PostgreSQL 空間st_contains,st_within空間包含搜索優化 - 降IO和降CPU(bound box)
標簽
PostgreSQL , st_contains , st_within , 空間包含 , 空間bound box , GiST索引 , 空間索引結構 , IO放大 , BOUND BOX放大
背景
點麵判斷、按麵圈選點或其他對象,是GIS幾何應用中非常典型的需求。
在PostgreSQL中通過建立GiST索引可以加速這類判斷,然而,建立索引就夠了嗎?
很多時候建立索引是不夠的,性能沒有到達巔峰,如果要更低的延遲,更少的CPU開銷,還有什麼優化手段呢?
實際上我以前寫過一篇類似的文章,講的是BTree索引訪問的優化,當數據存放與索引順序的線性相關性很差時,引入了一個問題,訪問時IO放大:
原理和解決辦法上麵的文檔已經講得很清楚了。對於空間索引也有類似的問題和優化方法。但是首先你需要了解空間索引的構造:
然後你可以通過空間聚集,來降低空間掃描的IO。
下麵以一個搜索為例,講解空間包含搜索的優化方法:
在表中有1000萬空間對象數據,查詢某個多邊形覆蓋到的空間對象。這個查詢有一個特點,這個多邊形是一個長條條的多邊形,包含這個多邊形的BOUND BOX是比較大的。
構建這個多邊形的方法
postgres=# select st_setsrid(st_makepolygon(ST_GeomFromText('LINESTRING(0 0,1 0,1 2.5,6 2.5,6 4,7 4,7 5,5 5,5 3,0 3,0 0)')), 4326);
st_setsrid
----------------------------
0103000020E6100000010000000B00000000000000000000000000000000000000000000000000F03F0000000000000000000000000000F03F000000000000044000000000000018400000000000000440000000000000184000000000000010400000000000001C4000000000000010400000000000001C40000000000000144000000000000014400000000000001440000000000000144000000000000008400000000000000000000000000000084000000000000000000000000000000000
(1 row)
優化手段1 - 空間聚集
1、建表
postgres=# create table e(id int8, pos geometry);
CREATE TABLE
2、寫入空間測試數據(1000萬個隨機點,覆蓋 +-50 的經緯度區間)
postgres=# insert into e select id, st_setsrid(st_makepoint(50-random()*100, 50-random()*100), 4326) from generate_series(1,10000000) t(id);
INSERT 0 10000000
3、創建空間索引
postgres=# create index idx_e on e using gist(pos);
CREATE INDEX
4、查詢滿足這個多邊形的BOUND BOX覆蓋的對象的BOUND BOX條件的對象。
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from e where pos @ st_setsrid(st_makepolygon(ST_GeomFromText('LINESTRING(0 0,1 0,1 2.5,6 2.5,6 4,7 4,7 5,5 5,5 3,0 3,0 0)')), 4326);
QUERY PLAN
-----------------------
Index Scan using idx_e on public.e (cost=0.42..12526.72 rows=10000 width=40) (actual time=0.091..39.449 rows=35081 loops=1)
Output: id, pos
Index Cond: (e.pos @ '0103000020E6100000010000000B00000000000000000000000000000000000000000000000000F03F0000000000000000000000000000F03F000000000000044000000000000018400000000000000440000000000000184000000000000010400000000000001C4000000000000010400000000000001C40000000000000144000000000000014400000000000001440000000000000144000000000000008400000000000000000000000000000084000000000000000000000000000000000'::geometry)
Buffers: shared hit=35323
Planning time: 0.108 ms
Execution time: 41.222 ms
(6 rows)
搜索了35323個數據塊,返回了35081條記錄。
5、查詢被這個多邊形包含的對象。
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from e where st_contains(st_setsrid(st_makepolygon(ST_GeomFromText('LINESTRING(0 0,1 0,1 2.5,6 2.5,6 4,7 4,7 5,5 5,5 3,0 3,0 0)')), 4326), pos);
QUERY PLAN
-----------------------
Index Scan using idx_e on public.e (cost=0.42..15026.72 rows=3333 width=40) (actual time=0.077..49.015 rows=8491 loops=1)
Output: id, pos
Index Cond: ('0103000020E6100000010000000B00000000000000000000000000000000000000000000000000F03F0000000000000000000000000000F03F000000000000044000000000000018400000000000000440000000000000184000000000000010400000000000001C4000000000000010400000000000001C40000000000000144000000000000014400000000000001440000000000000144000000000000008400000000000000000000000000000084000000000000000000000000000000000'::geometry ~ e.pos)
Filter: _st_contains('0103000020E6100000010000000B00000000000000000000000000000000000000000000000000F03F0000000000000000000000000000F03F000000000000044000000000000018400000000000000440000000000000184000000000000010400000000000001C4000000000000010400000000000001C40000000000000144000000000000014400000000000001440000000000000144000000000000008400000000000000000000000000000084000000000000000000000000000000000'::geometry, e.pos)
Rows Removed by Filter: 26590
Buffers: shared hit=35323
Planning time: 0.085 ms
Execution time: 49.460 ms
(8 rows)
搜索了35323個數據塊,搜索了35081條記錄,返回了8491條記錄,過濾了26590條不滿足條件的記錄。
5和4的查詢差異是BOUND BOX包含、實際的輪廓包含。索引的基礎是bound box。在以下文檔中我們也可以學習到這個原理。
我們看到,複合條件的記錄並不多,但是搜索了很多數據塊,通過空間聚集可以減少數據塊的掃描。
6、創建另一張表,按空間聚集,調整數據存儲順序。並建立空間索引。
postgres=# create table f(like e);
CREATE TABLE
postgres=# insert into f select * from e order by st_geohash(pos,15);
INSERT 0 10000000
postgres=# create index idx_f on f using gist(pos);
CREATE INDEX
7、優化後:
查詢滿足這個多邊形的BOUND BOX覆蓋的對象的BOUND BOX條件的對象。從掃描35323個數據塊降低到了訪問1648個數據塊。質的飛躍。
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from f where pos @ st_setsrid(st_makepolygon(ST_GeomFromText('LINESTRING(0 0,1 0,1 2.5,6 2.5,6 4,7 4,7 5,5 5,5 3,0 3,0 0)')), 4326);
QUERY PLAN
-----------------------
Index Scan using idx_f on public.f (cost=0.42..12526.72 rows=10000 width=40) (actual time=0.081..9.702 rows=35081 loops=1)
Output: id, pos
Index Cond: (f.pos @ '0103000020E6100000010000000B00000000000000000000000000000000000000000000000000F03F0000000000000000000000000000F03F000000000000044000000000000018400000000000000440000000000000184000000000000010400000000000001C4000000000000010400000000000001C40000000000000144000000000000014400000000000001440000000000000144000000000000008400000000000000000000000000000084000000000000000000000000000000000'::geometry)
Buffers: shared hit=1648
Planning time: 0.096 ms
Execution time: 11.404 ms
(6 rows)
8、優化後:
查詢被這個多邊形包含的對象。從掃描35323個數據塊降低到了訪問1648個數據塊。質的飛躍。
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from f where st_contains(st_setsrid(st_makepolygon(ST_GeomFromText('LINESTRING(0 0,1 0,1 2.5,6 2.5,6 4,7 4,7 5,5 5,5 3,0 3,0 0)')), 4326), pos);
QUERY PLAN
-----------------------
Index Scan using idx_f on public.f (cost=0.42..15026.72 rows=3333 width=40) (actual time=1.216..32.398 rows=8491 loops=1)
Output: id, pos
Index Cond: ('0103000020E6100000010000000B00000000000000000000000000000000000000000000000000F03F0000000000000000000000000000F03F000000000000044000000000000018400000000000000440000000000000184000000000000010400000000000001C4000000000000010400000000000001C40000000000000144000000000000014400000000000001440000000000000144000000000000008400000000000000000000000000000084000000000000000000000000000000000'::geometry ~ f.pos)
Filter: _st_contains('0103000020E6100000010000000B00000000000000000000000000000000000000000000000000F03F0000000000000000000000000000F03F000000000000044000000000000018400000000000000440000000000000184000000000000010400000000000001C4000000000000010400000000000001C40000000000000144000000000000014400000000000001440000000000000144000000000000008400000000000000000000000000000084000000000000000000000000000000000'::geometry, f.pos)
Rows Removed by Filter: 26590
Buffers: shared hit=1648
Planning time: 0.101 ms
Execution time: 32.837 ms
(8 rows)
使用空間聚集,從掃描35323個數據塊降低到了訪問1648個數據塊。質的飛躍。
優化手段2 - 空間分裂查詢
空間聚集的優化手段,解決了IO放大的問題,另一個優化點和空間索引的結構有關,是BOUND BOX放大的問題。
從本文的例子中,我們也看到了,空間索引實際上是針對bound box的,所以在有效麵積占比較低時,可能圈選到多數無效數據,導致IO和CPU同時放大,我們就來解決它。
下圖虛線部分包含的區間就是這個長條條的BOUND BOX。目前數據庫在使用GiST索引查詢滿足這個多邊形包含的POS的條件時,會將落在這個BOUND BOX中的對象都弄出來。
優化思路:
將這個多邊形,拆成4個BOX,完全杜絕bound box放大的問題。
explain (analyze,verbose,timing,costs,buffers) select * from f where
st_contains(st_setsrid(st_makebox2d(st_makepoint(0,0), st_makepoint(1,3)), 4326), pos)
or
st_contains(st_setsrid(st_makebox2d(st_makepoint(1,2.5), st_makepoint(5,3)), 4326), pos)
or
st_contains(st_setsrid(st_makebox2d(st_makepoint(5,2.5), st_makepoint(6,5)), 4326), pos)
or
st_contains(st_setsrid(st_makebox2d(st_makepoint(6,4), st_makepoint(7,5)), 4326), pos);
explain (analyze,verbose,timing,costs,buffers) select * from f where
pos @ st_setsrid(st_makebox2d(st_makepoint(0,0), st_makepoint(1,3)), 4326)
or
pos @ st_setsrid(st_makebox2d(st_makepoint(1,2.5), st_makepoint(5,3)), 4326)
or
pos @ st_setsrid(st_makebox2d(st_makepoint(5,2.5), st_makepoint(6,5)), 4326)
or
pos @ st_setsrid(st_makebox2d(st_makepoint(6,4), st_makepoint(7,5)), 4326);
1、組合1和2的優化手段後:
查詢滿足這個多邊形的BOUND BOX覆蓋的對象的BOUND BOX條件的對象。從掃描1648個數據塊降低到了訪問243個數據塊。質的飛躍。
explain (analyze,verbose,timing,costs,buffers) select * from f where
pos @ st_setsrid(st_makebox2d(st_makepoint(0,0), st_makepoint(1,3)), 4326)
or
pos @ st_setsrid(st_makebox2d(st_makepoint(1,2.5), st_makepoint(5,3)), 4326)
or
pos @ st_setsrid(st_makebox2d(st_makepoint(5,2.5), st_makepoint(6,5)), 4326)
or
pos @ st_setsrid(st_makebox2d(st_makepoint(6,4), st_makepoint(7,5)), 4326);
QUERY PLAN
-----------------------
Bitmap Heap Scan on public.f (cost=10000000690.01..10000037405.46 rows=39940 width=40) (actual time=1.502..2.329 rows=8491 loops=1)
Output: id, pos
Recheck Cond: ((f.pos @ '0103000020E610000001000000050000000000000000000000000000000000000000000000000000000000000000000840000000000000F03F0000000000000840000000000000F03F000000000000000000000000000000000000000000000000'::geometry) OR (f.pos @ '0103000020E61000000100000005000000000000000000F03F0000000000000440000000000000F03F00000000000008400000000000001440000000000000084000000000000014400000000000000440000000000000F03F0000000000000440'::geometry) OR (f.pos @ '0103000020E610000001000000050000000000000000001440000000000000044000000000000014400000000000001440000000000000184000000000000014400000000000001840000000000000044000000000000014400000000000000440'::geometry) OR (f.pos @ '0103000020E6100000010000000500000000000000000018400000000000001040000000000000184000000000000014400000000000001C4000000000000014400000000000001C40000000000000104000000000000018400000000000001040'::geometry))
Heap Blocks: exact=119
Buffers: shared hit=243
-> BitmapOr (cost=690.01..690.01 rows=40000 width=0) (actual time=1.483..1.483 rows=0 loops=1)
Buffers: shared hit=124
-> Bitmap Index Scan on idx_f (cost=0.00..162.52 rows=10000 width=0) (actual time=0.461..0.461 rows=3077 loops=1)
Index Cond: (f.pos @ '0103000020E610000001000000050000000000000000000000000000000000000000000000000000000000000000000840000000000000F03F0000000000000840000000000000F03F000000000000000000000000000000000000000000000000'::geometry)
Buffers: shared hit=37
-> Bitmap Index Scan on idx_f (cost=0.00..162.52 rows=10000 width=0) (actual time=0.423..0.423 rows=1991 loops=1)
Index Cond: (f.pos @ '0103000020E61000000100000005000000000000000000F03F0000000000000440000000000000F03F00000000000008400000000000001440000000000000084000000000000014400000000000000440000000000000F03F0000000000000440'::geometry)
Buffers: shared hit=33
-> Bitmap Index Scan on idx_f (cost=0.00..162.52 rows=10000 width=0) (actual time=0.366..0.366 rows=2435 loops=1)
Index Cond: (f.pos @ '0103000020E610000001000000050000000000000000001440000000000000044000000000000014400000000000001440000000000000184000000000000014400000000000001840000000000000044000000000000014400000000000000440'::geometry)
Buffers: shared hit=31
-> Bitmap Index Scan on idx_f (cost=0.00..162.52 rows=10000 width=0) (actual time=0.232..0.232 rows=988 loops=1)
Index Cond: (f.pos @ '0103000020E6100000010000000500000000000000000018400000000000001040000000000000184000000000000014400000000000001C4000000000000014400000000000001C40000000000000104000000000000018400000000000001040'::geometry)
Buffers: shared hit=23
Planning time: 0.104 ms
Execution time: 2.751 ms
(21 rows)
2、組合1和2的優化手段後:
查詢被這個多邊形包含的對象。從掃描1648個數據塊降低到了訪問243個數據塊。質的飛躍。
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from f where
st_contains(st_setsrid(st_makebox2d(st_makepoint(0,0), st_makepoint(1,3)), 4326), pos)
or
st_contains(st_setsrid(st_makebox2d(st_makepoint(1,2.5), st_makepoint(5,3)), 4326), pos)
or
st_contains(st_setsrid(st_makebox2d(st_makepoint(5,2.5), st_makepoint(6,5)), 4326), pos)
or
st_contains(st_setsrid(st_makebox2d(st_makepoint(6,4), st_makepoint(7,5)), 4326), pos);
QUERY PLAN
--------------------------------------------
Bitmap Heap Scan on public.f (cost=663.40..77378.85 rows=13327 width=40) (actual time=1.496..11.038 rows=8491 loops=1)
Output: id, pos
Recheck Cond: (('0103000020E610000001000000050000000000000000000000000000000000000000000000000000000000000000000840000000000000F03F0000000000000840000000000000F03F000000000000000000000000000000000000000000000000'::geometry ~ f.pos) OR
('0103000020E61000000100000005000000000000000000F03F0000000000000440000000000000F03F00000000000008400000000000001440000000000000084000000000000014400000000000000440000000000000F03F0000000000000440'::geometry ~ f.pos) OR ('0103000020E610000001000000050000000000000000001440000000000000044000000000000014400000000000001440000000000000184000000000000014400000000000001840000000000000044000000000000014400000000000000440'::geometry ~ f.pos) OR ('0103000020E6100000010000000500000000000000000018400000000000001040000000000000184000000000000014400000000000001C4000000000000014400000000000001C40000000000000104000000000000018400000000000001040'::geometry ~ f.pos))
Filter: ((('0103000020E610000001000000050000000000000000000000000000000000000000000000000000000000000000000840000000000000F03F0000000000000840000000000000F03F000000000000000000000000000000000000000000000000'::geometry ~ f.pos) AND _st_contains('0103000020E610000001000000050000000000000000000000000000000000000000000000000000000000000000000840000000000000F03F0000000000000840000000000000F03F000000000000000000000000000000000000000000000000'::geometry, f.pos)) OR (('0103000020E61000000100000005000000000000000000F03F0000000000000440000000000000F03F00000000000008400000000000001440000000000000084000000000000014400000000000000440000000000000F03F0000000000000440'::geometry ~ f.pos) AND _st_contains('0103000020E61000000100000005000000000000000000F03F0000000000000440000000000000F03F00000000000008400000000000001440000000000000084000000000000014400000000000000440000000000000F03F0000000000000440'::geometry, f.pos)) OR (('0103000020E610000001000000050000000000000000001440000000000000044000000000000014400000000000001440000000000000184000000000000014400000000000001840000000000000044000000000000014400000000000000440'::geometry ~ f.pos) AND _st_contains('0103000020E610000001000000050000000000000000001440000000000000044000000000000014400000000000001440000000000000184000000000000014400000000000001840000000000000044000000000000014400000000000000440'::geometry, f.pos)) OR (('0103000020E6100000010000000500000000000000000018400000000000001040000000000000184000000000000014400000000000001C4000000000000014400000000000001C40000000000000104000000000000018400000000000001040'::geometry ~ f.pos) AND _st_contains('0103000020E6100000010000000500000000000000000018400000000000001040000000000000184000000000000014400000000000001C4000000000000014400000000000001C40000000000000104000000000000018400000000000001040'::geometry, f.pos)))
Heap Blocks: exact=119
Buffers: shared hit=243
-> BitmapOr (cost=663.40..663.40 rows=40000 width=0) (actual time=1.472..1.472 rows=0 loops=1)
Buffers: shared hit=124
-> Bitmap Index Scan on idx_f (cost=0.00..162.52 rows=10000 width=0) (actual time=0.436..0.436 rows=3077 loops=1)
Index Cond: ('0103000020E610000001000000050000000000000000000000000000000000000000000000000000000000000000000840000000000000F03F0000000000000840000000000000F03F000000000000000000000000000000000000000000000000'::geometry ~ f.pos)
Buffers: shared hit=37
-> Bitmap Index Scan on idx_f (cost=0.00..162.52 rows=10000 width=0) (actual time=0.438..0.438 rows=1991 loops=1)
Index Cond: ('0103000020E61000000100000005000000000000000000F03F0000000000000440000000000000F03F00000000000008400000000000001440000000000000084000000000000014400000000000000440000000000000F03F0000000000000440'::geometry ~ f.pos)
Buffers: shared hit=33
-> Bitmap Index Scan on idx_f (cost=0.00..162.52 rows=10000 width=0) (actual time=0.365..0.365 rows=2435 loops=1)
Index Cond: ('0103000020E610000001000000050000000000000000001440000000000000044000000000000014400000000000001440000000000000184000000000000014400000000000001840000000000000044000000000000014400000000000000440'::geometry ~ f.pos)
Buffers: shared hit=31
-> Bitmap Index Scan on idx_f (cost=0.00..162.52 rows=10000 width=0) (actual time=0.234..0.234 rows=988 loops=1)
Index Cond: ('0103000020E6100000010000000500000000000000000018400000000000001040000000000000184000000000000014400000000000001C4000000000000014400000000000001C40000000000000104000000000000018400000000000001040'::geometry ~ f.pos)
Buffers: shared hit=23
Planning time: 0.163 ms
Execution time: 11.497 ms
(22 rows)
優化手段2,將長條條的polygon拆分成多個小的box,將大的bound box消除,搜索的BLOCK再次降低到243。質的飛躍。
將兩個手段合並起來用,起到了雙劍合璧的效果。
st_split 切分對象
PostGIS提供了切分對象的方法。
https://postgis.net/docs/manual-2.4/ST_Split.html
-- this creates a geometry collection consisting of the 2 halves of the polygon
-- this is similar to the example we demonstrated in ST_BuildArea
SELECT ST_Split(circle, line)
FROM (SELECT
ST_MakeLine(ST_MakePoint(10, 10),ST_MakePoint(190, 190)) As line,
ST_Buffer(ST_GeomFromText('POINT(100 90)'), 50) As circle) As foo;
-- result --
GEOMETRYCOLLECTION(POLYGON((150 90,149.039264020162 80.2454838991936,146.193976625564 70.8658283817455,...), POLYGON(...)))
-- To convert to individual polygons, you can use ST_Dump or ST_GeometryN
SELECT ST_AsText((ST_Dump(ST_Split(circle, line))).geom) As wkt
FROM (SELECT
ST_MakeLine(ST_MakePoint(10, 10),ST_MakePoint(190, 190)) As line,
ST_Buffer(ST_GeomFromText('POINT(100 90)'), 50) As circle) As foo;
-- result --
wkt
---------------
POLYGON((150 90,149.039264020162 80.2454838991936,...))
POLYGON((60.1371179574584 60.1371179574584,58.4265193848728 62.2214883490198,53.8060233744357 ...))
SELECT ST_AsText(ST_Split(mline, pt)) As wktcut
FROM (SELECT
ST_GeomFromText('MULTILINESTRING((10 10, 190 190), (15 15, 30 30, 100 90))') As mline,
ST_Point(30,30) As pt) As foo;
wktcut
------
GEOMETRYCOLLECTION(
LINESTRING(10 10,30 30),
LINESTRING(30 30,190 190),
LINESTRING(15 15,30 30),
LINESTRING(30 30,100 90)
)
我後麵寫了一篇文檔來簡化SPLIT:
《PostgreSQL 空間切割(st_split)功能擴展 - 空間對象網格化》
st_snap
https://postgis.net/docs/manual-2.4/ST_Snap.html
@, ~ 與 ST_Contains, ST_Within的區別
@, ~ 與 ST_Contains, ST_Within
都是對象包含的操作符或函數,他們有什麼區別呢?
@
A @ B
Returns TRUE if A's bounding box is contained by B's.
~
與 @
含義相反。
A ~ B
Returns TRUE if A's bounding box contains B's.
ST_Contains
ST_Contains(A, B)
Returns true if and only if no points of B lie in the exterior of A, and at least one point of the interior of B lies in the interior of A.
ST_Within
與 ST_Contains
含義相反。
ST_Within(A, B)
Returns true if the geometry A is completely inside geometry B
區別
@ 和 ~的操作並不是直接針對幾何對象,而是針對A和B的bound box的,也就是說包含對象的左下和右上的點組成的BOX。
ST_Within和ST_Contains是針對幾何對象的,但是從GiST索引搜索角度來看,是需要先用BOUND BOX去搜索,再通過CPU進行計算來判斷的。
例子
A @ Polygon,返回真
B @ Polygon,返回真
C @ Polygon,返回真
ST_Contains(Polygon, A),返回假
ST_Contains(Polygon, B),返回真
ST_Contains(Polygon, C),返回假
小結
空間搜索的兩個可以優化的點,原理如下:
1、空間數據在存儲時亂序存放,導致搜索一批數據時掃描的數據塊很多。(點查感覺不到這個問題。)
2、PostGIS的GiST空間索引,采用了BOUND BOX作為KEY,搜索時也是使用對象的BOUND BOX進行搜索,因此當對象是長條條時,可能造成大量的BOUND BOX空洞,放大了掃描範圍(對st_contains, st_within來說),增加了CPU過濾的開銷。
優化手段1:空間聚集,解決IO放大問題。
優化手段2:對輸入條件(長條條的多邊形)進行SPLIT,降低BOUND BOX放大引入的掃描範圍(對st_contains, st_within來說)放大的問題。
數據量:1000萬。
點麵判斷(長條形多邊形,或者離散多個多邊形對象覆蓋的空間對象)。
優化前 | 優化1(空間聚集) | 優化1,2(SPLIT多邊形) |
---|---|---|
訪問35323塊 | 訪問1648塊 | 訪問243塊 |
過濾26590條 | 過濾26590條 | 過濾0條 |
參考
《Greenplum 空間(GIS)數據檢索 b-tree & GiST 索引實踐 - 阿裏雲HybridDB for PostgreSQL最佳實踐》
《PostGIS空間索引(GiST、BRIN、R-Tree)選擇、優化 - 阿裏雲RDS PostgreSQL最佳實踐》
《PostgreSQL 空間切割(st_split)功能擴展 - 空間對象網格化》
https://postgis.net/docs/manual-2.4/ST_Within.html
https://postgis.net/docs/manual-2.4/ST_Contains.html
https://postgis.net/docs/manual-2.4/ST_Geometry_Contained.html
https://postgis.net/docs/manual-2.4/ST_Geometry_Contain.html
https://postgis.net/docs/manual-2.4/ST_Split.html
https://postgis.net/docs/manual-2.4/ST_Snap.html
最後更新:2017-10-28 23:04:19