背景

假设我们有一些物体的轨迹数据（经纬度、measure(通常存为epoch时间戳)），比如车辆、人、传感器等。

给定一个物体在某个时间范围的轨迹数据，查找有没有与这个物体接触的轨迹，并按亲密度排序。

http://postgis.net/docs/manual-2.4/geometry_distance_cpa.html

需求：

1、判断两个轨迹是否有亲密接触的可能。

2、如果有亲密接触的可能，那么是在什么时间点（measure）发生的。

3、如果有亲密接触的可能，那么他们接触的距离有多近。

4、如果有亲密接触的可能，那么他们最近距离接触的点是哪个。

使用PostGIS，可以满足相应的需求。

http://postgis.net/docs/manual-2.4/reference.html

  1. 8.13. Temporal Support  
  3. ST_IsValidTrajectory — Returns true if the geometry is a valid trajectory.  
  5. ST_ClosestPointOfApproach — Returns the measure at which points interpolated along two lines are closest.  
  7. ST_DistanceCPA — Returns the distance between closest points of approach in two trajectories.  
  9. ST_CPAWithin — Returns true if the trajectories' closest points of approach are within the specified distance.

时态分析可以做很多事情，比如地下活动。

1、轨迹格式

轨迹为带有measure的linestring，包括：经纬度(支持Z轴，3D坐标)、measure(递增)。

通常使用时间戳epoch来存储measure的内容。

例如：

  1. postgres=# select extract(epoch from now());  
  2.     date_part       
  3. ------------------  
  4.  1528347341.02161  
  5. (1 row)  
  7. postgres=# select extract(epoch from now());  
  8.     date_part       
  9. ------------------  
  10.  1528347342.99521  
  11. (1 row)  
  13. postgres=# select ST_MakeLine(ST_MakePointM(-350,300,1528347341),ST_MakePointM(-410,490,1528347342));  
  14.                                                     st_makeline                                                       
  15. --------------------------------------------------------------------------------------------------------------------  
  16.  0102000040020000000000000000E075C00000000000C07240000040B32EC6D6410000000000A079C00000000000A07E40000080B32EC6D641  
  17. (1 row)  
  19. postgres=# select st_astext(ST_MakeLine(ST_MakePointM(-350,300,1528347341),ST_MakePointM(-410,490,1528347342)));  
  20.                        st_astext                          
  21. --------------------------------------------------------  
  22.  LINESTRING M (-350 300 1528347341,-410 490 1528347342)  
  23. (1 row)

2、计算两个轨迹是否有近距离接触

指定距离阈值，判断两个轨迹是否有近距离接触。

http://postgis.net/docs/manual-2.4/ST_CPAWithin.html

Name

  1. ST_CPAWithin — Returns true if the trajectories' closest points of approach are within the specified distance.

Synopsis

  1. float8 ST_CPAWithin(geometry track1, geometry track2, float8 maxdist);

例子

  1. WITH inp AS ( SELECT  
  2.   ST_AddMeasure('LINESTRING Z (0 0 0, 10 0 5)'::geometry,  
  3.     extract(epoch from '2015-05-26 10:00'::timestamptz),  
  4.     extract(epoch from '2015-05-26 11:00'::timestamptz)  
  5.   ) a,  
  6.   ST_AddMeasure('LINESTRING Z (0 2 10, 12 1 2)'::geometry,  
  7.     extract(epoch from '2015-05-26 10:00'::timestamptz),  
  8.     extract(epoch from '2015-05-26 11:00'::timestamptz)  
  9.   ) b  
  10. )  
  11. SELECT ST_CPAWithin(a,b,2), ST_DistanceCPA(a,b) distance FROM inp;  
  13.  st_cpawithin |     distance  
  14. --------------+------------------  
  15.  t            | 1.96521473776207

3、计算两个轨迹近距离接触的MEASURE(时间戳)

http://postgis.net/docs/manual-2.4/ST_ClosestPointOfApproach.html

Name

  1. ST_ClosestPointOfApproach — Returns the measure at which points interpolated along two lines are closest.

Synopsis

  1. float8 ST_ClosestPointOfApproach(geometry track1, geometry track2);

例子

  1. -- Return the time in which two objects moving between 10:00 and 11:00  
  2. -- are closest to each other and their distance at that point  
  3. WITH inp AS ( SELECT  
  4.   ST_AddMeasure('LINESTRING Z (0 0 0, 10 0 5)'::geometry,  
  5.     extract(epoch from '2015-05-26 10:00'::timestamptz),  
  6.     extract(epoch from '2015-05-26 11:00'::timestamptz)  
  7.   ) a,  
  8.   ST_AddMeasure('LINESTRING Z (0 2 10, 12 1 2)'::geometry,  
  9.     extract(epoch from '2015-05-26 10:00'::timestamptz),  
  10.     extract(epoch from '2015-05-26 11:00'::timestamptz)  
  11.   ) b  
  12. ), cpa AS (  
  13.   SELECT ST_ClosestPointOfApproach(a,b) m FROM inp  
  14. ), points AS (  
  15.   SELECT ST_Force3DZ(ST_GeometryN(ST_LocateAlong(a,m),1)) pa,  
  16.          ST_Force3DZ(ST_GeometryN(ST_LocateAlong(b,m),1)) pb  
  17.   FROM inp, cpa  
  18. )  
  19. SELECT to_timestamp(m) t,  
  20.        ST_Distance(pa,pb) distance  
  21. FROM points, cpa;  
  23.                t               |     distance  
  24. -------------------------------+------------------  
  25.  2015-05-26 10:45:31.034483+02 | 1.96036833151395

4、计算两个轨迹近距离接触的位置

http://postgis.net/docs/manual-2.4/ST_LocateAlong.html

Name

  1. ST_LocateAlong — Return a derived geometry collection value with elements that match the specified measure. Polygonal elements are not supported.

Synopsis

  1. geometry ST_LocateAlong(geometry ageom_with_measure, float8 a_measure, float8 offset);

例子1

  1. SELECT ST_AsText(the_geom)  
  2.                 FROM  
  3.                 (SELECT ST_LocateAlong(  
  4.                         ST_GeomFromText('MULTILINESTRINGM((1 2 3, 3 4 2, 9 4 3),  
  5.                 (1 2 3, 5 4 5))'),3) As the_geom) As foo;  
  7.                                                  st_asewkt  
  8. -----------------------------------------------------------  
  9.  MULTIPOINT M (1 2 3)  
  11. --Geometry collections are difficult animals so dump them  
  12. --to make them more digestable  
  13. SELECT ST_AsText((ST_Dump(the_geom)).geom)  
  14.         FROM  
  15.         (SELECT ST_LocateAlong(  
  16.                         ST_GeomFromText('MULTILINESTRINGM((1 2 3, 3 4 2, 9 4 3),  
  17.         (1 2 3, 5 4 5))'),3) As the_geom) As foo;  
  19.    st_asewkt  
  20. ---------------  
  21.  POINTM(1 2 3)  
  22.  POINTM(9 4 3)  
  23.  POINTM(1 2 3)

例子2

  1. postgres=# WITH inp AS ( SELECT  
  2. postgres(#   ST_AddMeasure('LINESTRING Z (0 0 0, 10 0 5)'::geometry,  
  3. postgres(#     extract(epoch from '2015-05-26 10:00'::timestamptz),  
  4. postgres(#     extract(epoch from '2015-05-26 11:00'::timestamptz)  
  5. postgres(#   ) a,  
  6. postgres(#   ST_AddMeasure('LINESTRING Z (0 2 10, 12 1 2)'::geometry,  
  7. postgres(#     extract(epoch from '2015-05-26 10:00'::timestamptz),  
  8. postgres(#     extract(epoch from '2015-05-26 11:00'::timestamptz)  
  9. postgres(#   ) b  
  10. postgres(# ), cpa AS (  
  11. postgres(#   SELECT ST_ClosestPointOfApproach(a,b) m FROM inp  
  12. postgres(# ) select ST_LocateAlong(a, m), ST_LocateAlong(b, m) from inp,cpa;  
  13.                                         st_locatealong                                        |                                        st_locatealong                                          
  14. ----------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------  
  15.  01040000C00100000001010000C03A8EE39E46581E4000000000000000003A8EE39E46580E40F734C292F758D541 | 01040000C00100000001010000C02222222CF7342240E9933E8DB0DCF33FA44FFA34C2720F40F734C292F758D541  
  16. (1 row)  
  18. postgres=# WITH inp AS ( SELECT  
  19.   ST_AddMeasure('LINESTRING Z (0 0 0, 10 0 5)'::geometry,  
  20.     extract(epoch from '2015-05-26 10:00'::timestamptz),  
  21.     extract(epoch from '2015-05-26 11:00'::timestamptz)  
  22.   ) a,  
  23.   ST_AddMeasure('LINESTRING Z (0 2 10, 12 1 2)'::geometry,  
  24.     extract(epoch from '2015-05-26 10:00'::timestamptz),  
  25.     extract(epoch from '2015-05-26 11:00'::timestamptz)  
  26.   ) b  
  27. ), cpa AS (  
  28.   SELECT ST_ClosestPointOfApproach(a,b) m FROM inp  
  29. ) select st_astext(ST_LocateAlong(a, m)), st_astext(ST_LocateAlong(b, m)) from inp,cpa;  
  30.                               st_astext                               |                                      st_astext                                        
  31. ----------------------------------------------------------------------+-------------------------------------------------------------------------------------  
  32.  MULTIPOINT ZM (7.58620689643754 0 3.79310344821877 1432608331.03448) | MULTIPOINT ZM (9.10344827572505 1.24137931035625 3.93103448284997 1432608331.03448)  
  33. (1 row)

5、计算两个轨迹近距离接触的最近的距离

http://postgis.net/docs/manual-2.4/ST_DistanceCPA.html

Name

  1. ST_DistanceCPA — Returns the distance between closest points of approach in two trajectories.

Synopsis

  1. float8 ST_DistanceCPA(geometry track1, geometry track2);

例子

  1. -- Return the minimum distance of two objects moving between 10:00 and 11:00  
  2. WITH inp AS ( SELECT  
  3.   ST_AddMeasure('LINESTRING Z (0 0 0, 10 0 5)'::geometry,  
  4.     extract(epoch from '2015-05-26 10:00'::timestamptz),  
  5.     extract(epoch from '2015-05-26 11:00'::timestamptz)  
  6.   ) a,  
  7.   ST_AddMeasure('LINESTRING Z (0 2 10, 12 1 2)'::geometry,  
  8.     extract(epoch from '2015-05-26 10:00'::timestamptz),  
  9.     extract(epoch from '2015-05-26 11:00'::timestamptz)  
  10.   ) b  
  11. )  
  12. SELECT ST_DistanceCPA(a,b) distance FROM inp;  
  14.      distance  
  15. ------------------  
  16.  1.96036833151395

6、索引加速

http://postgis.net/docs/manual-2.4/geometry_distance_cpa.html

Name

  1. |=| — Returns the distance between A and B trajectories at their closest point of approach.

Synopsis

  1. double precision |=|( geometry A , geometry B );

Description

  1. The |=| operator returns the 3D distance between two trajectories (See ST_IsValidTrajectory).   
  3. This is the same as ST_DistanceCPA but as an operator it can be used for doing nearest   
  4. neightbor searches using an N-dimensional index   
  6. (requires PostgreSQL 9.5.0 or higher).

例子

  1. -- Save a literal query trajectory in a psql variable...  
  2. \set qt 'ST_AddMeasure(ST_MakeLine(ST_MakePointM(-350,300,0),ST_MakePointM(-410,490,0)),10,20)'  
  3. -- Run the query !  
  4. SELECT track_id, dist FROM (  
  5.   SELECT track_id, ST_DistanceCPA(tr,:qt) dist  
  6.   FROM trajectories  
  7.   ORDER BY tr |=| :qt  
  8.   LIMIT 5  
  9. ) foo;  
  10.  track_id        dist  
  11. ----------+-------------------  
  12.       395 | 0.576496831518066  
  13.       380 |  5.06797130410151  
  14.       390 |  7.72262293958322  
  15.       385 |   9.8004461358071  
  16.       405 |  10.9534397988433  
  17. (5 rows)

压测

1、创建一个生成随机轨迹的函数

  1. create or replace function gen_rand_linestring (  
  2.   seedx float8,    -- 起点x坐标  
  3.   seedy float8,    -- 起点y坐标  
  4.   seedstep float8, -- 运动步调最大值  
  5.   seedts float8,   -- 时间，measure 步调(second 单位)  
  6.   ts1 timestamp,   -- 时间区间最小值  
  7.   ts2 timestamp,   -- 时间区间最大值  
  8.   cnt int          -- 在轨迹中生成几个POINT  
  9. ) returns geometry as $$  
  10. declare  
  11.   ts timestamp := ts1 + ((random()*extract(epoch from (ts2-ts1)))||' sec')::interval;  
  12.   ts_epo float8;  
  13.   geo geometry[];  
  14. begin  
  15.   for i in 1..cnt loop   
  16.     ts_epo := extract(epoch from ts+((i*seedts)||' sec')::interval) ;  
  17.     geo := array_cat(geo, array[st_makepointm(seedx + i*(random()*seedstep), seedy + i*(random()*seedstep), ts_epo)]) ;  
  18.   end loop;   
  19.   return st_makeline(geo);   
  20. end;  
  21. $$ language plpgsql strict stable;

2、例子

  1. postgres=# select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10);  
  2. -[ RECORD 1 ]-------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------  
  3. gen_rand_linestring | 01020000400A0000000000503BA9CB124000004062BCE20940A4E1CEC382C6D6410000C0637DE10B400000C0C50AB82F40A4E1CEE182C6D64100005057B1D511400000C4CBE74C3040A4E1CEFF82C6D6410000C0558CD11C400000C09177B72940A4E1CE1D83C6D64100004067EAE646400000884E67E02C40A4E1CE3B83C6D641000088FAE5AA4240000000AD26AF2740A4E1CE5983C6D64100007CD8F8274F400000B8B89E4D2F40A4E1CE7783C6D641000000823E6B27400000902247B34C40A4E1CE9583C6D6410000D863843C56400000C06676921440A4E1CEB383C6D64100000C90922455400000386AD2743D40A4E1CED183C6D641  
  5. postgres=# select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10);  
  6. -[ RECORD 1 ]-------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------  
  7. gen_rand_linestring |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
  10. postgres=# select st_astext(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10));  
  11. -[ RECORD 1 ]---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------  
  12. st_astext | LINESTRING M (10.2174849007279 11.9571549287066 1528425468.02122,14.630109699443 3.11233511939645 1528425588.02122,21.6466929381713 21.7603580309078 1528425708.02122,4.62157236784697 22.9575021080673 1528425828.02122,47.6620979132131 23.719867666252 1528425948.02122,15.6148129086941 51.1239671874791 1528426068.02122,47.852089674212 18.3603029865772 1528426188.02122,33.4982615187764 36.1437245160341 1528426308.02122,83.4090811889619 7.33796327654272 1528426428.02122,80.737452045083 19.6353993359953 1528426548.02122)  
  14. postgres=# select st_astext(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10));  
  15. -[ RECORD 1 ]-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------  
  16. st_astext | LINESTRING M (3.91523572057486 7.61306651681662 1528390545.99534,16.9645196422935 20.0192420165986 1528390665.99534,13.6881912257522 22.0785792060196 1528390785.99534,32.2743593193591 9.22613327205181 1528390905.99534,40.4555864389986 15.4170794393867 1528391025.99534,7.14410931244493 49.0896332990378 1528391145.99534,67.4892951631919 13.0613004816696 1528391265.99534,38.844025567174 50.6820540204644 1528391385.99534,23.3702098755166 91.7289085481316 1528391505.99534,55.1767633520067 70.295524129644 1528391625.99534)  
  19. postgres=# select st_isvalidtrajectory(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10));  
  20.  st_isvalidtrajectory   
  21. ----------------------  
  22.  t  
  23. (1 row)  
  25. postgres=# select st_isvalidtrajectory(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10));  
  26.  st_isvalidtrajectory   
  27. ----------------------  
  28.  t  
  29. (1 row)  
  31. postgres=# select st_isvalidtrajectory(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10));  
  32.  st_isvalidtrajectory   
  33. ----------------------  
  34.  t  
  35. (1 row)

3、建表

  1. create table tbl_trc(uid int, tc geometry);

4、创建空间索引

  1. create index idx_tbl_trc_1 on tbl_trc using gist (tc);

5、压测

每600秒跟踪60个点。

  1. vi test.sql  
  4. \set uid random(1,100000000)  
  5. \set x random(1,1000)  
  6. \set y random(1,1000)  
  7. insert into tbl_trc values (:uid, gen_rand_linestring(:x,:y,10,600,now()::timestamp,(now()+interval '1 day')::timestamp,60));
  1. pgbench -M prepared -n -r -P 1 -f ./test.sql -c 32 -j 32 -T 1200 -h 127.0.0.1

6、查询测试

  1. with a as (select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10) tc)  
  2. select uid, tbl_trc.tc |=| a.tc, st_astext(tbl_trc.tc), st_astext(a.tc) from tbl_trc,a where ST_CPAWithin(tbl_trc.tc, a.tc, 100) limit 10;
  1. with a as (select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10) tc)  
  2. select uid, tbl_trc.tc |=| a.tc from tbl_trc,a where ST_CPAWithin(tbl_trc.tc, a.tc, 100) limit 10;  
  5. NOTICE:  Could not find point with M=1.52839e+09 on first geom  
  6. NOTICE:  Could not find point with M=1.52839e+09 on first geom  
  7. NOTICE:  Could not find point with M=1.52839e+09 on first geom  
  8. NOTICE:  Could not find point with M=1.52839e+09 on first geom  
  9. NOTICE:  Could not find point with M=1.5284e+09 on first geom  
  10. NOTICE:  Could not find point with M=1.52839e+09 on first geom  
  11. NOTICE:  Could not find point with M=1.52839e+09 on first geom  
  12.    uid    |     ?column?       
  13. ----------+------------------  
  14.  97041413 | 47.2605527818083  
  15.    627623 | 89.2835207317297  
  16.  65446299 |  75.474589493268  
  17.  86176035 | 52.5219858940626  
  18.  81450777 | 63.8253100431266  
  19.  97175328 | 61.8835334486386  
  20.  99585779 | 34.6884977809673  
  21.  73552807 | 17.7467079053642  
  22.  27098713 | 68.9482850607433  
  23.  84443616 | 62.2849622517964  
  24. (10 rows)

小结

使用PostgreSQL + PostGIS提供的Temporal Support以及时态分析索引，可以高效的实现轨迹的时态分析。

适应范围广泛，比如

地下情挖掘，一些无法琢磨的亲密关系，在时态分析上都可以做。又比如动物的发情期活动，哪些动物发生过交配等. 再比如在货运、私有运输行业，存在偷油现象，也可以用时态分析来洞察。

功能点：

1、判断两个轨迹是否有亲密接触的可能。

2、如果有亲密接触的可能，那么是在什么时间点（measure）发生的。

3、如果有亲密接触的可能，那么他们接触的距离有多近。

4、如果有亲密接触的可能，那么他们最近距离接触的点是哪个。

时空数据应用有很多好玩的场景，快来学习PostgreSQL.

《Oracle DBA 增值 PostgreSQL,Greenplum 学习计划》

参考

《PostgreSQL PostGIS 的5种空间距离排序(knn)算法》

http://postgis.net/docs/manual-2.4/geometry_distance_cpa.html

http://postgis.net/docs/manual-2.4/reference.html

http://postgis.net/docs/manual-2.4/ST_LocateAlong.html

轨迹亲密接触搜索索引加速

http://postgis.net/docs/manual-2.4/geometry_distance_cpa.html