
2561 : Datum
2562 160 : dist_bs(PG_FUNCTION_ARGS)
2563 : {
2564 160 : BOX *box = PG_GETARG_BOX_P(0);
2565 160 : LSEG *lseg = PG_GETARG_LSEG_P(1);
2566 :
2567 160 : PG_RETURN_FLOAT8(box_closept_lseg(NULL, box, lseg));
2568 : }
2569 :
2570 : static float8
2571 224 : dist_cpoly_internal(CIRCLE *circle, POLYGON *poly)
2572 : {
2573 : float8 result;
2574 :
2575 : /* calculate distance to center, and subtract radius */
2576 224 : result = float8_mi(dist_ppoly_internal(&circle->center, poly),
2577 : circle->radius);
2578 224 : if (result < 0.0)
2579 120 : result = 0.0;
2580 :
2581 224 : return result;
2582 : }
2583 :
2584 : /*
2585 : * Distance from a circle to a polygon
2586 : */
2587 : Datum
2588 224 : dist_cpoly(PG_FUNCTION_ARGS)
2589 : {
2590 224 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
2591 224 : POLYGON *poly = PG_GETARG_POLYGON_P(1);
2592 :
2593 224 : 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 280 : dist_ppoly(PG_FUNCTION_ARGS)
2613 : {
2614 280 : Point *point = PG_GETARG_POINT_P(0);
2615 280 : POLYGON *poly = PG_GETARG_POLYGON_P(1);
2616 :
2617 280 : PG_RETURN_FLOAT8(dist_ppoly_internal(point, poly));
2618 : }
2619 :
2620 : Datum
2621 22872 : dist_polyp(PG_FUNCTION_ARGS)
2622 : {
2623 22872 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
2624 22872 : Point *point = PG_GETARG_POINT_P(1);
2625 :
2626 22872 : PG_RETURN_FLOAT8(dist_ppoly_internal(point, poly));
2627 : }
2628 :
2629 : static float8
2630 23376 : dist_ppoly_internal(Point *pt, POLYGON *poly)
2631 : {
2632 : float8 result;
2633 : float8 d;
2634 : int i;
2635 : LSEG seg;
2636 :
2637 23376 : if (point_inside(pt, poly->npts, poly->p) != 0)
2638 120 : return 0.0;
2639 :
2640 : /* initialize distance with segment between first and last points */
2641 23256 : seg.p[0].x = poly->p[0].x;
2642 23256 : seg.p[0].y = poly->p[0].y;
2643 23256 : seg.p[1].x = poly->p[poly->npts - 1].x;
2644 23256 : seg.p[1].y = poly->p[poly->npts - 1].y;
2645 23256 : result = lseg_closept_point(NULL, &seg, pt);
2646 :
2647 : /* check distances for other segments */
2648 172008 : for (i = 0; i < poly->npts - 1; i++)
2649 : {
2650 148752 : seg.p[0].x = poly->p[i].x;
2651 148752 : seg.p[0].y = poly->p[i].y;
2652 148752 : seg.p[1].x = poly->p[i + 1].x;
2653 148752 : seg.p[1].y = poly->p[i + 1].y;
2654 148752 : d = lseg_closept_point(NULL, &seg, pt);
2655 148752 : if (float8_lt(d, result))
2656 4392 : result = d;
2657 : }
2658 :
2659 23256 : 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 1584860 : 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 1584860 : line_construct(&tmp, &lseg->p[0], lseg_sl(lseg));
2686 1584860 : if (!line_interpt_line(&interpt, &tmp, line))
2687 8108 : return false;
2688 :
2689 : /*
2690 : * Then, we check whether the intersection point is actually on the line
2691 : * segment.
2692 : */
2693 1576752 : if (!lseg_contain_point(lseg, &interpt))
2694 1513768 : return false;
2695 62984 : 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 62728 : if (point_eq_point(&lseg->p[0], &interpt))
2703 4408 : *result = lseg->p[0];
2704 58320 : else if (point_eq_point(&lseg->p[1], &interpt))
2705 8836 : *result = lseg->p[1];
2706 : else
2707 49484 : *result = interpt;
2708 : }
2709 :
2710 62984 : 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 1195440 : 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 1195440 : line_construct(&tmp, point, line_invsl(line));
2735 1195440 : 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 1195440 : if (result != NULL)
2744 400 : *result = closept;
2745 :
2746 1195440 : return point_dt(&closept, point);
2747 : }
2748 :
2749 : Datum
2750 400 : close_pl(PG_FUNCTION_ARGS)
2751 : {
2752 400 : Point *pt = PG_GETARG_POINT_P(0);
2753 400 : LINE *line = PG_GETARG_LINE_P(1);
2754 : Point *result;
2755 :
2756 400 : result = palloc_object(Point);
2757 :
2758 400 : if (isnan(line_closept_point(result, line, pt)))
2759 144 : PG_RETURN_NULL();
2760 :
2761 256 : 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 604064 : 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 604064 : line_construct(&tmp, pt, point_invsl(&lseg->p[0], &lseg->p[1]));
2782 604064 : lseg_closept_line(&closept, lseg, &tmp);
2783 :
2784 604064 : if (result != NULL)
2785 317444 : *result = closept;
2786 :
2787 604064 : return point_dt(&closept, pt);
2788 : }
2789 :
2790 : Datum
2791 320 : close_ps(PG_FUNCTION_ARGS)
2792 : {
2793 320 : Point *pt = PG_GETARG_POINT_P(0);
2794 320 : LSEG *lseg = PG_GETARG_LSEG_P(1);
2795 : Point *result;
2796 :
2797 320 : result = palloc_object(Point);
2798 :
2799 320 : if (isnan(lseg_closept_point(result, lseg, pt)))
2800 64 : PG_RETURN_NULL();
2801 :
2802 256 : PG_RETURN_POINT_P(result);
2803 : }
2804 :
2805 :
2806 : /*
2807 : * Closest point on line segment to line segment
2808 : */
2809 : static float8
2810 3512 : 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 3512 : if (lseg_interpt_lseg(result, on_lseg, to_lseg))
2818 16 : 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 3496 : dist = lseg_closept_point(result, on_lseg, &to_lseg->p[0]);
2825 3496 : d = lseg_closept_point(&point, on_lseg, &to_lseg->p[1]);
2826 3496 : if (float8_lt(d, dist))
2827 : {
2828 1164 : dist = d;
2829 1164 : if (result != NULL)
2830 544 : *result = point;
2831 : }
2832 :
2833 : /* The closest point can still be one of the endpoints, so we test them. */
2834 3496 : d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[0]);
2835 3496 : if (float8_lt(d, dist))
2836 : {
2837 768 : dist = d;
2838 768 : if (result != NULL)
2839 496 : *result = on_lseg->p[0];
2840 : }
2841 3496 : d = lseg_closept_point(NULL, to_lseg, &on_lseg->p[1]);
2842 3496 : if (float8_lt(d, dist))
2843 : {
2844 296 : dist = d;
2845 296 : if (result != NULL)
2846 168 : *result = on_lseg->p[1];
2847 : }
2848 :
2849 3496 : return dist;
2850 : }
2851 :
2852 : Datum
2853 256 : close_lseg(PG_FUNCTION_ARGS)
2854 : {
2855 256 : LSEG *l1 = PG_GETARG_LSEG_P(0);
2856 256 : LSEG *l2 = PG_GETARG_LSEG_P(1);
2857 : Point *result;
2858 :
2859 256 : if (lseg_sl(l1) == lseg_sl(l2))
2860 52 : PG_RETURN_NULL();
2861 :
2862 204 : result = palloc_object(Point);
2863 :
2864 204 : if (isnan(lseg_closept_lseg(result, l2, l1)))
2865 60 : PG_RETURN_NULL();
2866 :
2867 144 : 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 103992 : 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 103992 : if (box_contain_point(box, pt))
2887 : {
2888 28 : if (result != NULL)
2889 4 : *result = *pt;
2890 :
2891 28 : return 0.0;
2892 : }
2893 :
2894 : /* pairwise check lseg distances */
2895 103964 : point.x = box->low.x;
2896 103964 : point.y = box->high.y;
2897 103964 : statlseg_construct(&lseg, &box->low, &point);
2898 103964 : dist = lseg_closept_point(result, &lseg, pt);
2899 :
2900 103964 : statlseg_construct(&lseg, &box->high, &point);
2901 103964 : d = lseg_closept_point(&closept, &lseg, pt);
2902 103964 : if (float8_lt(d, dist))
2903 : {
2904 4956 : dist = d;
2905 4956 : if (result != NULL)
2906 36 : *result = closept;
2907 : }
2908 :
2909 103964 : point.x = box->high.x;
2910 103964 : point.y = box->low.y;
2911 103964 : statlseg_construct(&lseg, &box->low, &point);
2912 103964 : d = lseg_closept_point(&closept, &lseg, pt);
2913 103964 : if (float8_lt(d, dist))
2914 : {
2915 5292 : dist = d;
2916 5292 : if (result != NULL)
2917 4 : *result = closept;
2918 : }
2919 :
2920 103964 : statlseg_construct(&lseg, &box->high, &point);
2921 103964 : d = lseg_closept_point(&closept, &lseg, pt);
2922 103964 : if (float8_lt(d, dist))
2923 : {
2924 24 : dist = d;
2925 24 : if (result != NULL)
2926 8 : *result = closept;
2927 : }
2928 :
2929 103964 : return dist;
2930 : }
2931 :
2932 : Datum
2933 200 : close_pb(PG_FUNCTION_ARGS)
2934 : {
2935 200 : Point *pt = PG_GETARG_POINT_P(0);
2936 200 : BOX *box = PG_GETARG_BOX_P(1);
2937 : Point *result;
2938 :
2939 200 : result = palloc_object(Point);
2940 :
2941 200 : if (isnan(box_closept_point(result, box, pt)))
2942 20 : PG_RETURN_NULL();
2943 :
2944 180 : 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 604988 : lseg_closept_line(Point *result, LSEG *lseg, LINE *line)
2961 : {
2962 : float8 dist1,
2963 : dist2;
2964 :
2965 604988 : if (lseg_interpt_line(result, lseg, line))
2966 7868 : return 0.0;
2967 :
2968 597120 : dist1 = line_closept_point(NULL, line, &lseg->p[0]);
2969 597120 : dist2 = line_closept_point(NULL, line, &lseg->p[1]);
2970 :
2971 597120 : if (dist1 < dist2)
2972 : {
2973 317140 : if (result != NULL)
2974 317004 : *result = lseg->p[0];
2975 :
2976 317140 : return dist1;
2977 : }
2978 : else
2979 : {
2980 279980 : if (result != NULL)
2981 279612 : *result = lseg->p[1];
2982 :
2983 279980 : return dist2;
2984 : }
2985 : }
2986 :
2987 : Datum
2988 320 : close_ls(PG_FUNCTION_ARGS)
2989 : {
2990 320 : LINE *line = PG_GETARG_LINE_P(0);
2991 320 : LSEG *lseg = PG_GETARG_LSEG_P(1);
2992 : Point *result;
2993 :
2994 320 : if (lseg_sl(lseg) == line_sl(line))
2995 36 : PG_RETURN_NULL();
2996 :
2997 284 : result = palloc_object(Point);
2998 :
2999 284 : if (isnan(lseg_closept_line(result, lseg, line)))
3000 96 : PG_RETURN_NULL();
3001 :
3002 188 : 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 480 : 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 480 : if (box_interpt_lseg(result, box, lseg))
3022 96 : return 0.0;
3023 :
3024 : /* pairwise check lseg distances */
3025 384 : point.x = box->low.x;
3026 384 : point.y = box->high.y;
3027 384 : statlseg_construct(&bseg, &box->low, &point);
3028 384 : dist = lseg_closept_lseg(result, &bseg, lseg);
3029 :
3030 384 : statlseg_construct(&bseg, &box->high, &point);
3031 384 : d = lseg_closept_lseg(&closept, &bseg, lseg);
3032 384 : if (float8_lt(d, dist))
3033 : {
3034 96 : dist = d;
3035 96 : if (result != NULL)
3036 32 : *result = closept;
3037 : }
3038 :
3039 384 : point.x = box->high.x;
3040 384 : point.y = box->low.y;
3041 384 : statlseg_construct(&bseg, &box->low, &point);
3042 384 : d = lseg_closept_lseg(&closept, &bseg, lseg);
3043 384 : if (float8_lt(d, dist))
3044 : {
3045 12 : dist = d;
3046 12 : if (result != NULL)
3047 4 : *result = closept;
3048 : }
3049 :
3050 384 : statlseg_construct(&bseg, &box->high, &point);
3051 384 : d = lseg_closept_lseg(&closept, &bseg, lseg);
3052 384 : if (float8_lt(d, dist))
3053 : {
3054 12 : dist = d;
3055 12 : if (result != NULL)
3056 4 : *result = closept;
3057 : }
3058 :
3059 384 : return dist;
3060 : }
3061 :
3062 : Datum
3063 160 : close_sb(PG_FUNCTION_ARGS)
3064 : {
3065 160 : LSEG *lseg = PG_GETARG_LSEG_P(0);
3066 160 : BOX *box = PG_GETARG_BOX_P(1);
3067 : Point *result;
3068 :
3069 160 : result = palloc_object(Point);
3070 :
3071 160 : if (isnan(box_closept_lseg(result, box, lseg)))
3072 20 : PG_RETURN_NULL();
3073 :
3074 140 : 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 736 : line_contain_point(LINE *line, Point *point)
3088 : {
3089 736 : 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 400 : on_pl(PG_FUNCTION_ARGS)
3096 : {
3097 400 : Point *pt = PG_GETARG_POINT_P(0);
3098 400 : LINE *line = PG_GETARG_LINE_P(1);
3099 :
3100 400 : 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 2676572 : lseg_contain_point(LSEG *lseg, Point *pt)
3110 : {
3111 5353144 : return FPeq(point_dt(pt, &lseg->p[0]) +
3112 2676572 : point_dt(pt, &lseg->p[1]),
3113 : point_dt(&lseg->p[0], &lseg->p[1]));
3114 : }
3115 :
3116 : Datum
3117 320 : on_ps(PG_FUNCTION_ARGS)
3118 : {
3119 320 : Point *pt = PG_GETARG_POINT_P(0);
3120 320 : LSEG *lseg = PG_GETARG_LSEG_P(1);
3121 :
3122 320 : 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 291856 : box_contain_point(BOX *box, Point *point)
3131 : {
3132 169188 : return box->high.x >= point->x && box->low.x <= point->x &&
3133 461044 : box->high.y >= point->y && box->low.y <= point->y;
3134 : }
3135 :
3136 : Datum
3137 92168 : on_pb(PG_FUNCTION_ARGS)
3138 : {
3139 92168 : Point *pt = PG_GETARG_POINT_P(0);
3140 92168 : BOX *box = PG_GETARG_BOX_P(1);
3141 :
3142 92168 : PG_RETURN_BOOL(box_contain_point(box, pt));
3143 : }
3144 :
3145 : Datum
3146 95124 : box_contain_pt(PG_FUNCTION_ARGS)
3147 : {
3148 95124 : BOX *box = PG_GETARG_BOX_P(0);
3149 95124 : Point *pt = PG_GETARG_POINT_P(1);
3150 :
3151 95124 : 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 400 : on_ppath(PG_FUNCTION_ARGS)
3167 : {
3168 400 : Point *pt = PG_GETARG_POINT_P(0);
3169 400 : PATH *path = PG_GETARG_PATH_P(1);
3170 : int i,
3171 : n;
3172 : float8 a,
3173 : b;
3174 :
3175 : /*-- OPEN --*/
3176 400 : if (!path->closed)
3177 : {
3178 200 : n = path->npts - 1;
3179 200 : a = point_dt(pt, &path->p[0]);
3180 472 : for (i = 0; i < n; i++)
3181 : {
3182 292 : b = point_dt(pt, &path->p[i + 1]);
3183 292 : if (FPeq(float8_pl(a, b), point_dt(&path->p[i], &path->p[i + 1])))
3184 20 : PG_RETURN_BOOL(true);
3185 272 : a = b;
3186 : }
3187 180 : PG_RETURN_BOOL(false);
3188 : }
3189 :
3190 : /*-- CLOSED --*/
3191 200 : 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 320 : on_sl(PG_FUNCTION_ARGS)
3202 : {
3203 320 : LSEG *lseg = PG_GETARG_LSEG_P(0);
3204 320 : LINE *line = PG_GETARG_LINE_P(1);
3205 :
3206 320 : 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 160 : box_contain_lseg(BOX *box, LSEG *lseg)
3218 : {
3219 172 : return box_contain_point(box, &lseg->p[0]) &&
3220 12 : box_contain_point(box, &lseg->p[1]);
3221 : }
3222 :
3223 : Datum
3224 160 : on_sb(PG_FUNCTION_ARGS)
3225 : {
3226 160 : LSEG *lseg = PG_GETARG_LSEG_P(0);
3227 160 : BOX *box = PG_GETARG_BOX_P(1);
3228 :
3229 160 : PG_RETURN_BOOL(box_contain_lseg(box, lseg));
3230 : }
3231 :
3232 : /*---------------------------------------------------------------------
3233 : * inter_
3234 : * Whether one object intersects another.
3235 : *-------------------------------------------------------------------*/
3236 :
3237 : Datum
3238 320 : inter_sl(PG_FUNCTION_ARGS)
3239 : {
3240 320 : LSEG *lseg = PG_GETARG_LSEG_P(0);
3241 320 : LINE *line = PG_GETARG_LINE_P(1);
3242 :
3243 320 : 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 640 : box_interpt_lseg(Point *result, BOX *box, LSEG *lseg)
3264 : {
3265 : BOX lbox;
3266 : LSEG bseg;
3267 : Point point;
3268 :
3269 640 : lbox.low.x = float8_min(lseg->p[0].x, lseg->p[1].x);
3270 640 : lbox.low.y = float8_min(lseg->p[0].y, lseg->p[1].y);
3271 640 : lbox.high.x = float8_max(lseg->p[0].x, lseg->p[1].x);
3272 640 : 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 640 : if (!box_ov(&lbox, box))
3276 416 : return false;
3277 :
3278 224 : if (result != NULL)
3279 : {
3280 56 : box_cn(&point, box);
3281 56 : lseg_closept_point(result, lseg, &point);
3282 : }
3283 :
3284 : /* an endpoint of segment is inside box? then clearly intersects */
3285 400 : if (box_contain_point(box, &lseg->p[0]) ||
3286 176 : box_contain_point(box, &lseg->p[1]))
3287 64 : return true;
3288 :
3289 : /* pairwise check lseg intersections */
3290 160 : point.x = box->low.x;
3291 160 : point.y = box->high.y;
3292 160 : statlseg_construct(&bseg, &box->low, &point);
3293 160 : if (lseg_interpt_lseg(NULL, &bseg, lseg))
3294 64 : return true;
3295 :
3296 96 : statlseg_construct(&bseg, &box->high, &point);
3297 96 : if (lseg_interpt_lseg(NULL, &bseg, lseg))
3298 0 : return true;
3299 :
3300 96 : point.x = box->high.x;
3301 96 : point.y = box->low.y;
3302 96 : statlseg_construct(&bseg, &box->low, &point);
3303 96 : if (lseg_interpt_lseg(NULL, &bseg, lseg))
3304 0 : return true;
3305 :
3306 96 : statlseg_construct(&bseg, &box->high, &point);
3307 96 : if (lseg_interpt_lseg(NULL, &bseg, lseg))
3308 0 : return true;
3309 :
3310 : /* if we dropped through, no two segs intersected */
3311 96 : return false;
3312 : }
3313 :
3314 : Datum
3315 160 : inter_sb(PG_FUNCTION_ARGS)
3316 : {
3317 160 : LSEG *lseg = PG_GETARG_LSEG_P(0);
3318 160 : BOX *box = PG_GETARG_BOX_P(1);
3319 :
3320 160 : 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 200 : inter_lb(PG_FUNCTION_ARGS)
3329 : {
3330 200 : LINE *line = PG_GETARG_LINE_P(0);
3331 200 : BOX *box = PG_GETARG_BOX_P(1);
3332 : LSEG bseg;
3333 : Point p1,
3334 : p2;
3335 :
3336 : /* pairwise check lseg intersections */
3337 200 : p1.x = box->low.x;
3338 200 : p1.y = box->low.y;
3339 200 : p2.x = box->low.x;
3340 200 : p2.y = box->high.y;
3341 200 : statlseg_construct(&bseg, &p1, &p2);
3342 200 : if (lseg_interpt_line(NULL, &bseg, line))
3343 44 : PG_RETURN_BOOL(true);
3344 156 : p1.x = box->high.x;
3345 156 : p1.y = box->high.y;
3346 156 : statlseg_construct(&bseg, &p1, &p2);
3347 156 : if (lseg_interpt_line(NULL, &bseg, line))
3348 8 : PG_RETURN_BOOL(true);
3349 148 : p2.x = box->high.x;
3350 148 : p2.y = box->low.y;
3351 148 : statlseg_construct(&bseg, &p1, &p2);
3352 148 : if (lseg_interpt_line(NULL, &bseg, line))
3353 0 : PG_RETURN_BOOL(true);
3354 148 : p1.x = box->low.x;
3355 148 : p1.y = box->low.y;
3356 148 : statlseg_construct(&bseg, &p1, &p2);
3357 148 : if (lseg_interpt_line(NULL, &bseg, line))
3358 0 : PG_RETURN_BOOL(true);
3359 :
3360 : /* if we dropped through, no intersection */
3361 148 : 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 40338 : 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 40338 : x1 = x2 = poly->p[0].x;
3387 40338 : y2 = y1 = poly->p[0].y;
3388 481378 : for (i = 1; i < poly->npts; i++)
3389 : {
3390 441040 : if (float8_lt(poly->p[i].x, x1))
3391 44 : x1 = poly->p[i].x;
3392 441040 : if (float8_gt(poly->p[i].x, x2))
3393 240707 : x2 = poly->p[i].x;
3394 441040 : if (float8_lt(poly->p[i].y, y1))
3395 120267 : y1 = poly->p[i].y;
3396 441040 : if (float8_gt(poly->p[i].y, y2))
3397 120404 : y2 = poly->p[i].y;
3398 : }
3399 :
3400 40338 : poly->boundbox.low.x = x1;
3401 40338 : poly->boundbox.high.x = x2;
3402 40338 : poly->boundbox.low.y = y1;
3403 40338 : poly->boundbox.high.y = y2;
3404 40338 : }
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 269 : poly_in(PG_FUNCTION_ARGS)
3416 : {
3417 269 : char *str = PG_GETARG_CSTRING(0);
3418 269 : Node *escontext = fcinfo->context;
3419 : POLYGON *poly;
3420 : int npts;
3421 : int size;
3422 : int base_size;
3423 : bool isopen;
3424 :
3425 269 : if ((npts = pair_count(str, ',')) <= 0)
3426 24 : ereturn(escontext, (Datum) 0,
3427 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
3428 : errmsg("invalid input syntax for type %s: \"%s\"",
3429 : "polygon", str)));
3430 :
3431 245 : base_size = sizeof(poly->p[0]) * npts;
3432 245 : size = offsetof(POLYGON, p) + base_size;
3433 :
3434 : /* Check for integer overflow */
3435 245 : 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 245 : poly = (POLYGON *) palloc0(size); /* zero any holes */
3441 :
3442 245 : SET_VARSIZE(poly, size);
3443 245 : poly->npts = npts;
3444 :
3445 245 : if (!path_decode(str, false, npts, &(poly->p[0]), &isopen, NULL, "polygon",
3446 : str, escontext))
3447 8 : PG_RETURN_NULL();
3448 :
3449 233 : make_bound_box(poly);
3450 :
3451 233 : 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 47755 : poly_out(PG_FUNCTION_ARGS)
3460 : {
3461 47755 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
3462 :
3463 47755 : 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 196 : poly_left(PG_FUNCTION_ARGS)
3534 : {
3535 196 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3536 196 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3537 : bool result;
3538 :
3539 196 : result = polya->boundbox.high.x < polyb->boundbox.low.x;
3540 :
3541 : /*
3542 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3543 : */
3544 196 : PG_FREE_IF_COPY(polya, 0);
3545 196 : PG_FREE_IF_COPY(polyb, 1);
3546 :
3547 196 : 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 196 : poly_overleft(PG_FUNCTION_ARGS)
3557 : {
3558 196 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3559 196 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3560 : bool result;
3561 :
3562 196 : result = polya->boundbox.high.x <= polyb->boundbox.high.x;
3563 :
3564 : /*
3565 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3566 : */
3567 196 : PG_FREE_IF_COPY(polya, 0);
3568 196 : PG_FREE_IF_COPY(polyb, 1);
3569 :
3570 196 : 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 196 : poly_right(PG_FUNCTION_ARGS)
3580 : {
3581 196 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3582 196 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3583 : bool result;
3584 :
3585 196 : result = polya->boundbox.low.x > polyb->boundbox.high.x;
3586 :
3587 : /*
3588 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3589 : */
3590 196 : PG_FREE_IF_COPY(polya, 0);
3591 196 : PG_FREE_IF_COPY(polyb, 1);
3592 :
3593 196 : 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 196 : poly_overright(PG_FUNCTION_ARGS)
3603 : {
3604 196 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3605 196 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3606 : bool result;
3607 :
3608 196 : result = polya->boundbox.low.x >= polyb->boundbox.low.x;
3609 :
3610 : /*
3611 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3612 : */
3613 196 : PG_FREE_IF_COPY(polya, 0);
3614 196 : PG_FREE_IF_COPY(polyb, 1);
3615 :
3616 196 : 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 196 : poly_below(PG_FUNCTION_ARGS)
3626 : {
3627 196 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3628 196 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3629 : bool result;
3630 :
3631 196 : result = polya->boundbox.high.y < polyb->boundbox.low.y;
3632 :
3633 : /*
3634 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3635 : */
3636 196 : PG_FREE_IF_COPY(polya, 0);
3637 196 : PG_FREE_IF_COPY(polyb, 1);
3638 :
3639 196 : 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 196 : poly_overbelow(PG_FUNCTION_ARGS)
3649 : {
3650 196 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3651 196 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3652 : bool result;
3653 :
3654 196 : result = polya->boundbox.high.y <= polyb->boundbox.high.y;
3655 :
3656 : /*
3657 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3658 : */
3659 196 : PG_FREE_IF_COPY(polya, 0);
3660 196 : PG_FREE_IF_COPY(polyb, 1);
3661 :
3662 196 : 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 196 : poly_above(PG_FUNCTION_ARGS)
3672 : {
3673 196 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3674 196 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3675 : bool result;
3676 :
3677 196 : result = polya->boundbox.low.y > polyb->boundbox.high.y;
3678 :
3679 : /*
3680 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3681 : */
3682 196 : PG_FREE_IF_COPY(polya, 0);
3683 196 : PG_FREE_IF_COPY(polyb, 1);
3684 :
3685 196 : 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 196 : poly_overabove(PG_FUNCTION_ARGS)
3695 : {
3696 196 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3697 196 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3698 : bool result;
3699 :
3700 196 : result = polya->boundbox.low.y >= polyb->boundbox.low.y;
3701 :
3702 : /*
3703 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3704 : */
3705 196 : PG_FREE_IF_COPY(polya, 0);
3706 196 : PG_FREE_IF_COPY(polyb, 1);
3707 :
3708 196 : 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 4197 : poly_same(PG_FUNCTION_ARGS)
3721 : {
3722 4197 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3723 4197 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3724 : bool result;
3725 :
3726 4197 : if (polya->npts != polyb->npts)
3727 136 : result = false;
3728 : else
3729 4061 : result = plist_same(polya->npts, polya->p, polyb->p);
3730 :
3731 : /*
3732 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3733 : */
3734 4197 : PG_FREE_IF_COPY(polya, 0);
3735 4197 : PG_FREE_IF_COPY(polyb, 1);
3736 :
3737 4197 : PG_RETURN_BOOL(result);
3738 : }
3739 :
3740 : /*-----------------------------------------------------------------
3741 : * Determine if polygon A overlaps polygon B
3742 : *-----------------------------------------------------------------*/
3743 : static bool
3744 19612 : 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 19612 : 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 19612 : 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 7076 : sa.p[0] = polya->p[polya->npts - 1];
3767 7076 : result = false;
3768 :
3769 84364 : for (ia = 0; ia < polya->npts && !result; ia++)
3770 : {
3771 : /* Second point of polya's edge is a current one */
3772 77288 : sa.p[1] = polya->p[ia];
3773 :
3774 : /* Init first of polyb's edge with last point */
3775 77288 : sb.p[0] = polyb->p[polyb->npts - 1];
3776 :
3777 384676 : for (ib = 0; ib < polyb->npts && !result; ib++)
3778 : {
3779 307388 : sb.p[1] = polyb->p[ib];
3780 307388 : result = lseg_interpt_lseg(NULL, &sa, &sb);
3781 307388 : sb.p[0] = sb.p[1];
3782 : }
3783 :
3784 : /*
3785 : * move current endpoint to the first point of next edge
3786 : */
3787 77288 : sa.p[0] = sa.p[1];
3788 : }
3789 :
3790 7076 : if (!result)
3791 : {
3792 9268 : result = (point_inside(polya->p, polyb->npts, polyb->p) ||
3793 2952 : point_inside(polyb->p, polya->npts, polya->p));
3794 : }
3795 : }
3796 :
3797 19612 : return result;
3798 : }
3799 :
3800 : Datum
3801 19416 : poly_overlap(PG_FUNCTION_ARGS)
3802 : {
3803 19416 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3804 19416 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3805 : bool result;
3806 :
3807 19416 : result = poly_overlap_internal(polya, polyb);
3808 :
3809 : /*
3810 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3811 : */
3812 19416 : PG_FREE_IF_COPY(polya, 0);
3813 19416 : PG_FREE_IF_COPY(polyb, 1);
3814 :
3815 19416 : 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 404 : 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 404 : t.p[0] = *a;
3836 404 : t.p[1] = *b;
3837 :
3838 404 : if (point_eq_point(a, s->p))
3839 : {
3840 48 : if (lseg_contain_point(&t, s->p + 1))
3841 0 : return lseg_inside_poly(b, s->p + 1, poly, start);
3842 : }
3843 356 : else if (point_eq_point(a, s->p + 1))
3844 : {
3845 104 : if (lseg_contain_point(&t, s->p))
3846 0 : return lseg_inside_poly(b, s->p, poly, start);
3847 : }
3848 252 : else if (lseg_contain_point(&t, s->p))
3849 : {
3850 0 : return lseg_inside_poly(b, s->p, poly, start);
3851 : }
3852 252 : 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 404 : 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 132184 : lseg_inside_poly(Point *a, Point *b, POLYGON *poly, int start)
3867 : {
3868 : LSEG s,
3869 : t;
3870 : int i;
3871 132184 : bool res = true,
3872 132184 : intersection = false;
3873 :
3874 : /* since this function recurses, it could be driven to stack overflow */
3875 132184 : check_stack_depth();
3876 :
3877 132184 : t.p[0] = *a;
3878 132184 : t.p[1] = *b;
3879 132184 : s.p[0] = poly->p[(start == 0) ? (poly->npts - 1) : (start - 1)];
3880 :
3881 653796 : for (i = start; i < poly->npts && res; i++)
3882 : {
3883 : Point interpt;
3884 :
3885 521924 : CHECK_FOR_INTERRUPTS();
3886 :
3887 521924 : s.p[1] = poly->p[i];
3888 :
3889 521924 : if (lseg_contain_point(&s, t.p))
3890 : {
3891 524 : if (lseg_contain_point(&s, t.p + 1))
3892 312 : return true; /* t is contained by s */
3893 :
3894 : /* Y-cross */
3895 212 : res = touched_lseg_inside_poly(t.p, t.p + 1, &s, poly, i + 1);
3896 : }
3897 521400 : else if (lseg_contain_point(&s, t.p + 1))
3898 : {
3899 : /* Y-cross */
3900 192 : res = touched_lseg_inside_poly(t.p + 1, t.p, &s, poly, i + 1);
3901 : }
3902 521208 : else if (lseg_interpt_lseg(&interpt, &t, &s))
3903 : {
3904 : /*
3905 : * segments are X-crossing, go to check each subsegment
3906 : */
3907 :
3908 900 : intersection = true;
3909 900 : res = lseg_inside_poly(t.p, &interpt, poly, i + 1);
3910 900 : if (res)
3911 772 : res = lseg_inside_poly(t.p + 1, &interpt, poly, i + 1);
3912 : }
3913 :
3914 521612 : s.p[0] = s.p[1];
3915 : }
3916 :
3917 131872 : 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 130972 : p.x = float8_div(float8_pl(t.p[0].x, t.p[1].x), 2.0);
3926 130972 : p.y = float8_div(float8_pl(t.p[0].y, t.p[1].y), 2.0);
3927 :
3928 130972 : res = point_inside(&p, poly->npts, poly->p);
3929 : }
3930 :
3931 131872 : return res;
3932 : }
3933 :
3934 : /*
3935 : * Check whether the first polygon contains the second
3936 : */
3937 : static bool
3938 56620 : 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 56620 : if (!box_contain_box(&contains_poly->boundbox, &contained_poly->boundbox))
3950 38228 : return false;
3951 :
3952 18392 : s.p[0] = contained_poly->p[contained_poly->npts - 1];
3953 :
3954 140592 : for (i = 0; i < contained_poly->npts; i++)
3955 : {
3956 130512 : s.p[1] = contained_poly->p[i];
3957 130512 : if (!lseg_inside_poly(s.p, s.p + 1, contains_poly, 0))
3958 8312 : return false;
3959 122200 : s.p[0] = s.p[1];
3960 : }
3961 :
3962 10080 : return true;
3963 : }
3964 :
3965 : Datum
3966 256 : poly_contain(PG_FUNCTION_ARGS)
3967 : {
3968 256 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3969 256 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3970 : bool result;
3971 :
3972 256 : result = poly_contain_poly(polya, polyb);
3973 :
3974 : /*
3975 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3976 : */
3977 256 : PG_FREE_IF_COPY(polya, 0);
3978 256 : PG_FREE_IF_COPY(polyb, 1);
3979 :
3980 256 : PG_RETURN_BOOL(result);
3981 : }
3982 :
3983 :
3984 : /*-----------------------------------------------------------------
3985 : * Determine if polygon A is contained by polygon B
3986 : *-----------------------------------------------------------------*/
3987 : Datum
3988 56364 : poly_contained(PG_FUNCTION_ARGS)
3989 : {
3990 56364 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
3991 56364 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
3992 : bool result;
3993 :
3994 : /* Just switch the arguments and pass it off to poly_contain */
3995 56364 : result = poly_contain_poly(polyb, polya);
3996 :
3997 : /*
3998 : * Avoid leaking memory for toasted inputs ... needed for rtree indexes
3999 : */
4000 56364 : PG_FREE_IF_COPY(polya, 0);
4001 56364 : PG_FREE_IF_COPY(polyb, 1);
4002 :
4003 56364 : PG_RETURN_BOOL(result);
4004 : }
4005 :
4006 :
4007 : Datum
4008 296 : poly_contain_pt(PG_FUNCTION_ARGS)
4009 : {
4010 296 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
4011 296 : Point *p = PG_GETARG_POINT_P(1);
4012 :
4013 296 : PG_RETURN_BOOL(point_inside(p, poly->npts, poly->p) != 0);
4014 : }
4015 :
4016 : Datum
4017 321 : pt_contained_poly(PG_FUNCTION_ARGS)
4018 : {
4019 321 : Point *p = PG_GETARG_POINT_P(0);
4020 321 : POLYGON *poly = PG_GETARG_POLYGON_P(1);
4021 :
4022 321 : PG_RETURN_BOOL(point_inside(p, poly->npts, poly->p) != 0);
4023 : }
4024 :
4025 :
4026 : Datum
4027 196 : poly_distance(PG_FUNCTION_ARGS)
4028 : {
4029 196 : POLYGON *polya = PG_GETARG_POLYGON_P(0);
4030 196 : POLYGON *polyb = PG_GETARG_POLYGON_P(1);
4031 196 : float8 min = 0.0; /* initialize to keep compiler quiet */
4032 196 : 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 196 : if (poly_overlap_internal(polya, polyb))
4045 100 : 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 352 : for (i = 0; i < polya->npts; i++)
4053 : {
4054 : int iprev;
4055 :
4056 256 : if (i > 0)
4057 160 : iprev = i - 1;
4058 : else
4059 96 : iprev = polya->npts - 1;
4060 :
4061 872 : for (j = 0; j < polyb->npts; j++)
4062 : {
4063 : int jprev;
4064 :
4065 616 : if (j > 0)
4066 360 : jprev = j - 1;
4067 : else
4068 256 : jprev = polyb->npts - 1;
4069 :
4070 616 : statlseg_construct(&seg1, &polya->p[iprev], &polya->p[i]);
4071 616 : statlseg_construct(&seg2, &polyb->p[jprev], &polyb->p[j]);
4072 :
4073 616 : tmp = lseg_closept_lseg(NULL, &seg1, &seg2);
4074 616 : if (!have_min || float8_lt(tmp, min))
4075 : {
4076 128 : min = tmp;
4077 128 : have_min = true;
4078 : }
4079 : }
4080 : }
4081 :
4082 96 : if (!have_min)
4083 0 : PG_RETURN_NULL();
4084 :
4085 96 : PG_RETURN_FLOAT8(min);
4086 : }
4087 :
4088 :
4089 : /***********************************************************************
4090 : **
4091 : ** Routines for 2D points.
4092 : **
4093 : ***********************************************************************/
4094 :
4095 : Datum
4096 688675 : construct_point(PG_FUNCTION_ARGS)
4097 : {
4098 688675 : float8 x = PG_GETARG_FLOAT8(0);
4099 688675 : float8 y = PG_GETARG_FLOAT8(1);
4100 : Point *result;
4101 :
4102 688675 : result = palloc_object(Point);
4103 :
4104 688675 : point_construct(result, x, y);
4105 :
4106 688675 : PG_RETURN_POINT_P(result);
4107 : }
4108 :
4109 :
4110 : static inline void
4111 2048 : point_add_point(Point *result, Point *pt1, Point *pt2)
4112 : {
4113 2048 : point_construct(result,
4114 : float8_pl(pt1->x, pt2->x),
4115 : float8_pl(pt1->y, pt2->y));
4116 2048 : }
4117 :
4118 : Datum
4119 400 : point_add(PG_FUNCTION_ARGS)
4120 : {
4121 400 : Point *p1 = PG_GETARG_POINT_P(0);
4122 400 : Point *p2 = PG_GETARG_POINT_P(1);
4123 : Point *result;
4124 :
4125 400 : result = palloc_object(Point);
4126 :
4127 400 : point_add_point(result, p1, p2);
4128 :
4129 400 : PG_RETURN_POINT_P(result);
4130 : }
4131 :
4132 :
4133 : static inline void
4134 1880 : point_sub_point(Point *result, Point *pt1, Point *pt2)
4135 : {
4136 1880 : point_construct(result,
4137 : float8_mi(pt1->x, pt2->x),
4138 : float8_mi(pt1->y, pt2->y));
4139 1880 : }
4140 :
4141 : Datum
4142 400 : point_sub(PG_FUNCTION_ARGS)
4143 : {
4144 400 : Point *p1 = PG_GETARG_POINT_P(0);
4145 400 : Point *p2 = PG_GETARG_POINT_P(1);
4146 : Point *result;
4147 :
4148 400 : result = palloc_object(Point);
4149 :
4150 400 : point_sub_point(result, p1, p2);
4151 :
4152 400 : PG_RETURN_POINT_P(result);
4153 : }
4154 :
4155 :
4156 : static inline void
4157 1480 : point_mul_point(Point *result, Point *pt1, Point *pt2)
4158 : {
4159 1480 : 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 1476 : }
4165 :
4166 : Datum
4167 200 : point_mul(PG_FUNCTION_ARGS)
4168 : {
4169 200 : Point *p1 = PG_GETARG_POINT_P(0);
4170 200 : Point *p2 = PG_GETARG_POINT_P(1);
4171 : Point *result;
4172 :
4173 200 : result = palloc_object(Point);
4174 :
4175 200 : point_mul_point(result, p1, p2);
4176 :
4177 196 : PG_RETURN_POINT_P(result);
4178 : }
4179 :
4180 :
4181 : static inline void
4182 396 : point_div_point(Point *result, Point *pt1, Point *pt2)
4183 : {
4184 : float8 div;
4185 :
4186 396 : div = float8_pl(float8_mul(pt2->x, pt2->x), float8_mul(pt2->y, pt2->y));
4187 :
4188 388 : 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 376 : }
4194 :
4195 : Datum
4196 88 : point_div(PG_FUNCTION_ARGS)
4197 : {
4198 88 : Point *p1 = PG_GETARG_POINT_P(0);
4199 88 : Point *p2 = PG_GETARG_POINT_P(1);
4200 : Point *result;
4201 :
4202 88 : result = palloc_object(Point);
4203 :
4204 88 : point_div_point(result, p1, p2);
4205 :
4206 80 : PG_RETURN_POINT_P(result);
4207 : }
4208 :
4209 :
4210 : /***********************************************************************
4211 : **
4212 : ** Routines for 2D boxes.
4213 : **
4214 : ***********************************************************************/
4215 :
4216 : Datum
4217 161124 : points_box(PG_FUNCTION_ARGS)
4218 : {
4219 161124 : Point *p1 = PG_GETARG_POINT_P(0);
4220 161124 : Point *p2 = PG_GETARG_POINT_P(1);
4221 : BOX *result;
4222 :
4223 161124 : result = palloc_object(BOX);
4224 :
4225 161124 : box_construct(result, p1, p2);
4226 :
4227 161124 : PG_RETURN_BOX_P(result);
4228 : }
4229 :
4230 : Datum
4231 200 : box_add(PG_FUNCTION_ARGS)
4232 : {
4233 200 : BOX *box = PG_GETARG_BOX_P(0);
4234 200 : Point *p = PG_GETARG_POINT_P(1);
4235 : BOX *result;
4236 :
4237 200 : result = palloc_object(BOX);
4238 :
4239 200 : point_add_point(&result->high, &box->high, p);
4240 200 : point_add_point(&result->low, &box->low, p);
4241 :
4242 200 : PG_RETURN_BOX_P(result);
4243 : }
4244 :
4245 : Datum
4246 200 : box_sub(PG_FUNCTION_ARGS)
4247 : {
4248 200 : BOX *box = PG_GETARG_BOX_P(0);
4249 200 : Point *p = PG_GETARG_POINT_P(1);
4250 : BOX *result;
4251 :
4252 200 : result = palloc_object(BOX);
4253 :
4254 200 : point_sub_point(&result->high, &box->high, p);
4255 200 : point_sub_point(&result->low, &box->low, p);
4256 :
4257 200 : PG_RETURN_BOX_P(result);
4258 : }
4259 :
4260 : Datum
4261 100 : box_mul(PG_FUNCTION_ARGS)
4262 : {
4263 100 : BOX *box = PG_GETARG_BOX_P(0);
4264 100 : Point *p = PG_GETARG_POINT_P(1);
4265 : BOX *result;
4266 : Point high,
4267 : low;
4268 :
4269 100 : result = palloc_object(BOX);
4270 :
4271 100 : point_mul_point(&high, &box->high, p);
4272 100 : point_mul_point(&low, &box->low, p);
4273 :
4274 100 : box_construct(result, &high, &low);
4275 :
4276 100 : PG_RETURN_BOX_P(result);
4277 : }
4278 :
4279 : Datum
4280 40 : box_div(PG_FUNCTION_ARGS)
4281 : {
4282 40 : BOX *box = PG_GETARG_BOX_P(0);
4283 40 : Point *p = PG_GETARG_POINT_P(1);
4284 : BOX *result;
4285 : Point high,
4286 : low;
4287 :
4288 40 : result = palloc_object(BOX);
4289 :
4290 40 : point_div_point(&high, &box->high, p);
4291 40 : point_div_point(&low, &box->low, p);
4292 :
4293 40 : box_construct(result, &high, &low);
4294 :
4295 40 : PG_RETURN_BOX_P(result);
4296 : }
4297 :
4298 : /*
4299 : * Convert point to empty box
4300 : */
4301 : Datum
4302 244 : point_box(PG_FUNCTION_ARGS)
4303 : {
4304 244 : Point *pt = PG_GETARG_POINT_P(0);
4305 : BOX *box;
4306 :
4307 244 : box = palloc_object(BOX);
4308 :
4309 244 : box->high.x = pt->x;
4310 244 : box->low.x = pt->x;
4311 244 : box->high.y = pt->y;
4312 244 : box->low.y = pt->y;
4313 :
4314 244 : PG_RETURN_BOX_P(box);
4315 : }
4316 :
4317 : /*
4318 : * Smallest bounding box that includes both of the given boxes
4319 : */
4320 : Datum
4321 100 : boxes_bound_box(PG_FUNCTION_ARGS)
4322 : {
4323 100 : BOX *box1 = PG_GETARG_BOX_P(0),
4324 100 : *box2 = PG_GETARG_BOX_P(1),
4325 : *container;
4326 :
4327 100 : container = palloc_object(BOX);
4328 :
4329 100 : container->high.x = float8_max(box1->high.x, box2->high.x);
4330 100 : container->low.x = float8_min(box1->low.x, box2->low.x);
4331 100 : container->high.y = float8_max(box1->high.y, box2->high.y);
4332 100 : container->low.y = float8_min(box1->low.y, box2->low.y);
4333 :
4334 100 : 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 324 : path_add(PG_FUNCTION_ARGS)
4349 : {
4350 324 : PATH *p1 = PG_GETARG_PATH_P(0);
4351 324 : PATH *p2 = PG_GETARG_PATH_P(1);
4352 : PATH *result;
4353 : int size,
4354 : base_size;
4355 : int i;
4356 :
4357 324 : if (p1->closed || p2->closed)
4358 260 : PG_RETURN_NULL();
4359 :
4360 64 : base_size = sizeof(p1->p[0]) * (p1->npts + p2->npts);
4361 64 : size = offsetof(PATH, p) + base_size;
4362 :
4363 : /* Check for integer overflow */
4364 64 : 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 64 : result = (PATH *) palloc(size);
4371 :
4372 64 : SET_VARSIZE(result, size);
4373 64 : result->npts = (p1->npts + p2->npts);
4374 64 : result->closed = p1->closed;
4375 : /* prevent instability in unused pad bytes */
4376 64 : result->dummy = 0;
4377 :
4378 224 : for (i = 0; i < p1->npts; i++)
4379 : {
4380 160 : result->p[i].x = p1->p[i].x;
4381 160 : result->p[i].y = p1->p[i].y;
4382 : }
4383 224 : for (i = 0; i < p2->npts; i++)
4384 : {
4385 160 : result->p[i + p1->npts].x = p2->p[i].x;
4386 160 : result->p[i + p1->npts].y = p2->p[i].y;
4387 : }
4388 :
4389 64 : PG_RETURN_PATH_P(result);
4390 : }
4391 :
4392 : /* path_add_pt()
4393 : * Translation operators.
4394 : */
4395 : Datum
4396 360 : path_add_pt(PG_FUNCTION_ARGS)
4397 : {
4398 360 : PATH *path = PG_GETARG_PATH_P_COPY(0);
4399 360 : Point *point = PG_GETARG_POINT_P(1);
4400 : int i;
4401 :
4402 1120 : for (i = 0; i < path->npts; i++)
4403 760 : point_add_point(&path->p[i], &path->p[i], point);
4404 :
4405 360 : PG_RETURN_PATH_P(path);
4406 : }
4407 :
4408 : Datum
4409 360 : path_sub_pt(PG_FUNCTION_ARGS)
4410 : {
4411 360 : PATH *path = PG_GETARG_PATH_P_COPY(0);
4412 360 : Point *point = PG_GETARG_POINT_P(1);
4413 : int i;
4414 :
4415 1120 : for (i = 0; i < path->npts; i++)
4416 760 : point_sub_point(&path->p[i], &path->p[i], point);
4417 :
4418 360 : PG_RETURN_PATH_P(path);
4419 : }
4420 :
4421 : /* path_mul_pt()
4422 : * Rotation and scaling operators.
4423 : */
4424 : Datum
4425 360 : path_mul_pt(PG_FUNCTION_ARGS)
4426 : {
4427 360 : PATH *path = PG_GETARG_PATH_P_COPY(0);
4428 360 : Point *point = PG_GETARG_POINT_P(1);
4429 : int i;
4430 :
4431 1120 : for (i = 0; i < path->npts; i++)
4432 760 : point_mul_point(&path->p[i], &path->p[i], point);
4433 :
4434 360 : PG_RETURN_PATH_P(path);
4435 : }
4436 :
4437 : Datum
4438 76 : path_div_pt(PG_FUNCTION_ARGS)
4439 : {
4440 76 : PATH *path = PG_GETARG_PATH_P_COPY(0);
4441 76 : Point *point = PG_GETARG_POINT_P(1);
4442 : int i;
4443 :
4444 228 : for (i = 0; i < path->npts; i++)
4445 156 : point_div_point(&path->p[i], &path->p[i], point);
4446 :
4447 72 : PG_RETURN_PATH_P(path);
4448 : }
4449 :
4450 :
4451 : Datum
4452 60 : path_poly(PG_FUNCTION_ARGS)
4453 : {
4454 60 : 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 60 : if (!path->closed)
4461 4 : 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 56 : size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * path->npts;
4470 56 : poly = (POLYGON *) palloc(size);
4471 :
4472 56 : SET_VARSIZE(poly, size);
4473 56 : poly->npts = path->npts;
4474 :
4475 168 : for (i = 0; i < path->npts; i++)
4476 : {
4477 112 : poly->p[i].x = path->p[i].x;
4478 112 : poly->p[i].y = path->p[i].y;
4479 : }
4480 :
4481 56 : make_bound_box(poly);
4482 :
4483 56 : PG_RETURN_POLYGON_P(poly);
4484 : }
4485 :
4486 :
4487 : /***********************************************************************
4488 : **
4489 : ** Routines for 2D polygons.
4490 : **
4491 : ***********************************************************************/
4492 :
4493 : Datum
4494 84 : poly_npoints(PG_FUNCTION_ARGS)
4495 : {
4496 84 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
4497 :
4498 84 : PG_RETURN_INT32(poly->npts);
4499 : }
4500 :
4501 :
4502 : Datum
4503 28 : poly_center(PG_FUNCTION_ARGS)
4504 : {
4505 28 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
4506 : Point *result;
4507 : CIRCLE circle;
4508 :
4509 28 : result = palloc_object(Point);
4510 :
4511 28 : poly_to_circle(&circle, poly);
4512 28 : *result = circle.center;
4513 :
4514 28 : PG_RETURN_POINT_P(result);
4515 : }
4516 :
4517 :
4518 : Datum
4519 28 : poly_box(PG_FUNCTION_ARGS)
4520 : {
4521 28 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
4522 : BOX *box;
4523 :
4524 28 : box = palloc_object(BOX);
4525 28 : *box = poly->boundbox;
4526 :
4527 28 : PG_RETURN_BOX_P(box);
4528 : }
4529 :
4530 :
4531 : /* box_poly()
4532 : * Convert a box to a polygon.
4533 : */
4534 : Datum
4535 12420 : box_poly(PG_FUNCTION_ARGS)
4536 : {
4537 12420 : 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 12420 : size = offsetof(POLYGON, p) + sizeof(poly->p[0]) * 4;
4543 12420 : poly = (POLYGON *) palloc(size);
4544 :
4545 12420 : SET_VARSIZE(poly, size);
4546 12420 : poly->npts = 4;
4547 :
4548 12420 : poly->p[0].x = box->low.x;
4549 12420 : poly->p[0].y = box->low.y;
4550 12420 : poly->p[1].x = box->low.x;
4551 12420 : poly->p[1].y = box->high.y;
4552 12420 : poly->p[2].x = box->high.x;
4553 12420 : poly->p[2].y = box->high.y;
4554 12420 : poly->p[3].x = box->high.x;
4555 12420 : poly->p[3].y = box->low.y;
4556 :
4557 12420 : box_construct(&poly->boundbox, &box->high, &box->low);
4558 :
4559 12420 : PG_RETURN_POLYGON_P(poly);
4560 : }
4561 :
4562 :
4563 : Datum
4564 28 : poly_path(PG_FUNCTION_ARGS)
4565 : {
4566 28 : 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 28 : size = offsetof(PATH, p) + sizeof(path->p[0]) * poly->npts;
4576 28 : path = (PATH *) palloc(size);
4577 :
4578 28 : SET_VARSIZE(path, size);
4579 28 : path->npts = poly->npts;
4580 28 : path->closed = true;
4581 : /* prevent instability in unused pad bytes */
4582 28 : path->dummy = 0;
4583 :
4584 112 : for (i = 0; i < poly->npts; i++)
4585 : {
4586 84 : path->p[i].x = poly->p[i].x;
4587 84 : path->p[i].y = poly->p[i].y;
4588 : }
4589 :
4590 28 : 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 270 : circle_in(PG_FUNCTION_ARGS)
4612 : {
4613 270 : char *str = PG_GETARG_CSTRING(0);
4614 270 : Node *escontext = fcinfo->context;
4615 270 : CIRCLE *circle = palloc_object(CIRCLE);
4616 : char *s,
4617 : *cp;
4618 270 : int depth = 0;
4619 :
4620 270 : s = str;
4621 286 : while (isspace((unsigned char) *s))
4622 16 : s++;
4623 270 : if (*s == LDELIM_C)
4624 220 : depth++, s++;
4625 50 : else if (*s == LDELIM)
4626 : {
4627 : /* If there are two left parens, consume the first one */
4628 34 : cp = (s + 1);
4629 42 : while (isspace((unsigned char) *cp))
4630 8 : cp++;
4631 34 : if (*cp == LDELIM)
4632 14 : depth++, s = cp;
4633 : }
4634 :
4635 : /* pair_decode will consume parens around the pair, if any */
4636 270 : if (!pair_decode(s, &circle->center.x, &circle->center.y, &s, "circle", str,
4637 : escontext))
4638 8 : PG_RETURN_NULL();
4639 :
4640 254 : if (*s == DELIM)
4641 254 : s++;
4642 :
4643 254 : if (!single_decode(s, &circle->radius, &s, "circle", str, escontext))
4644 0 : PG_RETURN_NULL();
4645 :
4646 : /* We have to accept NaN. */
4647 254 : if (circle->radius < 0.0)
4648 12 : ereturn(escontext, (Datum) 0,
4649 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
4650 : errmsg("invalid input syntax for type %s: \"%s\"",
4651 : "circle", str)));
4652 :
4653 468 : while (depth > 0)
4654 : {
4655 230 : if ((*s == RDELIM) || ((*s == RDELIM_C) && (depth == 1)))
4656 : {
4657 226 : depth--;
4658 226 : s++;
4659 238 : while (isspace((unsigned char) *s))
4660 12 : s++;
4661 : }
4662 : else
4663 4 : 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 238 : if (*s != '\0')
4670 4 : ereturn(escontext, (Datum) 0,
4671 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
4672 : errmsg("invalid input syntax for type %s: \"%s\"",
4673 : "circle", str)));
4674 :
4675 234 : PG_RETURN_CIRCLE_P(circle);
4676 : }
4677 :
4678 : /* circle_out - convert a circle to external form.
4679 : */
4680 : Datum
4681 6104 : circle_out(PG_FUNCTION_ARGS)
4682 : {
4683 6104 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
4684 : StringInfoData str;
4685 :
4686 6104 : initStringInfo(&str);
4687 :
4688 6104 : appendStringInfoChar(&str, LDELIM_C);
4689 6104 : appendStringInfoChar(&str, LDELIM);
4690 6104 : pair_encode(circle->center.x, circle->center.y, &str);
4691 6104 : appendStringInfoChar(&str, RDELIM);
4692 6104 : appendStringInfoChar(&str, DELIM);
4693 6104 : single_encode(circle->radius, &str);
4694 6104 : appendStringInfoChar(&str, RDELIM_C);
4695 :
4696 6104 : 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 = palloc_object(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 257 : circle_same(PG_FUNCTION_ARGS)
4752 : {
4753 257 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4754 257 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4755 :
4756 257 : 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 12812 : circle_overlap(PG_FUNCTION_ARGS)
4765 : {
4766 12812 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4767 12812 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4768 :
4769 12812 : 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 256 : circle_overleft(PG_FUNCTION_ARGS)
4778 : {
4779 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4780 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4781 :
4782 256 : 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 256 : circle_left(PG_FUNCTION_ARGS)
4790 : {
4791 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4792 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4793 :
4794 256 : 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 256 : circle_right(PG_FUNCTION_ARGS)
4802 : {
4803 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4804 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4805 :
4806 256 : 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 256 : circle_overright(PG_FUNCTION_ARGS)
4815 : {
4816 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4817 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4818 :
4819 256 : 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 256 : circle_contained(PG_FUNCTION_ARGS)
4827 : {
4828 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4829 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4830 :
4831 256 : 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 264 : circle_contain(PG_FUNCTION_ARGS)
4839 : {
4840 264 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4841 264 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4842 :
4843 264 : 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 256 : circle_below(PG_FUNCTION_ARGS)
4852 : {
4853 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4854 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4855 :
4856 256 : 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 256 : circle_above(PG_FUNCTION_ARGS)
4864 : {
4865 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4866 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4867 :
4868 256 : 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 256 : circle_overbelow(PG_FUNCTION_ARGS)
4877 : {
4878 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4879 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4880 :
4881 256 : 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 256 : circle_overabove(PG_FUNCTION_ARGS)
4890 : {
4891 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4892 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4893 :
4894 256 : 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 256 : circle_eq(PG_FUNCTION_ARGS)
4904 : {
4905 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4906 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4907 :
4908 256 : PG_RETURN_BOOL(FPeq(circle_ar(circle1), circle_ar(circle2)));
4909 : }
4910 :
4911 : Datum
4912 256 : circle_ne(PG_FUNCTION_ARGS)
4913 : {
4914 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4915 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4916 :
4917 256 : PG_RETURN_BOOL(FPne(circle_ar(circle1), circle_ar(circle2)));
4918 : }
4919 :
4920 : Datum
4921 1052 : circle_lt(PG_FUNCTION_ARGS)
4922 : {
4923 1052 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4924 1052 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4925 :
4926 1052 : PG_RETURN_BOOL(FPlt(circle_ar(circle1), circle_ar(circle2)));
4927 : }
4928 :
4929 : Datum
4930 256 : circle_gt(PG_FUNCTION_ARGS)
4931 : {
4932 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4933 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4934 :
4935 256 : PG_RETURN_BOOL(FPgt(circle_ar(circle1), circle_ar(circle2)));
4936 : }
4937 :
4938 : Datum
4939 256 : circle_le(PG_FUNCTION_ARGS)
4940 : {
4941 256 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4942 256 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4943 :
4944 256 : PG_RETURN_BOOL(FPle(circle_ar(circle1), circle_ar(circle2)));
4945 : }
4946 :
4947 : Datum
4948 324 : circle_ge(PG_FUNCTION_ARGS)
4949 : {
4950 324 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
4951 324 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
4952 :
4953 324 : 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 320 : circle_add_pt(PG_FUNCTION_ARGS)
4966 : {
4967 320 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
4968 320 : Point *point = PG_GETARG_POINT_P(1);
4969 : CIRCLE *result;
4970 :
4971 320 : result = palloc_object(CIRCLE);
4972 :
4973 320 : point_add_point(&result->center, &circle->center, point);
4974 320 : result->radius = circle->radius;
4975 :
4976 320 : PG_RETURN_CIRCLE_P(result);
4977 : }
4978 :
4979 : Datum
4980 320 : circle_sub_pt(PG_FUNCTION_ARGS)
4981 : {
4982 320 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
4983 320 : Point *point = PG_GETARG_POINT_P(1);
4984 : CIRCLE *result;
4985 :
4986 320 : result = palloc_object(CIRCLE);
4987 :
4988 320 : point_sub_point(&result->center, &circle->center, point);
4989 320 : result->radius = circle->radius;
4990 :
4991 320 : PG_RETURN_CIRCLE_P(result);
4992 : }
4993 :
4994 :
4995 : /* circle_mul_pt()
4996 : * Rotation and scaling operators.
4997 : */
4998 : Datum
4999 320 : circle_mul_pt(PG_FUNCTION_ARGS)
5000 : {
5001 320 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5002 320 : Point *point = PG_GETARG_POINT_P(1);
5003 : CIRCLE *result;
5004 :
5005 320 : result = palloc_object(CIRCLE);
5006 :
5007 320 : point_mul_point(&result->center, &circle->center, point);
5008 320 : result->radius = float8_mul(circle->radius, hypot(point->x, point->y));
5009 :
5010 320 : PG_RETURN_CIRCLE_P(result);
5011 : }
5012 :
5013 : Datum
5014 72 : circle_div_pt(PG_FUNCTION_ARGS)
5015 : {
5016 72 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5017 72 : Point *point = PG_GETARG_POINT_P(1);
5018 : CIRCLE *result;
5019 :
5020 72 : result = palloc_object(CIRCLE);
5021 :
5022 72 : point_div_point(&result->center, &circle->center, point);
5023 64 : result->radius = float8_div(circle->radius, hypot(point->x, point->y));
5024 :
5025 64 : PG_RETURN_CIRCLE_P(result);
5026 : }
5027 :
5028 :
5029 : /* circle_area - returns the area of the circle.
5030 : */
5031 : Datum
5032 340 : circle_area(PG_FUNCTION_ARGS)
5033 : {
5034 340 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5035 :
5036 340 : PG_RETURN_FLOAT8(circle_ar(circle));
5037 : }
5038 :
5039 :
5040 : /* circle_diameter - returns the diameter of the circle.
5041 : */
5042 : Datum
5043 64 : circle_diameter(PG_FUNCTION_ARGS)
5044 : {
5045 64 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5046 :
5047 64 : 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 12504 : circle_radius(PG_FUNCTION_ARGS)
5055 : {
5056 12504 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5057 :
5058 12504 : PG_RETURN_FLOAT8(circle->radius);
5059 : }
5060 :
5061 :
5062 : /* circle_distance - returns the distance between
5063 : * two circles.
5064 : */
5065 : Datum
5066 112 : circle_distance(PG_FUNCTION_ARGS)
5067 : {
5068 112 : CIRCLE *circle1 = PG_GETARG_CIRCLE_P(0);
5069 112 : CIRCLE *circle2 = PG_GETARG_CIRCLE_P(1);
5070 : float8 result;
5071 :
5072 112 : result = float8_mi(point_dt(&circle1->center, &circle2->center),
5073 : float8_pl(circle1->radius, circle2->radius));
5074 112 : if (result < 0.0)
5075 48 : result = 0.0;
5076 :
5077 112 : PG_RETURN_FLOAT8(result);
5078 : }
5079 :
5080 :
5081 : Datum
5082 16 : circle_contain_pt(PG_FUNCTION_ARGS)
5083 : {
5084 16 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5085 16 : Point *point = PG_GETARG_POINT_P(1);
5086 : float8 d;
5087 :
5088 16 : d = point_dt(&circle->center, point);
5089 16 : PG_RETURN_BOOL(d <= circle->radius);
5090 : }
5091 :
5092 :
5093 : Datum
5094 40 : pt_contained_circle(PG_FUNCTION_ARGS)
5095 : {
5096 40 : Point *point = PG_GETARG_POINT_P(0);
5097 40 : CIRCLE *circle = PG_GETARG_CIRCLE_P(1);
5098 : float8 d;
5099 :
5100 40 : d = point_dt(&circle->center, point);
5101 40 : 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 564 : dist_pc(PG_FUNCTION_ARGS)
5110 : {
5111 564 : Point *point = PG_GETARG_POINT_P(0);
5112 564 : CIRCLE *circle = PG_GETARG_CIRCLE_P(1);
5113 : float8 result;
5114 :
5115 564 : result = float8_mi(point_dt(point, &circle->center),
5116 : circle->radius);
5117 564 : if (result < 0.0)
5118 76 : result = 0.0;
5119 :
5120 564 : PG_RETURN_FLOAT8(result);
5121 : }
5122 :
5123 : /*
5124 : * Distance from a circle to a point
5125 : */
5126 : Datum
5127 12484 : dist_cpoint(PG_FUNCTION_ARGS)
5128 : {
5129 12484 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5130 12484 : Point *point = PG_GETARG_POINT_P(1);
5131 : float8 result;
5132 :
5133 12484 : result = float8_mi(point_dt(point, &circle->center), circle->radius);
5134 12484 : if (result < 0.0)
5135 0 : result = 0.0;
5136 :
5137 12484 : PG_RETURN_FLOAT8(result);
5138 : }
5139 :
5140 : /* circle_center - returns the center point of the circle.
5141 : */
5142 : Datum
5143 12604 : circle_center(PG_FUNCTION_ARGS)
5144 : {
5145 12604 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5146 : Point *result;
5147 :
5148 12604 : result = palloc_object(Point);
5149 12604 : result->x = circle->center.x;
5150 12604 : result->y = circle->center.y;
5151 :
5152 12604 : PG_RETURN_POINT_P(result);
5153 : }
5154 :
5155 :
5156 : /* circle_ar - returns the area of the circle.
5157 : */
5158 : static float8
5159 5140 : circle_ar(CIRCLE *circle)
5160 : {
5161 5140 : return float8_mul(float8_mul(circle->radius, circle->radius), M_PI);
5162 : }
5163 :
5164 :
5165 : /*----------------------------------------------------------
5166 : * Conversion operators.
5167 : *---------------------------------------------------------*/
5168 :
5169 : Datum
5170 120110 : cr_circle(PG_FUNCTION_ARGS)
5171 : {
5172 120110 : Point *center = PG_GETARG_POINT_P(0);
5173 120110 : float8 radius = PG_GETARG_FLOAT8(1);
5174 : CIRCLE *result;
5175 :
5176 120110 : result = palloc_object(CIRCLE);
5177 :
5178 120110 : result->center.x = center->x;
5179 120110 : result->center.y = center->y;
5180 120110 : result->radius = radius;
5181 :
5182 120110 : PG_RETURN_CIRCLE_P(result);
5183 : }
5184 :
5185 : Datum
5186 32 : circle_box(PG_FUNCTION_ARGS)
5187 : {
5188 32 : CIRCLE *circle = PG_GETARG_CIRCLE_P(0);
5189 : BOX *box;
5190 : float8 delta;
5191 :
5192 32 : box = palloc_object(BOX);
5193 :
5194 32 : delta = float8_div(circle->radius, sqrt(2.0));
5195 :
5196 32 : box->high.x = float8_pl(circle->center.x, delta);
5197 32 : box->low.x = float8_mi(circle->center.x, delta);
5198 32 : box->high.y = float8_pl(circle->center.y, delta);
5199 32 : box->low.y = float8_mi(circle->center.y, delta);
5200 :
5201 32 : PG_RETURN_BOX_P(box);
5202 : }
5203 :
5204 : /* box_circle()
5205 : * Convert a box to a circle.
5206 : */
5207 : Datum
5208 12420 : box_circle(PG_FUNCTION_ARGS)
5209 : {
5210 12420 : BOX *box = PG_GETARG_BOX_P(0);
5211 : CIRCLE *circle;
5212 :
5213 12420 : circle = palloc_object(CIRCLE);
5214 :
5215 12420 : circle->center.x = float8_div(float8_pl(box->high.x, box->low.x), 2.0);
5216 12420 : circle->center.y = float8_div(float8_pl(box->high.y, box->low.y), 2.0);
5217 :
5218 12420 : circle->radius = point_dt(&circle->center, &box->high);
5219 :
5220 12420 : PG_RETURN_CIRCLE_P(circle);
5221 : }
5222 :
5223 :
5224 : Datum
5225 40057 : circle_poly(PG_FUNCTION_ARGS)
5226 : {
5227 40057 : int32 npts = PG_GETARG_INT32(0);
5228 40057 : 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 40057 : if (FPzero(circle->radius))
5237 4 : ereport(ERROR,
5238 : (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
5239 : errmsg("cannot convert circle with radius zero to polygon")));
5240 :
5241 40053 : if (npts < 2)
5242 4 : ereport(ERROR,
5243 : (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
5244 : errmsg("must request at least 2 points")));
5245 :
5246 40049 : base_size = sizeof(poly->p[0]) * npts;
5247 40049 : size = offsetof(POLYGON, p) + base_size;
5248 :
5249 : /* Check for integer overflow */
5250 40049 : 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 40049 : poly = (POLYGON *) palloc0(size); /* zero any holes */
5256 40049 : SET_VARSIZE(poly, size);
5257 40049 : poly->npts = npts;
5258 :
5259 40049 : anglestep = float8_div(2.0 * M_PI, npts);
5260 :
5261 520541 : for (i = 0; i < npts; i++)
5262 : {
5263 480492 : angle = float8_mul(anglestep, i);
5264 :
5265 480492 : poly->p[i].x = float8_mi(circle->center.x,
5266 : float8_mul(circle->radius, cos(angle)));
5267 480492 : poly->p[i].y = float8_pl(circle->center.y,
5268 : float8_mul(circle->radius, sin(angle)));
5269 : }
5270 :
5271 40049 : make_bound_box(poly);
5272 :
5273 40049 : 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 48 : poly_to_circle(CIRCLE *result, POLYGON *poly)
5286 : {
5287 : int i;
5288 :
5289 : Assert(poly->npts > 0);
5290 :
5291 48 : result->center.x = 0;
5292 48 : result->center.y = 0;
5293 48 : result->radius = 0;
5294 :
5295 216 : for (i = 0; i < poly->npts; i++)
5296 168 : point_add_point(&result->center, &result->center, &poly->p[i]);
5297 48 : result->center.x = float8_div(result->center.x, poly->npts);
5298 48 : result->center.y = float8_div(result->center.y, poly->npts);
5299 :
5300 216 : for (i = 0; i < poly->npts; i++)
5301 168 : result->radius = float8_pl(result->radius,
5302 : point_dt(&poly->p[i], &result->center));
5303 48 : result->radius = float8_div(result->radius, poly->npts);
5304 48 : }
5305 :
5306 : Datum
5307 20 : poly_circle(PG_FUNCTION_ARGS)
5308 : {
5309 20 : POLYGON *poly = PG_GETARG_POLYGON_P(0);
5310 : CIRCLE *result;
5311 :
5312 20 : result = palloc_object(CIRCLE);
5313 :
5314 20 : poly_to_circle(result, poly);
5315 :
5316 20 : 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 164433 : point_inside(Point *p, int npts, Point *plist)
5341 : {
5342 : float8 x0,
5343 : y0;
5344 : float8 prev_x,
5345 : prev_y;
5346 164433 : int i = 0;
5347 : float8 x,
5348 : y;
5349 : int cross,
5350 164433 : total_cross = 0;
5351 :
5352 : Assert(npts > 0);
5353 :
5354 : /* compute first polygon point relative to single point */
5355 164433 : x0 = float8_mi(plist[0].x, p->x);
5356 164433 : y0 = float8_mi(plist[0].y, p->y);
5357 :
5358 164433 : prev_x = x0;
5359 164433 : prev_y = y0;
5360 : /* loop over polygon points and aggregate total_cross */
5361 758628 : for (i = 1; i < npts; i++)
5362 : {
5363 : /* compute next polygon point relative to single point */
5364 594283 : x = float8_mi(plist[i].x, p->x);
5365 594283 : y = float8_mi(plist[i].y, p->y);
5366 :
5367 : /* compute previous to current point crossing */
5368 594283 : if ((cross = lseg_crossing(x, y, prev_x, prev_y)) == POINT_ON_POLYGON)
5369 88 : return 2;
5370 594195 : total_cross += cross;
5371 :
5372 594195 : prev_x = x;
5373 594195 : prev_y = y;
5374 : }
5375 :
5376 : /* now do the first point */
5377 164345 : if ((cross = lseg_crossing(x0, y0, prev_x, prev_y)) == POINT_ON_POLYGON)
5378 72 : return 2;
5379 164273 : total_cross += cross;
5380 :
5381 164273 : if (total_cross != 0)
5382 126129 : return 1;
5383 38144 : 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 758628 : lseg_crossing(float8 x, float8 y, float8 prev_x, float8 prev_y)
5398 : {
5399 : float8 z;
5400 : int y_sign;
5401 :
5402 758628 : if (FPzero(y))
5403 : { /* y == 0, on X axis */
5404 1162 : if (FPzero(x)) /* (x,y) is (0,0)? */
5405 152 : return POINT_ON_POLYGON;
5406 1010 : else if (FPgt(x, 0))
5407 : { /* x > 0 */
5408 673 : if (FPzero(prev_y)) /* y and prev_y are zero */
5409 : /* prev_x > 0? */
5410 40 : return FPgt(prev_x, 0.0) ? 0 : POINT_ON_POLYGON;
5411 633 : return FPlt(prev_y, 0.0) ? 1 : -1;
5412 : }
5413 : else
5414 : { /* x < 0, x not on positive X axis */
5415 337 : if (FPzero(prev_y))
5416 : /* prev_x < 0? */
5417 16 : return FPlt(prev_x, 0.0) ? 0 : POINT_ON_POLYGON;
5418 321 : return 0;
5419 : }
5420 : }
5421 : else
5422 : { /* y != 0 */
5423 : /* compute y crossing direction from previous point */
5424 757466 : y_sign = FPgt(y, 0.0) ? 1 : -1;
5425 :
5426 757466 : if (FPzero(prev_y))
5427 : /* previous point was on X axis, so new point is either off or on */
5428 1018 : return FPlt(prev_x, 0.0) ? 0 : y_sign;
5429 756448 : else if ((y_sign < 0 && FPlt(prev_y, 0.0)) ||
5430 386704 : (y_sign > 0 && FPgt(prev_y, 0.0)))
5431 : /* both above or below X axis */
5432 481664 : return 0; /* same sign */
5433 : else
5434 : { /* y and prev_y cross X-axis */
5435 274784 : if (FPge(x, 0.0) && FPgt(prev_x, 0.0))
5436 : /* both non-negative so cross positive X-axis */
5437 99924 : return 2 * y_sign;
5438 174860 : if (FPlt(x, 0.0) && FPle(prev_x, 0.0))
5439 : /* both non-positive so do not cross positive X-axis */
5440 88296 : return 0;
5441 :
5442 : /* x and y cross axes, see URL above point_inside() */
5443 86564 : z = float8_mi(float8_mul(float8_mi(x, prev_x), y),
5444 : float8_mul(float8_mi(y, prev_y), x));
5445 86564 : if (FPzero(z))
5446 8 : return POINT_ON_POLYGON;
5447 86556 : if ((y_sign < 0 && FPlt(z, 0.0)) ||
5448 49664 : (y_sign > 0 && FPgt(z, 0.0)))
5449 48456 : return 0;
5450 38100 : return 2 * y_sign;
5451 : }
5452 : }
5453 : }
5454 :
5455 :
5456 : static bool
5457 4061 : plist_same(int npts, Point *p1, Point *p2)
5458 : {
5459 : int i,
5460 : ii,
5461 : j;
5462 :
5463 : /* find match for first point */
5464 4173 : for (i = 0; i < npts; i++)
5465 : {
5466 4149 : if (point_eq_point(&p2[i], &p1[0]))
5467 : {
5468 :
5469 : /* match found? then look forward through remaining points */
5470 12122 : for (ii = 1, j = i + 1; ii < npts; ii++, j++)
5471 : {
5472 8093 : if (j >= npts)
5473 12 : j = 0;
5474 8093 : if (!point_eq_point(&p2[j], &p1[ii]))
5475 24 : break;
5476 : }
5477 4053 : if (ii == npts)
5478 4029 : return true;
5479 :
5480 : /* match not found forwards? then look backwards */
5481 56 : for (ii = 1, j = i - 1; ii < npts; ii++, j--)
5482 : {
5483 48 : if (j < 0)
5484 8 : j = (npts - 1);
5485 48 : if (!point_eq_point(&p2[j], &p1[ii]))
5486 16 : break;
5487 : }
5488 24 : if (ii == npts)
5489 8 : return true;
5490 : }
5491 : }
5492 :
5493 24 : return false;
5494 : }
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