1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
|
<?xml version="1.0" encoding="UTF-8"?>
<sect1 id="reference_sfcgal">
<sect1info>
<abstract>
<para>
SFCGAL is a C++ wrapper library around CGAL that provides advanced 2D and 3D functions.
For robustness, geometry coordinates have an exact rational number representation.
</para>
<para>
Installation instructions of the library can be found on SFCGAL home page <ulink url="http://www.sfcgal.org">http://www.sfcgal.org</ulink>.
To load the functions create extension postgis_sfcgal.
</para>
<para>
Some SFCGAL functions replace standard ones (ST_Intersects, ST_Intersection, ST_Difference, ST_Union, ST_Area and ST_Distance), to switch between standard functions and SFCGAL function use:
<programlisting>SET postgis.backend = sfcgal;</programlisting>
and
<programlisting>SET postgis.backend = geos;</programlisting>
</para>
</abstract>
</sect1info>
<title>SFCGAL Functions</title>
<refentry id="postgis_sfcgal_version">
<refnamediv>
<refname>postgis_sfcgal_version</refname>
<refpurpose>Returns the version of SFCGAL in use</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>text <function>postgis_sfcgal_version</function></funcdef>
<void/>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Availability: 2.1.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
</refentry>
<refentry id="ST_Extrude">
<refnamediv>
<refname>ST_Extrude</refname>
<refpurpose>Extrude a surface to a related volume</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>geometry <function>ST_Extrude</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom</parameter></paramdef>
<paramdef><type>float</type> <parameter>x</parameter></paramdef>
<paramdef><type>float</type> <parameter>y</parameter></paramdef>
<paramdef><type>float</type> <parameter>z</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Availability: 2.1.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
<refsection><title>Examples</title>
<para>3D images were generated using PostGIS <xref linkend="ST_AsX3D" /> and rendering in HTML using <ulink url="http://www.x3dom.org">X3Dom HTML Javascript rendering library</ulink>.</para>
<informaltable>
<tgroup cols="2">
<tbody>
<row>
<entry><para>
<programlisting>SELECT ST_Buffer(ST_GeomFromText('POINT(100 90)'),
50, 'quad_segs=2'),0,0,30);</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_extrude01.png" />
</imageobject>
<caption><para>Original octagon formed from buffering point</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
<entry><para>
<programlisting>ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(100 90)'),
50, 'quad_segs=2'),0,0,30);</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_extrude02.png" />
</imageobject>
<caption><para>Hexagon extruded 30 units along Z produces a PolyhedralSurfaceZ</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
</row>
<row>
<entry><para>
<programlisting>SELECT ST_GeomFromText('LINESTRING(50 50, 100 90, 95 150)')</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_extrude03.png" />
</imageobject>
<caption><para>Original linestring</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
<entry><para>
<programlisting>SELECT ST_Extrude(
ST_GeomFromText('LINESTRING(50 50, 100 90, 95 150)'),0,0,10));</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_extrude04.png" />
</imageobject>
<caption><para>LineString Extruded along Z produces a PolyhedralSurfaceZ</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
</row>
</tbody>
</tgroup>
</informaltable>
</refsection>
<refsection>
<title>See Also</title>
<para><xref linkend="ST_AsX3D" /></para>
</refsection>
</refentry>
<refentry id="ST_StraightSkeleton">
<refnamediv>
<refname>ST_StraightSkeleton</refname>
<refpurpose>Compute a straight skeleton from a geometry</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>geometry <function>ST_StraightSkeleton</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Availability: 2.1.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
<refsection><title>Examples</title>
<programlisting>SELECT ST_StraightSkeleton(ST_GeomFromText('POLYGON (( 190 190, 10 190, 10 10, 190 10, 190 20, 160 30, 60 30, 60 130, 190 140, 190 190 ))'));</programlisting>
<informaltable>
<tgroup cols="2">
<tbody>
<row>
<entry><para><informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_straightskeleton01.png" />
</imageobject>
<caption><para>Original polygon</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
<entry><para><informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_straightskeleton02.png" />
</imageobject>
<caption><para>Straight Skeleton of polygon</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
</row>
</tbody>
</tgroup>
</informaltable>
</refsection>
</refentry>
<refentry id="ST_ApproximateMedialAxis">
<refnamediv>
<refname>ST_ApproximateMedialAxis</refname>
<refpurpose>Compute the approximate medial axis of an areal geometry.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>geometry <function>ST_ApproximateMedialAxis</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>
Return an approximate medial axis for the areal input based on
its straight skeleton. Uses an SFCGAL specific API when built against
a capable version (1.2.0+). Otherwise the function is just a wrapper
around ST_StraightSkeleton (slower case).
</para>
<para>Availability: 2.2.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
<refsection><title>Examples</title>
<programlisting>SELECT ST_ApproximateMedialAxis(ST_GeomFromText('POLYGON (( 190 190, 10 190, 10 10, 190 10, 190 20, 160 30, 60 30, 60 130, 190 140, 190 190 ))'));</programlisting>
<informaltable>
<tgroup cols="1">
<tbody>
<row>
<entry><para><informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_approximatemedialaxis01.png" />
</imageobject>
<caption><para>A polygon and its approximate medial axis</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
</row>
</tbody>
</tgroup>
</informaltable>
</refsection>
<refsection>
<title>See Also</title>
<para><xref linkend="ST_StraightSkeleton" /></para>
</refsection>
</refentry>
<refentry id="ST_IsPlanar">
<refnamediv>
<refname>ST_IsPlanar</refname>
<refpurpose>Check if a surface is or not planar</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>boolean <function>ST_IsPlanar</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Availability: 2.2.0: This was documented in 2.1.0 but got accidentally left out in 2.1 release.</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
</refentry>
<refentry id="ST_Orientation">
<refnamediv>
<refname>ST_Orientation</refname>
<refpurpose>Determine surface orientation</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>integer <function>ST_Orientation</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>The function only applies to polygons. It returns -1 if the polygon is counterclockwise oriented and 1 if the polygon is clockwise oriented.</para>
<para>Availability: 2.1.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
</refsection>
</refentry>
<refentry id="ST_ForceLHR">
<refnamediv>
<refname>ST_ForceLHR</refname>
<refpurpose>Force LHR orientation</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>geometry <function>ST_ForceLHR</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Availability: 2.1.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
</refentry>
<refentry id="ST_MinkowskiSum">
<refnamediv>
<refname>ST_MinkowskiSum</refname>
<refpurpose>Performs Minkowski sum</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>geometry <function>ST_MinkowskiSum</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom1</parameter></paramdef>
<paramdef><type>geometry</type> <parameter>geom2</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>This function performs a 2D minkowski sum of a point, line or polygon with a polygon.</para>
<para>A minkowski sum of two geometries A and B is the set of all points that are the sum of any point in A and B. Minkowski sums are often used in motion planning and computer-aided design. More details on <ulink url="https://en.wikipedia.org/wiki/Minkowski_addition">Wikipedia Minkowski addition</ulink>.</para>
<para>The first parameter can be any 2D geometry (point, linestring, polygon). If a 3D geometry is passed, it will be converted to 2D by forcing Z to 0, leading to possible cases of invalidity. The second parameter must be a 2D polygon.</para>
<para>Implementation utilizes <ulink url="http://doc.cgal.org/latest/Minkowski_sum_2/">CGAL 2D Minkowskisum</ulink>.</para>
<para>Availability: 2.1.0</para>
<para>&sfcgal_required;</para>
</refsection>
<refsection><title>Examples</title>
<para>Minkowski Sum of Linestring and circle polygon where Linestring cuts thru the circle</para>
<informaltable>
<tgroup cols="2">
<tbody>
<row>
<entry>
<para>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_minkowskisum01.png" />
</imageobject>
<caption><para>Before Summing</para></caption>
</mediaobject>
</informalfigure>
</para>
</entry>
<entry>
<para>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_minkowskisum02.png" />
</imageobject>
<caption><para>After summing</para></caption>
</mediaobject>
</informalfigure>
</para>
</entry>
</row>
</tbody>
</tgroup>
</informaltable>
<programlisting>
SELECT ST_MinkowskiSum(line, circle))
FROM (SELECT
ST_MakeLine(ST_MakePoint(10, 10),ST_MakePoint(100, 100)) As line,
ST_Buffer(ST_GeomFromText('POINT(50 50)'), 30) As circle) As foo;
-- wkt --
MULTIPOLYGON(((30 59.9999999999999,30.5764415879031 54.1472903395161,32.2836140246614 48.5194970290472,35.0559116309237 43.3328930094119,38.7867965644036 38.7867965644035,43.332893009412 35.0559116309236,48.5194970290474 32.2836140246614,54.1472903395162 30.5764415879031,60.0000000000001 30,65.8527096604839 30.5764415879031,71.4805029709527 32.2836140246614,76.6671069905881 35.0559116309237,81.2132034355964 38.7867965644036,171.213203435596 128.786796564404,174.944088369076 133.332893009412,177.716385975339 138.519497029047,179.423558412097 144.147290339516,180 150,179.423558412097 155.852709660484,177.716385975339 161.480502970953,174.944088369076 166.667106990588,171.213203435596 171.213203435596,166.667106990588 174.944088369076,
161.480502970953 177.716385975339,155.852709660484 179.423558412097,150 180,144.147290339516 179.423558412097,138.519497029047 177.716385975339,133.332893009412 174.944088369076,128.786796564403 171.213203435596,38.7867965644035 81.2132034355963,35.0559116309236 76.667106990588,32.2836140246614 71.4805029709526,30.5764415879031 65.8527096604838,30 59.9999999999999)))
</programlisting>
<para>Minkowski Sum of a polygon and multipoint</para>
<informaltable>
<tgroup cols="2">
<tbody>
<row>
<entry>
<para>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_minkowskisum03.png" />
</imageobject>
<caption><para>Before Summing</para></caption>
</mediaobject>
</informalfigure>
</para>
</entry>
<entry>
<para>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_minkowskisum04.png" />
</imageobject>
<caption><para>After summing: polygon is duplicated and translated to position of points</para></caption>
</mediaobject>
</informalfigure>
</para>
</entry>
</row>
</tbody>
</tgroup>
</informaltable>
<programlisting>SELECT ST_MinkowskiSum(mp, poly)
FROM (SELECT 'MULTIPOINT(25 50,70 25)'::geometry As mp,
'POLYGON((130 150, 20 40, 50 60, 125 100, 130 150))'::geometry As poly
) As foo
-- wkt --
MULTIPOLYGON(
((70 115,100 135,175 175,225 225,70 115)),
((120 65,150 85,225 125,275 175,120 65))
)
</programlisting>
</refsection>
</refentry>
<refentry id="ST_3DIntersection">
<refnamediv>
<refname>ST_3DIntersection</refname>
<refpurpose>Perform 3D intersection</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>geometry <function>ST_3DIntersection</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom1</parameter></paramdef>
<paramdef><type>geometry</type> <parameter>geom2</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Return a geometry that is the shared portion between geom1 and geom2.</para>
<para>Availability: 2.1.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
<refsection>
<title>Examples</title>
<para>3D images were generated using PostGIS <xref linkend="ST_AsX3D" /> and rendering in HTML using <ulink url="http://www.x3dom.org">X3Dom HTML Javascript rendering library</ulink>.</para>
<informaltable>
<tgroup cols="2">
<tbody>
<row>
<entry><para>
<programlisting>SELECT ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(100 90)'),
50, 'quad_segs=2'),0,0,30) AS geom1,
ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(80 80)'),
50, 'quad_segs=1'),0,0,30) AS geom2;
</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_3ddifference01.png" />
</imageobject>
<caption><para>Original 3D geometries overlaid. geom2 is shown semi-transparent</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
<entry><para>
<programlisting>SELECT ST_3DIntersection(geom1,geom2)
FROM ( SELECT ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(100 90)'),
50, 'quad_segs=2'),0,0,30) AS geom1,
ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(80 80)'),
50, 'quad_segs=1'),0,0,30) AS geom2 ) As t;</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_3dintersection01.png" />
</imageobject>
<caption><para>Intersection of geom1 and geom2</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
</row>
</tbody>
</tgroup>
</informaltable>
<para>3D linestrings and polygons</para>
<programlisting> SELECT ST_AsText(ST_3DIntersection(linestring, polygon)) As wkt
FROM ST_GeomFromText('LINESTRING Z (2 2 6,1.5 1.5 7,1 1 8,0.5 0.5 8,0 0 10)') AS linestring
CROSS JOIN ST_GeomFromText('POLYGON((0 0 8, 0 1 8, 1 1 8, 1 0 8, 0 0 8))') AS polygon;
wkt
--------------------------------
LINESTRING Z (1 1 8,0.5 0.5 8)
</programlisting>
<para>Cube (closed Polyhedral Surface) and Polygon Z</para>
<programlisting>SELECT ST_AsText(ST_3DIntersection(
ST_GeomFromText('POLYHEDRALSURFACE Z( ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)),
((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)), ((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)),
((1 1 0, 1 1 1, 1 0 1, 1 0 0, 1 1 0)),
((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0)), ((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)) )'),
'POLYGON Z ((0 0 0, 0 0 0.5, 0 0.5 0.5, 0 0.5 0, 0 0 0))'::geometry))</programlisting>
<screen>TIN Z (((0 0 0,0 0 0.5,0 0.5 0.5,0 0 0)),((0 0.5 0,0 0 0,0 0.5 0.5,0 0.5 0)))</screen>
<para>Intersection of 2 solids that result in volumetric intersection is also a solid (ST_Dimension returns 3)</para>
<programlisting>SELECT ST_AsText(ST_3DIntersection( ST_Extrude(ST_Buffer('POINT(10 20)'::geometry,10,1),0,0,30),
ST_Extrude(ST_Buffer('POINT(10 20)'::geometry,10,1),2,0,10) ));</programlisting>
<screen>POLYHEDRALSURFACE Z (((13.3333333333333 13.3333333333333 10,20 20 0,20 20 10,13.3333333333333 13.3333333333333 10)),
((20 20 10,16.6666666666667 23.3333333333333 10,13.3333333333333 13.3333333333333 10,20 20 10)),
((20 20 0,16.6666666666667 23.3333333333333 10,20 20 10,20 20 0)),
((13.3333333333333 13.3333333333333 10,10 10 0,20 20 0,13.3333333333333 13.3333333333333 10)),
((16.6666666666667 23.3333333333333 10,12 28 10,13.3333333333333 13.3333333333333 10,16.6666666666667 23.3333333333333 10)),
((20 20 0,9.99999999999995 30 0,16.6666666666667 23.3333333333333 10,20 20 0)),
((10 10 0,9.99999999999995 30 0,20 20 0,10 10 0)),((13.3333333333333 13.3333333333333 10,12 12 10,10 10 0,13.3333333333333 13.3333333333333 10)),
((12 28 10,12 12 10,13.3333333333333 13.3333333333333 10,12 28 10)),
((16.6666666666667 23.3333333333333 10,9.99999999999995 30 0,12 28 10,16.6666666666667 23.3333333333333 10)),
((10 10 0,0 20 0,9.99999999999995 30 0,10 10 0)),
((12 12 10,11 11 10,10 10 0,12 12 10)),((12 28 10,11 11 10,12 12 10,12 28 10)),
((9.99999999999995 30 0,11 29 10,12 28 10,9.99999999999995 30 0)),((0 20 0,2 20 10,9.99999999999995 30 0,0 20 0)),
((10 10 0,2 20 10,0 20 0,10 10 0)),((11 11 10,2 20 10,10 10 0,11 11 10)),((12 28 10,11 29 10,11 11 10,12 28 10)),
((9.99999999999995 30 0,2 20 10,11 29 10,9.99999999999995 30 0)),((11 11 10,11 29 10,2 20 10,11 11 10)))</screen>
</refsection>
</refentry>
<refentry id="ST_3DDifference">
<refnamediv>
<refname>ST_3DDifference</refname>
<refpurpose>Perform 3D difference</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>geometry <function>ST_3DDifference</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom1</parameter></paramdef>
<paramdef><type>geometry</type> <parameter>geom2</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Returns that part of geom1 that is not part of geom2.</para>
<para>Availability: 2.2.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
<refsection>
<title>Examples</title>
<para>3D images were generated using PostGIS <xref linkend="ST_AsX3D" /> and rendering in HTML using <ulink url="http://www.x3dom.org">X3Dom HTML Javascript rendering library</ulink>.</para>
<informaltable>
<tgroup cols="2">
<tbody>
<row>
<entry><para>
<programlisting>SELECT ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(100 90)'),
50, 'quad_segs=2'),0,0,30) AS geom1,
ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(80 80)'),
50, 'quad_segs=1'),0,0,30) AS geom2;
</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_3ddifference01.png" />
</imageobject>
<caption><para>Original 3D geometries overlaid. geom2 is the part that will be removed.</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
<entry><para>
<programlisting>SELECT ST_3DDifference(geom1,geom2)
FROM ( SELECT ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(100 90)'),
50, 'quad_segs=2'),0,0,30) AS geom1,
ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(80 80)'),
50, 'quad_segs=1'),0,0,30) AS geom2 ) As t;</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_3ddifference02.png" />
</imageobject>
<caption><para>What's left after removing geom2</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
</row>
</tbody>
</tgroup>
</informaltable>
</refsection>
<refsection>
<title>See Also</title>
<para>
<xref linkend="ST_Extrude" />,
<xref linkend="ST_AsX3D" />, <xref linkend="ST_3DIntersection" />
<xref linkend="ST_3DUnion" />
</para>
</refsection>
</refentry>
<refentry id="ST_3DUnion">
<refnamediv>
<refname>ST_3DUnion</refname>
<refpurpose>Perform 3D union</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>geometry <function>ST_3DUnion</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom1</parameter></paramdef>
<paramdef><type>geometry</type> <parameter>geom2</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Availability: 2.2.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
<refsection>
<title>Examples</title>
<para>3D images were generated using PostGIS <xref linkend="ST_AsX3D" /> and rendering in HTML using <ulink url="http://www.x3dom.org">X3Dom HTML Javascript rendering library</ulink>.</para>
<informaltable>
<tgroup cols="2">
<tbody>
<row>
<entry><para>
<programlisting>SELECT ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(100 90)'),
50, 'quad_segs=2'),0,0,30) AS geom1,
ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(80 80)'),
50, 'quad_segs=1'),0,0,30) AS geom2;
</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_3ddifference01.png" />
</imageobject>
<caption><para>Original 3D geometries overlaid. geom2 is the one with transparency.</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
<entry><para>
<programlisting>SELECT ST_3DUnion(geom1,geom2)
FROM ( SELECT ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(100 90)'),
50, 'quad_segs=2'),0,0,30) AS geom1,
ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(80 80)'),
50, 'quad_segs=1'),0,0,30) AS geom2 ) As t;</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_3dunion01.png" />
</imageobject>
<caption><para>Union of geom1 and geom2</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
</row>
</tbody>
</tgroup>
</informaltable>
</refsection>
<refsection>
<title>See Also</title>
<para>
<xref linkend="ST_Extrude" />,
<xref linkend="ST_AsX3D" />, <xref linkend="ST_3DIntersection" />
<xref linkend="ST_3DDifference" />
</para>
</refsection>
</refentry>
<refentry id="ST_3DArea">
<refnamediv>
<refname>ST_3DArea</refname>
<refpurpose>Computes area of 3D surface geometries. Will return 0 for solids.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>float<function>ST_3DArea</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom1</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Availability: 2.1.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
<refsection><title>Examples</title>
<para>Note: By default a PolyhedralSurface built from WKT is a surface geometry, not solid. It therefore has surface area. Once converted to a solid, no area.</para>
<programlisting>SELECT ST_3DArea(geom) As cube_surface_area,
ST_3DArea(ST_MakeSolid(geom)) As solid_surface_area
FROM (SELECT 'POLYHEDRALSURFACE( ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)),
((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)),
((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)),
((1 1 0, 1 1 1, 1 0 1, 1 0 0, 1 1 0)),
((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0)),
((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)) )'::geometry) As f(geom);
cube_surface_area | solid_surface_area
-------------------+--------------------
6 | 0 </programlisting>
</refsection>
<refsection>
<title>See Also</title>
<para><xref linkend="ST_Area" />, <xref linkend="ST_MakeSolid" />, <xref linkend="ST_IsSolid" />, <xref linkend="ST_Area" /></para>
</refsection>
</refentry>
<refentry id="ST_Tesselate">
<refnamediv>
<refname>ST_Tesselate</refname>
<refpurpose>Perform surface Tesselation of a polygon or polyhedralsurface and returns as a TIN or collection of TINS</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>geometry <function>ST_Tesselate</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Takes as input a surface such a MULTI(POLYGON) or POLYHEDRALSURFACE and returns a TIN representation via the process of tesselation using triangles.</para>
<para>Availability: 2.1.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
<refsection><title>Examples</title>
<informaltable>
<tgroup cols="2">
<tbody>
<row>
<entry><para>
<programlisting>SELECT ST_GeomFromText('POLYHEDRALSURFACE Z( ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)),
((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)), ((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)),
((1 1 0, 1 1 1, 1 0 1, 1 0 0, 1 1 0)),
((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0)), ((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)) )');</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_tesselate01.png" />
</imageobject>
<caption><para>Original Cube</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
<entry><para>
<programlisting>SELECT ST_Tesselate(ST_GeomFromText('POLYHEDRALSURFACE Z( ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)),
((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)), ((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)),
((1 1 0, 1 1 1, 1 0 1, 1 0 0, 1 1 0)),
((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0)), ((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)) )'));</programlisting></para>
<para>ST_AsText output:</para>
<screen>TIN Z (((0 0 0,0 0 1,0 1 1,0 0 0)),((0 1 0,0 0 0,0 1 1,0 1 0)),
((0 0 0,0 1 0,1 1 0,0 0 0)),
((1 0 0,0 0 0,1 1 0,1 0 0)),((0 0 1,1 0 0,1 0 1,0 0 1)),
((0 0 1,0 0 0,1 0 0,0 0 1)),
((1 1 0,1 1 1,1 0 1,1 1 0)),((1 0 0,1 1 0,1 0 1,1 0 0)),
((0 1 0,0 1 1,1 1 1,0 1 0)),((1 1 0,0 1 0,1 1 1,1 1 0)),
((0 1 1,1 0 1,1 1 1,0 1 1)),((0 1 1,0 0 1,1 0 1,0 1 1)))</screen>
<para> <informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_tesselate02.png" />
</imageobject>
<caption><para>Tesselated Cube with triangles colored</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
</row>
<row>
<entry><para>
<programlisting>SELECT 'POLYGON (( 10 190, 10 70, 80 70, 80 130, 50 160, 120 160, 120 190, 10 190 ))'::geometry;</programlisting>
<informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_tesselate03.png" />
</imageobject>
<caption><para>Original polygon</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
<entry><para>
<programlisting>SELECT
ST_Tesselate('POLYGON (( 10 190, 10 70, 80 70, 80 130, 50 160, 120 160, 120 190, 10 190 ))'::geometry);</programlisting>
</para>
<para>ST_AsText output</para>
<screen>TIN(((80 130,50 160,80 70,80 130)),((50 160,10 190,10 70,50 160)),
((80 70,50 160,10 70,80 70)),((120 160,120 190,50 160,120 160)),
((120 190,10 190,50 160,120 190)))</screen>
<para><informalfigure>
<mediaobject>
<imageobject>
<imagedata fileref="images/st_tesselate04.png" />
</imageobject>
<caption><para>Tesselated Polygon</para></caption>
</mediaobject>
</informalfigure></para>
</entry>
</row>
</tbody>
</tgroup>
</informaltable>
</refsection>
</refentry>
<refentry id="ST_Volume">
<refnamediv>
<refname>ST_Volume</refname>
<refpurpose>Computes the volume of a 3D solid. If applied to surface (even closed) geometries will return 0.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>float <function>ST_Volume</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom1</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Availability: 2.2.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
<refsection>
<title>Example</title>
<para>When closed surfaces are created with WKT, they are treated as areal rather than solid. To make them solid, you need to use <xref linkend="ST_MakeSolid" />.
Areal geometries have no volume. Here is an example to demonstrate.</para>
<programlisting>SELECT ST_Volume(geom) As cube_surface_vol,
ST_Volume(ST_MakeSolid(geom)) As solid_surface_vol
FROM (SELECT 'POLYHEDRALSURFACE( ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)),
((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)),
((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)),
((1 1 0, 1 1 1, 1 0 1, 1 0 0, 1 1 0)),
((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0)),
((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)) )'::geometry) As f(geom);
cube_surface_vol | solid_surface_vol
------------------+-------------------
0 | 1
</programlisting>
</refsection>
<refsection>
<title>See Also</title>
<para><xref linkend="ST_3DArea" />, <xref linkend="ST_MakeSolid" />, <xref linkend="ST_IsSolid" /></para>
</refsection>
</refentry>
<refentry id="ST_MakeSolid">
<refnamediv>
<refname>ST_MakeSolid</refname>
<refpurpose>Cast the geometry into a solid. No check is performed. To obtain a valid solid, the input geometry must be a closed Polyhedral Surface or a closed TIN.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>geometry<function>ST_MakeSolid</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom1</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Availability: 2.2.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
</refentry>
<refentry id="ST_IsSolid">
<refnamediv>
<refname>ST_IsSolid</refname>
<refpurpose>Test if the geometry is a solid. No validity check is performed.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<funcsynopsis>
<funcprototype>
<funcdef>boolean<function>ST_IsSolid</function></funcdef>
<paramdef><type>geometry</type> <parameter>geom1</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
<refsection>
<title>Description</title>
<para>Availability: 2.2.0</para>
<para>&sfcgal_required;</para>
<para>&Z_support;</para>
<para>&P_support;</para>
<para>&T_support;</para>
</refsection>
</refentry>
</sect1>
|
