[postgis-users] Grid of points inside Polygon

[James David Smith]

Hi all,

Would appreciate some advice on the best way to accomplish this please.

Our situation is that we have a single polygon which has been created
by buffering all of the major roads in the UK. Projection is OSGB36
(27700). Obviously it's quite a big polygon.

--> SELECT st_area(geom) FROM roadbufferunion;
st_area
------------------
77228753220.8271

What we now want to do is create a regular grid of 20 metre x 20 metre
points instead the polygon area. So we wrote this function (based on
some googling, apologies for not being able to recall the exact person
who originally wrote it):

CREATE OR REPLACE FUNCTION makegrid(geometry, integer, integer)
RETURNS geometry AS
'SELECT ST_Collect(st_setsrid(ST_POINT(x,y),$3)) FROM
generate_series(53320::int, 667380::int,$2) as x
,generate_series(7780::int, 1226580::int,$2) as y
where st_intersects($1,st_setsrid(ST_POINT(x,y),$3))'
LANGUAGE sql

and we then run this by doing the following:

SELECT st_x((ST_Dump(makegrid(geom, 20, 27700))).geom) as x,
st_y((ST_Dump(makegrid(geom, 20, 27700))).geom) as y INTO grid_points
from roadbufferunion;

However after over 2 days of the query running on a pretty powerful
linux cluster, we still have no result. I'm not sure if it is
actually running or not to be honest.

Does the query look right?
Any ideas how we can make it run quicker?

Thanks

James
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[Rémi Cura]

Hey,
the whole point on using a sgbds like postgis is using index.

If you have one line you don't use indexes...

So in short, don't make one polygon with a buffer of all the road, but a table with a line for the buffer for every road, then do you computation to create grid of points inside of polygons, then union the result of points!

And it s always a bad idea to run a function on big data when you have not tested it fully (including scaling behavior) on small data.

Cheers

Rémi-C

2013/11/11 James David Smith <james.da...@gmail.com>

[James David Smith]

Hey Remi,

Thanks for your reply. So in your mind you think we should have a
database of say 300 polygons, and then we run a command like this
right?

SELECT
ST_Collect(st_setsrid(ST_POINT(x,y),27700))
FROM
generate_series(53320::int, 667380::int,20) as x,
generate_series(7780::int, 1226580::int,20) as y,
road_polygons_table
WHERE
st_intersects(road_polygons_table.the_geom, st_setsrid(ST_POINT(x,y),27700))

What do you think?

Thanks

James

[Rémi Cura]

This would be an improvement but still non efficient.

you have 2 possibilities, supposing that what you want is points 20 meter spaced in all road_buf  : 

either you compute for each road_buffer the points inside, one road at a time ( figuratively ).

This means you write a function which generates points 20-meter spaced in the bounding box of the road you are working on, and keep those in the real road buffer, and group result points as a multipoints (for cosmetic purpose)

.

You would then use it like this : 

SELECT road_id, points_insidea_road(the_geom) AS my_points_inside_the_road

FROM road_polygons_table

You would have as output a line per road with a multipoint containing all the point 20 meter spaced inside the road.

Or (what you wrote) you generate all points and keep those intersecting one or many road.

The first one is mandatory, because it avoids to manipulate (incredibly) big table of all points spaced by 20 meters for UK (around 500 * 10^6 points ! )

Even with indexes it's not a good idea to use such number of rows.

That's the first point (write a function working for one road, then use it for all road).

The second point is the way you compute is very inefficient. If your road is going from south-West to NorthEast, you will generate a very big number of points, and very few will be in the road_buffer. This is problematic as for a road of only 20 kms, you may generate as many as 100k points and keep only few of them. If you want to process hundreds of ks or roads it will become very problematic. Also you would have to generate points each time.

So here is what  I suggest you : change your strategy :

 instead of generating all point in bounding box and then keeping only those in road_buffer,

generate a line every 20 meters going North south and an line every 20 meters going East-West , then use the function ST_Intersection to keep only part of this lines being inside the road_polygon, then you have the points inside road_polygons as the intersections of these EW lines with the SN lines.

It will be very efficient because you can create a table with all the lines going East-West and South-North for great britain (about 25k + 50k lines), and build index on it (index on geom and on the column saying if it is SN or EW).

The trick is the number of lines is around 500km * 50 line/km + 1000km * 50 line/km , where the number of points is  500km * 50 line/km * 1000km * 50 line/km

Hope it helps,

Cheers,

Rémi-C

2013/11/13 James David Smith <james.da...@gmail.com>

[James David Smith]

Hi Remi,

Thanks so much for this detailed response. Your idea about creating
the lines and the only storing where they intersect and are within the
polygons is a great idea. I'm going to give that a go now.

Thanks again,

James

[James David Smith]

Hi Remi,

Apologies. One more thing which I am not sure about. We need the
final grid of points that we make to be multiples of 20. For example:

53320, 7780 = Yes
53323, 7780 = No
53320, 7794 = No
53321, 7754 = No

That is why in the original function that we wrote, we put the numbers
in as below.

SELECT ST_Collect(st_setsrid(ST_POINT(x,y),$3)) FROM
generate_series(53320::int, 667380::int,$2) as x
,generate_series(7780::int, 1226580::int,$2) as y
where st_intersects($1,st_setsrid(ST_POINT(x,y),$3))'

We did this because the points in the grid have to 'align' with the
values of mutliple 20.

If we do the N-S and E-W lines solution that you suggest, I don't
think that this will work will it?

Thanks

James


On 13 November 2013 11:49, James David Smith

[Rémi Cura]

Using the lines you exactly do the same as with points.

The lines will be spaced exactly by 20 meters, end and start being exactly on the 20 meters grid, line being either perfectly veritcla or perfectly horizontal.

So intersections are guaranteed to be on the 20 meter grid, because this is the definition of a 20 meter grid =) .

 

Here is a not optimal way to do it :

For instance if UK is enclosed in a bouding box (xmin,ymin,xmax,ymax), where xmin-max and ymin-max are rounded to the nearest 20 meters multiple (ie x or y % 20 = 0)

(Please note that this is not clever because we generate too much SN lines, GB being only 500 km wide at most, so we would need to filter, but you don't care, following would take less than a minute anyway, and you need to do it only once).

WITH minmax AS (

SELECT xmin,ymin,xmax,ymax, bbox_of_england

),

WITH series AS (

SELECT s

FROM generate_series(0,1000*(1000/20)::bigint,20) AS s --casting to bigint to be safe against going over int limit

),

WITH lines AS (

SELECT ST_MakeLine (ST_MakePoint(xmin+s,ymin),ST_MakePoint(xmin+s,ymax)) AS lineSN, 

 ST_MakeLine(ST_MakePoint(xmin, ymin+s), ST_MakePoint(xmax,ymin+s) AS lineEW

FROM series, minmax

),

unioned_lines AS (

SELECT lineSN AS line, 'SN' as direction

FROM lines,minmax

WHERE ST_Interesects(lineSN,bbox_of_england)= TRUE

UNION 

SELECT lineEW AS line, 'EW' AS direction

FFROM lines,minmax

WHERE ST_Interesects(lineEW,bbox_of_england)= TRUE

)

SELECT row_number() over() AS uid, line, direction

FROM unioned_line

then creating table and index on geom and on direction (and possibly on uid, but better create a primary key then if you use it)

Of course I didn't test this query, but you should be able to use it easily.

Cheers,

Rémi-C

[Pierre Racine]

You can use ST_PixelAsCentroids(ST_AsRaster()) to generate a regular grid of points inside a polygon.

Pierre

[James David Smith]

Hey Remi,

I don't quite get what the query you gave does to be honest. But
working with some of the ideas and notions you gave me I have put the
below together. The final bit of the code is the key query. The tables
of NS and EW lines were done very quickly. Nice. But now doing the
'intersects within polygon' is taking some time so I'll see how it
gets on when I get in to work tomorrow morning:

DROP TABLE IF EXISTS north_to_south;
DROP TABLE IF EXISTS east_to_west;

-- Make a table of north to south lines
CREATE TABLE north_to_south tablespace jamestabs AS
( SELECT st_setsrid(st_makeline(st_makepoint(x, 7780), st_makepoint(x,
1226580)),27700) as the_geom
FROM generate_series(53320::int, 667380::int, 20) as x);

-- Add an index
CREATE INDEX north_to_south_geom_index ON north_to_south USING GIST (
the_geom );

-- Make a table of east to west lines
CREATE TABLE east_to_west tablespace jamestabs AS
( SELECT st_setsrid(st_makeline(st_makepoint(53320, y),
st_makepoint(667380, y)),27700) as the_geom
FROM generate_series(7780::int, 1226580::int, 20) as y);

-- Add an index
CREATE INDEX east_to_west_geom_index ON east_to_west USING GIST ( the_geom );

-- Import the Road Buffer file using the pg_loader interface

-- Update the geometry field as the loader didn't seem to do this.
SELECT UpdateGeometrySRID('ukmajrdbuffer','geom',27700);

-- Merge the road buffer polygons into one big polygon
-- Should maybe consider leaving them as they are, but am merging for now.
SELECT st_union(geom) as geom INTO union_roads FROM ukmajrdbuffer;

-- The unioned roads file isn't valid geom. So I simplify it a little
to make it valid.
-- We simplify with a 70 metres factor. Geom is now valid.
SELECT ST_SimplifyPreserveTopology(geom, 70) AS geom INTO
buff_union_roads FROM union_roads;

-- Now calculate the points where the lines intersect and also where
they are within the polygon.
CREATE TABLE gridpoints tablespace jamestabs
AS (SELECT ST_Intersection(east_to_west.the_geom, north_to_south.the_geom)
FROM east_to_west, north_to_south, buff_union_roads
WHERE st_within(buff_union_roads.geom,
ST_Intersection(east_to_west.the_geom, north_to_south.the_geom)) =
TRUE);

Thanks

James

[Rémi Cura]

All lines should be in one table, you can add a column to differentiate between line going SN and EW, 

this is what the query I wrote does.

Not changing your code much, it gives for the line table :

CREATE TABLE all_lines tablespace jamestabs AS

( SELECT st_setsrid(st_makeline(st_makepoint(x, 7780), st_makepoint(x,

1226580)),27700) as the_geom, 'SN' AS direction

FROM generate_series(53320::int, 667380::int, 20) as x)

UNION 

( SELECT st_setsrid(st_makeline(st_makepoint(53320, y),
st_makepoint(667380, y)),27700) as the_geom, 'EW' AS direction

FROM generate_series(7780::int, 1226580::int, 20) as y)

then building index on it.

"-- Merge the road buffer polygons into one big polygon
-- Should maybe consider leaving them as they are, but am merging for now.
SELECT st_union(geom) as geom INTO union_roads FROM ukmajrdbuffer;"

You must not do it ! 

As I told you "blabla index blabla".

instead, create an index on table ukmajrdbuffer, and use it without unioning.

Then you query is not going to work at all ... (or *very very* slowly) 

"FROM east_to_west, north_to_south, buff_union_roads" : it potentially generates 1000*50*1000*50 * number_of_road rows to filter, very bad idea, you'll get the same problem as with points...

(please see some example on internet to understand WITH, it is simple , useful, and makes query much more clear)

First you could try :

CREATE TABLE lines_for_each_road tablespace jamestabs AS

WITH all_lines AS ( --this subquerry gets all the lines

SELECT * 

FROM all_lines

),

SELECT row_number() over() AS id--,*

FROM ukmajrdbuffer, all_lines

WHERE ST_Intersects(ukmajrdbuffer.the_geom, all_lines.the_geom)=TRUE;

This will give you (if you uncomment the "--,*", ), for every road, all the lines intersecting the road

example :

road_1 | line_2_EW

road_1 | line_3_EW

road_1 | line_78_SN

road_1 | line_7_EW

road_2 ...

How long is it (don't uncomment plz), and how many rows do you get (select count(*) from lines_for_each_road )?

If it is not too long, we will go on and "cut" the lines so that for every road, we keep the part of the lines that are inside the road_buffer.

(I have to leave now, tomorrow)

Cheers,

Rémi-C

[James David Smith]

Hi Remi,

Thanks for your continued guidance with this big data problem. I
wasn't in the office yesterday so am looking at it again now. I've
just ran the below below query running, and will let you know how many
rows there are once it's finished.

CREATE TABLE lines_for_each_road AS
WITH all_lines AS (
SELECT *
FROM all_lines
)

SELECT row_number() over() AS id--,*
FROM ukmajrdbuffer, all_lines

WHERE ST_Intersects(ukmajrdbuffer.geom, all_lines.the_geom)=TRUE;

In the meantime however, I have noticed something else that is a
worry. I did this:

SELECT st_isvalid(geom) FROM ukmajrdbuffer;

NOTICE: Ring Self-intersection at or near point 367541.09074241668
311890.25257437676
NOTICE: Ring Self-intersection at or near point 209901.50000000186
706890.50000000373
NOTICE: Ring Self-intersection at or near point 444961.46434461698
161217.66612910852
NOTICE: Ring Self-intersection at or near point 559818.64931676909
103089.14606037363
NOTICE: Ring Self-intersection at or near point 420114.82424666081
298567.38722311892
st_isvalid
------------
f
f
t
f
f
f
t
t
(8 rows)

I guess that I should try to fix these geometries first before we
attempt to continue any further right?

[Rémi Cura]

Yep, maybe something like 

UPDATE ukmajrdbuffer SET the_geom = ST_MakeValid(the_geom) 

WHERE ST_IsValid(the_geom) = FALSE

Cheers,

Rémi-C

2013/11/15 James David Smith <james.da...@gmail.com>

[Sandro Santilli]

On Fri, Nov 15, 2013 at 11:50:42AM +0100, Rémi Cura wrote:
> Yep, maybe something like
>
> UPDATE ukmajrdbuffer SET the_geom = ST_MakeValid(the_geom)
> WHERE ST_IsValid(the_geom) = FALSE

ST_MakeValid internally checks for ST_IsValid, so no need
to add the condition (which would run the test twice).

--strk;

[James David Smith]

Thanks both. Geometries now fixed.

The query 'CREATE TABLE lines_for_each_road....' has now been set
running. Will report back when it's done. I suspect it may take a
while!

James

[Rémi Cura]

Hey Sandro,

Thanks for this, it is at least twice faster =)

Cheers,

Rémi-C 

2013/11/15 James David Smith <james.da...@gmail.com>

Thanks both. Geometries now fixed.

[Rémi Cura]

It should be finished by now,

can you check you have geom indexes on :

"ukmajrdbuffer.geom" and  "all_lines.the_geom"

How many geoms do you have in "ukmajrdbuffer"?

Cheers,

Rémi-C

2013/11/15 Rémi Cura <remi...@gmail.com>

[Rémi Cura]

Also if you do have indexes,

can you run a "VACUUM ANALYZE", so that the indexes will be used?

Cheers,

Rémi-C

[James David Smith]

Hey.

Yes, it's done. Was just getting some lunch! :-)

select count(*) from lines_for_each_road
Result = 187033

I have also just ran 'VACUUM ANALYZE' on the tables
'lines_for_each_road' as well as the table 'all_lines'

I also can confirm that I have ran the following commands:

CREATE INDEX all_lines_index ON all_lines USING GIST ( the_geom )
CREATE INDEX ukmajrdbuffer_index ON ukmajrdbuffer USING GIST (geom);

Should we now uncomment this line from the previous query?

" SELECT row_number() over() AS id--,* "

Thanks again Remi,

James

[Rémi Cura]

Good !

Something is strange with the result,

you get only 190k lines intersecting road buffer,

it is very few , I expected at least 10times this!

How many time took this computing by the way?

How many road buffer geom do you have ? (select count(*) from ukmajrdbuffer ).

Cheers,

Rémi-C

[James David Smith]

Hey Remi,

I'll do a few checks and get back to you. Maybe I did something wrong
because I set this query going on my local PostgreSQL installation but
also on our Linux Cluster machine which is much more powerful. And it
finished on my local installation BEFORE the cluster. So maybe I did
something wrong on the local query.

The query that has finished took about 1 hour.
The query on our cluster is still running.

select count(*) from ukmajrdbuffer = 8
This is because before I was given the data the roads buffer had
already been dissolved unfortunately.

James

[Rémi Cura]

Outch,

you have only 8 roads in GB? =)

This is not going to go fast till you don't have some dozens k's of roads.

I'm guessing you are not at will to send those roads?

The next step will be (when you'll be sure everything is OK)

CREATE TABLE lines_for_each_road AS
WITH all_lines AS (
SELECT *
FROM all_lines

),

cutted_lines AS ( --we cut the line to keep only part of lines inside road_buffer

SELECT ST_Intersection(all_lines.the_geom,ukmajrdbuffer.geom) as lines_cutted, direction
FROM ukmajrdbuffer, all_lines

WHERE ST_Intersects(ukmajrdbuffer.geom, all_lines.the_geom)=TRUE 

),

cutted_lines_SN AS ( --this is the cutted lines which going from South to North

SELECT *

FROM cutted_lines 

WHERE direction = 'SN'

),

cutted_lines_EW AS ( --this is the cutted lines going from East toWest

SELECT *

FROM cutted_lines 

WHERE direction = 'EW'

),

points AS ( -- we take the intersection of EW  lines with SN lines , that is the points on the grid.

SELECT ST_Intersection(clSN.lines_cutted, clEW.lines_cutted) AS point

FROM cutted_lines_SN as clSN, cutted_lines_EW AS clEW

WHERE ST_Intersects(clSN.lines_cutted, clEW.lines_cutted)=TRUE --no point ot compute an intersection if lines don't intersect

)

SELECT row_number() over() AS id  , point 

FROM points ;

 

Cheers,

Rémi-C

[James David Smith]

Hey Remi,

Do you think before I try running the big query you have just sent me,
that I should go back and try to get the original file of uk roads? I
mean the very original file that has not had any buffers applied or
any merging done.

Or shall we just go for it and see if it has finished when I come into
work on Monday?! haha.

Thanks

James

[Rémi Cura]

You should try to get the original road file, because i will be very easy to reapply some buffer and filtering to keep only major road.
Yet, why not let it run during the week end?

Cheers,

Rémi-C

[James David Smith]

Remi,

Ok. Cool. I've set the below query running. On Monday I will also
attempt to get the original road lines file too. Let's see if we have
a result on Monday.
----------------------------------

------------------------------------------
Thanks

James

[Rémi Cura]

Still is a shame : 

with proper data we should have some result with about one hour i guess.

Cheers,

Rémi C

[James David Smith]

Hey Remi,

I've actually managed to get the file 'ukmajorroads' already and have loaded it into my database.  There are 395356 rows in the database. There is a field called 'geom' and I have built an index on it as below;

CREATE INDEX ukrds_index ON ukrds USING GIST (geom);

So should I now run the same query, but do the buffering of the roads 'on the fly' maybe?  For example as below?

CREATE TABLE lines_for_each_road AS

WITH all_lines AS (

SELECT *

FROM all_lines

),

cutted_lines AS ( --we cut the line to keep only part of lines inside road_buffer

SELECT ST_Intersection(all_lines.the_geom,st_buffer(ukmajrdbuffer.geom, 1000)) as lines_cutted, direction

FROM ukmajrdbuffer, all_lines

WHERE ST_Intersects(st_buffer(ukmajrdbuffer.geom, 1000), all_lines.the_geom)=TRUE 

),

cutted_lines_SN AS ( --this is the cutted lines which going from South to North

SELECT *

FROM cutted_lines 

WHERE direction = 'SN'

),

cutted_lines_EW AS ( --this is the cutted lines going from East toWest

SELECT *

FROM cutted_lines 

WHERE direction = 'EW'

),

points AS ( -- we take the intersection of EW  lines with SN lines , that is the points on the grid.

SELECT ST_Intersection(clSN.lines_cutted, clEW.lines_cutted) AS point

FROM cutted_lines_SN as clSN, cutted_lines_EW AS clEW

WHERE ST_Intersects(clSN.lines_cutted, clEW.lines_cutted)=TRUE --no point ot compute an intersection if lines don't intersect

)

SELECT row_number() over() AS id  , point 

FROM points ;

[Rémi Cura]

good =) 

It is better to do the buffer computation first,

because this way you are sure youwon't compute the same buffer many times.

Something like (not so sure without trying it)

UPDATE ukmajrdbuffer SET geom = ST_Buffer(geom,1000); 

You may have an error if you hav e a fixed geom data type, then you could just add a new column like

ALTER TABLE ukmajrdbuffer ADD COLUMN the_geom geometry ;

UPDATE ukmajrdbuffer SET the_geom = ST_Buffer(geom,1000); 

Cheers,

Rémi-C

[James David Smith]

Hi Remi / all,

I am just coming back to this project. I have made some progress. But
would appreciate advice on how best to proceed now. What I have now is
a table with two columns, 'st_x' and 'st_y'. They are the 20 metre by
20 metre grid points that are within 1km of main roads in the UK. The
table has 499,677,666 rows! Because of the method that I used to
create this however, I have alot of duplication of points. So I think
I need to do something like:

CREATE TABLE grid_no_duplications AS (SELECT DISTINCT(x, y) FROM grid);

However I thought that first I could put an index on it?

CREATE INDEX grid_x_y ON grid (st_x, st_y);

Is this a good approach?

Cheers

James

[Rémi Cura]

First, 

do you really need no duplicates?

Then, Creating an index on a 500 million row table is going to take time and a lot of spaces (several gigas??).

I don't think you have a choice here.

Yet I'm not sure the index would be used,  I'm not an expert.

What you can do is 

_create a table with only a part of points to test

_create an index on it

_check how much time distinct takes, and if it uses index.

CREATE TABLE grid_temp AS 

SELECT st_x,st_y

FROM grid

LIMIT 1000000; --only 1 million points

CREATE INDEX ON grid_temp(st_x);

CREATE INDEX ON grid_temp(st_y);

EXPLAIN ANALYZE 

SELECT DISTINCT st_x, st_y

FROM grid_temp ; 

--(if you see some index uses in the return, it's good news)

Then doing it on all your data.

For the record, 

The ideal solution would have been  : 

no have a X | Y table , but a X | Y | id_of_the_road table

This way you can create a table y grouping points by id_of_the_road  (creating so a multipoint per road).

With this , you would have far less rows, you could create an index on geom.

Then you would get the intersecting multipoints (which would be efficient), and dedup only pair by pair (which would be efficient).

Cheers,

Rémi-C

2013/11/29 James David Smith <james.da...@gmail.com>