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59 Commits

Author SHA1 Message Date
Javier Goizueta
8414bdff31 Release 0.13.0 2016-01-29 17:53:51 +01:00
Javier Goizueta
5f96908df4 Merge pull request #185 from CartoDB/overviews
Overviews (new feature)
2016-01-29 17:44:47 +01:00
Javier Goizueta
06dd31f4ad Fix: should be floating point divistion, not integer division 2016-01-29 16:51:52 +01:00
Javier Goizueta
6a11698a16 Merge branch 'overviews' into sql_lang 2016-01-29 16:29:23 +01:00
Javier Goizueta
00bd302f01 Avoid creating GridCluster overviews for non-point datasets 2016-01-29 16:19:35 +01:00
Javier Goizueta
93d4a6ead0 Restrict SECURITY DEFINER to overview registration
And check it is applied only overview tables with valid names
2016-01-28 17:04:06 +01:00
Javier Goizueta
66387c2d44 Make CDB_CreateOverviews a SECURITY DEFINER function
So that it can change the permissions of overview tables
(by updating pg_class) even when executed by non-priviledeged users.
2016-01-28 16:32:40 +01:00
Javier Goizueta
26c95347cd Merge branch 'master' into overviews 2016-01-27 16:56:15 +01:00
Javier Goizueta
6a5e4b0460 Fix overviews tests
The aggregation method for strings has changed
2016-01-27 16:54:30 +01:00
Javier Goizueta
b8d50204dd Avoid aggregation which causes out-of-memory crashes in PostgreSQL
The use of multiple string_agg functions, even if applied to groups
of one single record causes out of memory crashes in PG 9.3.4 for
some (large) tables.
2016-01-27 15:24:04 +01:00
Javier Goizueta
474de01757 Change the overview table naming scheme
The scheme is changed from table_ovN to _vovw_N_table for
lower collision probability.
Also future naming changes will be easier by using the functions
_CDB_OverviewTableDiscriminator, _CDB_OverviewTableName,
_CDB_IsOverviewTableOf, etc.
2016-01-26 13:20:28 +01:00
Javier Goizueta
1ebaeb76ac Overload CDB_Overviews to accept either a single table or an array
The result of CDB_Overviews has been expandend with a base_table column
2016-01-26 10:39:26 +01:00
Javier Goizueta
7033a8d9ac Fixes for table names that require quotes or which include a schema name
Some cases left unsolved, with FIXME comments
2016-01-13 18:49:27 +01:00
Javier Goizueta
46bc774d38 Fix CDB_Overviews for the case that the table name requires quoting 2016-01-13 18:24:06 +01:00
Javier Goizueta
a9e2d19918 Document CDB_DropOverviews 2016-01-12 16:20:11 +01:00
Javier Goizueta
d352e1c463 Update Overviews tests 2016-01-12 15:36:07 +01:00
Javier Goizueta
5b47c51221 Add function to drop overviews 2016-01-12 15:35:50 +01:00
Javier Goizueta
ebaded0c7a Merge branch 'master' into overviews 2016-01-12 13:34:26 +01:00
Javier Goizueta
ccdf8de59e Enhance documentation, update comments 2016-01-12 12:08:41 +01:00
Javier Goizueta
a2f6cb4c04 Fix documentation 2016-01-12 11:59:57 +01:00
Javier Goizueta
02f386be33 Regard the GridCluster reduction strategy as private
The *strategy* parameteriation will be considered an
implementation detail for the time being.
2016-01-12 11:59:42 +01:00
Javier Goizueta
a7c70fe497 Fix: CDB_ZoomFromScale deviation for lowest zoom levels 2016-01-12 11:46:47 +01:00
Javier Goizueta
0a066e0126 Change the default overview reduction strategy to GridCluster 2016-01-11 15:35:04 +01:00
Javier Goizueta
913640e2dc Preserve the column ordering of the base table in overviews 2016-01-11 15:34:10 +01:00
Javier Goizueta
ef7e613d41 Change CDB_ColumnNames to order columns names as in table 2016-01-11 15:28:27 +01:00
Javier Goizueta
fd7a8cff71 Change regular expression for consistency 2016-01-11 15:27:05 +01:00
Javier Goizueta
6ea63af974 Add function to obtain existing overviews of a table 2016-01-11 14:50:10 +01:00
Javier Goizueta
496f079b1c Copy dataset privileges to overview tables 2016-01-04 18:06:56 +01:00
Javier Goizueta
4580c9cd5c Change the cartodb_ids of aggregated overviews
Instead of arbitrary ids, the id of one of the aggregated records
is used, so that if it is used in the UI to query point
the information of one of the records grouped at the point will be
retrieved.
2016-01-04 10:33:39 +01:00
Javier Goizueta
08828b8b7d Set owner of overlays to the owner of the base table 2015-12-29 15:22:12 +01:00
Javier Goizueta
cecba655eb Preserve aggregated attributes of singleton groups 2015-12-29 14:56:47 +01:00
Javier Goizueta
b34a752172 Generate overviews for all Z levels
Skipping levels produces visually inferior results
2015-12-29 14:56:04 +01:00
Javier Goizueta
8ba9e74c4a Order columns of aggregated overlays as in the base table 2015-12-29 13:38:07 +01:00
Javier Goizueta
6a6a5bc96a Fix Sampling reduction to avoid RandomTids problems
The fixed cases will not be common but do occur in tests.
This is an interim fix which should be reverted if CDB_randomTids changes.
2015-12-28 19:41:14 +01:00
Javier Goizueta
2ff686de27 Clean up: remove spurious comment 2015-12-28 19:30:20 +01:00
Javier Goizueta
07326626b7 More efficient sampling strategy
It is also renamed properly.
2015-12-28 19:28:20 +01:00
Javier Goizueta
4afc427008 Rename Ref. Z strategy function
It's not that *dummy* anymore, so choose a more descriptive name
2015-12-28 17:47:57 +01:00
Javier Goizueta
8d1bbc63fa Add overview tests 2015-12-23 16:33:34 +01:00
Javier Goizueta
06ca4f74ee Enable Overviews module in the extension 2015-12-23 16:32:44 +01:00
Javier Goizueta
a8a2c04d71 Remove invalid comment 2015-12-23 14:20:57 +01:00
Javier Goizueta
a5bca7d715 Add function for post-processing new overview tables 2015-12-23 14:17:50 +01:00
Javier Goizueta
552206464e Make strategy function public 2015-12-23 12:50:04 +01:00
Javier Goizueta
2af0b9a57f Add function comments 2015-12-23 12:42:40 +01:00
Javier Goizueta
1b5de84c9a Add missing attribute-aggregationto the point reduction strategy 2015-12-23 12:17:37 +01:00
Javier Goizueta
c36a5d35c3 Merge branch 'overviews' of github.com:CartoDB/cartodb-postgresql into overviews 2015-12-22 18:02:16 +01:00
Javier Goizueta
5a78ee2896 Optimize the gridded clustering strategy
The internal grid_px parameter is adjusted for best results with default symbol size
2015-12-22 17:59:49 +01:00
Rafa de la Torre
480e2d0979 Merge pull request #187 from CartoDB/overviews-rtorre
Overviews rtorre touches
2015-12-22 17:45:14 +01:00
Javier Goizueta
c8a1ef6f68 Slight optimization of gridded clustering 2015-12-22 15:25:21 +01:00
Paul Norman
ea7c16fbaf Convert some simple functions from plpgsql to sql
SQL is a faster language to call, and these are very simple functions.
2015-12-21 23:59:26 -08:00
Rafa de la Torre
564ab75d2d Use _cdb_estimated_extent instead of ST_Extent
With a 3.8M points table, this was a ~30% gain in my local env.
2015-12-21 18:41:50 +01:00
Rafa de la Torre
5010109c7d Add _cdb_estimated_extent to get the extent from stats 2015-12-21 18:41:45 +01:00
Rafa de la Torre
e60f73a31b A bit of internal documentation 2015-12-21 13:16:57 +01:00
Javier Goizueta
415a09392f Gridded clustering aggregation strategy for overviews 2015-12-16 17:45:36 +01:00
Javier Goizueta
e5cc9ef0bd Fix: typo 2015-12-16 17:26:17 +01:00
Javier Goizueta
f7857945c1 Change feature density computation algorithm
Now parameterize by the number of levels to traverse and
start with the level that covers the extent of the table
with at least N*N tiles (N=4).
2015-12-16 16:39:38 +01:00
Javier Goizueta
554464e43e Use tile-recursive computation of feature density
This is a more adaptive way of estimating the feature density to
determine the base Z level.
Applying technique from http://javisantana.com/2014/10/22/traversing-quadtree.html
2015-12-16 12:14:37 +01:00
Javier Goizueta
d7c8f3d7e8 Fix: overlay generation was not using the proper scale 2015-12-15 19:13:39 +01:00
Javier Goizueta
4c85d7f3ad Compute the reference Z level for a table 2015-12-15 19:12:48 +01:00
Javier Goizueta
d0e66910a0 Sketch for new Overview-creation functionality 2015-12-15 17:36:27 +01:00
13 changed files with 3174 additions and 33 deletions

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@@ -1,7 +1,7 @@
# cartodb/Makefile
EXTENSION = cartodb
EXTVERSION = 0.12.0
EXTVERSION = 0.13.0
SED = sed
@@ -57,6 +57,7 @@ UPGRADABLE = \
0.11.4 \
0.11.5 \
0.12.0 \
0.13.0 \
$(EXTVERSION)dev \
$(EXTVERSION)next \
$(END)

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@@ -1,3 +1,7 @@
0.13.0 (2016-01-29)
* Add CDB_CreateOverviews, CDB_DropOverviews and CDB_Overviews for vector overviews support. [185](https://github.com/CartoDB/cartodb-postgresql/pull/185)
* Convert some simple functions from plpgsql to sql. [188](https://github.com/CartoDB/cartodb-postgresql/pull/188)
0.12.0 (2016-01-27)
-------------------
* Remove schema_triggers extension dependency, to ensure compatibility with PostgreSQL 9.5. [#190](https://github.com/CartoDB/cartodb-postgresql/pull/190)

105
doc/CDB_Overviews.md Normal file
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@@ -0,0 +1,105 @@
Overviews are tables that represent a *reduced* version of a dataset intended
for efficient rendering at certain zoom levels while preserving the
general visual appearance of the complete dataset.
The *reduction* consists in a fewer number of records
(while each overview record may represent an aggregation of multiple records)
and/or simplified record geometries.
Overviews are created through the `CDB_CreateOverviews`.
The statement timeout may need to be adjusted before using this function,
as overview creation for large tables is a time-consuming operation.
The `CDB_Overviews` function can be used determine what overview tables
exist for a given dataset table and which zoom levels correspond to it.
The `CDB_DropOverviews` remove a dataset's existing overviews.
### CDB_CreateOverviews
Create overviews for vector dataset.
#### Using the function
The table for which overviews will be generated should be
a Cartodbfied dataset with vector geometry.
```sql
SELECT CDB_CreateOverviews('table_name');
--- Generates overview tables for the dataset
```
#### Arguments
CDB_CreateOverviews(table_name, ref_z_strategy, reduction_strategy)
* **table_name** regclass, table for which overviews will be generated
* **ref_z_strategy** regproc, optional function that provides
the Z-scale strategy.
It returns the base Z level for the dataset.
It should have these arguments:
- **table_name** regclass, table to compute the reference Z scale for
* **reduction_strategy** regproc, optional function that provides
the reduction strategy to generate an overview table from a table
for a smaller scale (higher Z number).
It returns the name of the generated table.
It should have these arguments:
- **base_table_name** regclass, base table to be reduced.
- **base_z** integer, base Z level assigned to the base table.
- **overview_z** integer, Z level for which to generate the overview.
### CDB_Overviews
Obtain overview metadata for a given table (existing overviews).
The returned relation will be empty if the table has no overviews.
The function can be applied to a single table:
```sql
SELECT CDB_Overviews('table_name');
--- Return existing overview Z levels and corresponding tables
```
Or to multiple tables passed as an array; this can be used
to obtain the overviews that can be applied to a query by
combining it with `CDB_QueryTablesText`:
```sql
SELECT CDB_Overviews(CDB_QueryTablesText('SELECT * FROM table1, table2'));
--- Return existing overview Z levels and corresponding tables
```
The result of `CDB_Overviews` has three columns:
| base_table | z | overview_table |
|------------+---+----------------|
| table1 | 1 | table1_ov1 |
| table1 | 2 | table1_ov2 |
| table1 | 4 | table1_ov4 |
| table2 | 1 | table1_ov1 |
| table2 | 2 | table1_ov2 |
#### Arguments
CDB_Overviews(table_name)
* **table_name** regclass, oid of table to obtain existing overviews for
CDB_Overviews(table_names)
* **table_names** regclass[], array of table oids
### CDB_DropOverviews
Remove the overviews of a table, if present.
```sql
SELECT CDB_DropOverviews('table_name');
```
#### Arguments
CDB_Overviews(table_name)
* **table_name** regclass, table for which to drop existing overviews.

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@@ -8,8 +8,9 @@ AS $$
WHERE table_name = _tn.relname
AND table_schema = _sn.nspname
AND _tn.oid = $1::oid
AND _sn.oid = _tn.relnamespace;
AND _sn.oid = _tn.relnamespace
ORDER BY ordinal_position;
$$ LANGUAGE SQL;
-- This is to migrate from pre-0.2.0 version

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@@ -8,16 +8,12 @@
--
CREATE OR REPLACE FUNCTION CDB_LatLng (lat NUMERIC, lng NUMERIC) RETURNS geometry as $$
BEGIN
-- this function is silly
RETURN ST_SetSRID(ST_MakePoint(lng,lat),4326);
END;
$$ language plpgsql IMMUTABLE;
SELECT ST_SetSRID(ST_MakePoint(lng,lat),4326);
$$ language SQL IMMUTABLE;
CREATE OR REPLACE FUNCTION CDB_LatLng (lat FLOAT8, lng FLOAT8) RETURNS geometry as $$
BEGIN
-- this function is silly
RETURN ST_SetSRID(ST_MakePoint(lng,lat),4326);
END;
$$ language plpgsql IMMUTABLE;
SELECT ST_SetSRID(ST_MakePoint(lng,lat),4326);
$$ language SQL IMMUTABLE;

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@@ -0,0 +1,687 @@
-- security definer
-- Pattern that can be used to detect overview tables and Extract
-- the intended zoom level from the table name.
-- Scope: private.
CREATE OR REPLACE FUNCTION _CDB_OverviewTableDiscriminator()
RETURNS TEXT
AS $$
BEGIN
RETURN '\A_vovw_(\d+)_';
END;
$$ LANGUAGE PLPGSQL IMMUTABLE;
-- substring(tablename from _CDB_OverviewTableDiscriminator())
-- Pattern matched by the overview tables of a given base table name.
-- Scope: private.
CREATE OR REPLACE FUNCTION _CDB_OverviewTablePattern(base_table TEXT)
RETURNS TEXT
AS $$
BEGIN
RETURN _CDB_OverviewTableDiscriminator() || base_table;
END;
$$ LANGUAGE PLPGSQL IMMUTABLE;
-- tablename SIMILAR TO _CDB_OverviewTablePattern(base_table)
-- Name of an overview table, given the base table name and the Z level
-- Scope: private.
CREATE OR REPLACE FUNCTION _CDB_OverviewTableName(base_table TEXT, z INTEGER)
RETURNS TEXT
AS $$
BEGIN
RETURN '_vovw_' || z::text || '_' || base_table;
END;
$$ LANGUAGE PLPGSQL IMMUTABLE;
-- Condition to check if a tabla is an overview table of some base table
-- Scope: private.
CREATE OR REPLACE FUNCTION _CDB_IsOverviewTableOf(base_table TEXT, otable TEXT)
RETURNS BOOLEAN
AS $$
BEGIN
RETURN otable SIMILAR TO _CDB_OverviewTablePattern(base_table);
END;
$$ LANGUAGE PLPGSQL IMMUTABLE;
-- Extract the Z level from an overview table name
-- Scope: private.
CREATE OR REPLACE FUNCTION _CDB_OverviewTableZ(otable TEXT)
RETURNS INTEGER
AS $$
BEGIN
RETURN substring(otable from _CDB_OverviewTableDiscriminator())::integer;
END;
$$ LANGUAGE PLPGSQL IMMUTABLE;
-- Name of the base table corresponding to an overview table
-- Scope: private.
CREATE OR REPLACE FUNCTION _CDB_OverviewBaseTableName(overview_table TEXT)
RETURNS TEXT
AS $$
BEGIN
IF _CDB_OverviewTableZ(overview_table) IS NULL THEN
RETURN overview_table;
ELSE
RETURN regexp_replace(overview_table, _CDB_OverviewTableDiscriminator(), '');
END IF;
END;
$$ LANGUAGE PLPGSQL IMMUTABLE;
-- Remove a dataset's existing overview tables.
-- Scope: public
-- Parameters:
-- reloid: oid of the table.
CREATE OR REPLACE FUNCTION CDB_DropOverviews(reloid REGCLASS)
RETURNS void
AS $$
DECLARE
row record;
BEGIN
FOR row IN
SELECT * FROM CDB_Overviews(reloid)
LOOP
EXECUTE Format('DROP TABLE %s;', row.overview_table);
RAISE NOTICE 'Dropped overview for level %: %', row.z, row.overview_table;
END LOOP;
END;
$$ LANGUAGE PLPGSQL VOLATILE;
-- Return existing overviews (if any) for a given dataset table
-- Scope: public
-- Parameters
-- reloid: oid of the input table.
-- Return relation of overviews for the table with
-- the base table oid,
-- z level of the overview and overview table oid, ordered by z.
CREATE OR REPLACE FUNCTION CDB_Overviews(reloid REGCLASS)
RETURNS TABLE(base_table REGCLASS, z integer, overview_table REGCLASS)
AS $$
-- FIXME: this will fail if the overview tables
-- require a explicit schema name
-- possible solutions: return table names as text instead of regclass
-- or add schema of reloid before casting to regclass
SELECT
reloid AS base_table,
_CDB_OverviewTableZ(cdb_usertables) AS z,
cdb_usertables::regclass AS overview_table
FROM CDB_UserTables()
WHERE _CDB_IsOverviewTableOf((SELECT relname FROM pg_class WHERE oid=reloid), cdb_usertables)
ORDER BY z;
$$ LANGUAGE SQL;
-- Return existing overviews (if any) for multiple dataset tables.
-- Scope: public
-- Parameters
-- tables: Array of input tables oids
-- Return relation of overviews for the table with
-- the base table oid,
-- z level of the overview and overview table oid, ordered by z.
-- Note: CDB_Overviews can be applied to the result of CDB_QueryTablesText
-- to obtain the overviews applicable to a query.
CREATE OR REPLACE FUNCTION CDB_Overviews(tables regclass[])
RETURNS TABLE(base_table REGCLASS, z integer, overview_table REGCLASS)
AS $$
SELECT
base_table::regclass AS base_table,
_CDB_OverviewTableZ(cdb_usertables) AS z,
cdb_usertables::regclass AS overview_table
FROM
CDB_UserTables(), unnest(tables) base_table
WHERE _CDB_IsOverviewTableOf((SELECT relname FROM pg_class WHERE oid=base_table), cdb_usertables)
ORDER BY base_table, z;
$$ LANGUAGE SQL;
-- Schema and relation names of a table given its reloid
-- Scope: private.
-- Parameters
-- reloid: oid of the table.
-- Return (schema_name, table_name)
-- note that returned names will be quoted if necessary
CREATE OR REPLACE FUNCTION _cdb_split_table_name(reloid REGCLASS, OUT schema_name TEXT, OUT table_name TEXT)
AS $$
BEGIN
SELECT n.nspname, c.relname
INTO STRICT schema_name, table_name
FROM pg_class c JOIN pg_namespace n ON c.relnamespace = n.oid
WHERE c.oid = reloid;
END
$$ LANGUAGE PLPGSQL IMMUTABLE;
-- Calculate the estimated extent of a cartodbfy'ed table.
-- Scope: private.
-- Parameters
-- reloid: oid of the input table.
-- Return value A box2d extent in 3857.
CREATE OR REPLACE FUNCTION _cdb_estimated_extent(reloid REGCLASS)
RETURNS box2d
AS $$
DECLARE
ext box2d;
ext_query text;
table_id record;
BEGIN
SELECT n.nspname AS schema_name, c.relname table_name INTO STRICT table_id
FROM pg_class c JOIN pg_namespace n on n.oid = c.relnamespace WHERE c.oid = reloid::oid;
ext_query = format(
'SELECT ST_EstimatedExtent(''%1$I'', ''%2$I'', ''%3$I'');',
table_id.schema_name, table_id.table_name, 'the_geom_webmercator'
);
BEGIN
EXECUTE ext_query INTO ext;
EXCEPTION
-- This is the typical ERROR: stats for "mytable" do not exist
WHEN internal_error THEN
-- Get stats and execute again
EXECUTE format('ANALYZE %1$I', reloid);
EXECUTE ext_query INTO ext;
END;
RETURN ext;
END;
$$ LANGUAGE PLPGSQL VOLATILE;
-- Determine the max feature density of a given dataset.
-- Scope: private.
-- Parameters
-- reloid: oid of the input table. It must be a cartodbfy'ed table.
-- nz: number of zoom levels to consider from z0 upward.
-- Return value: feature density (num_features / webmercator_squared_meters).
CREATE OR REPLACE FUNCTION _CDB_Feature_Density(reloid REGCLASS, nz integer)
RETURNS FLOAT8
AS $$
DECLARE
fd FLOAT8;
min_features TEXT;
n integer = 4;
c FLOAT8;
BEGIN
-- TODO: for small total count or extents we could just:
-- EXECUTE 'SELECT Count(*)/ST_Area(ST_Extent(the_geom_webmercator)) FROM ' || reloid::text || ';' INTO fd;
-- min_features is a SQL subexpression which can depend on z and represents
-- the minimum number of features to recursively consider a tile.
-- We can either use a fixed minimum number of features per tile
-- or a minimum feature density by dividing the number of features by
-- the area of tiles at level Z: c*c*power(2, -2*z)
-- with c = CDB_XYZ_Resolution(-8) (earth circumference)
min_features = '500';
SELECT CDB_XYZ_Resolution(-8) INTO c;
-- We first compute a set of *seed* tiles, of the minimum Z level, z0, such that
-- they cover the extent of the table and we have at least n of them in each
-- linear dimension (i.e. at least n*n tiles cover the extent).
-- We compute the number of features in these tiles, and recursively in
-- subtiles up to level z0 + nz. Then we compute the maximum of the feature
-- density (per tile area in webmercator squared meters) for all the
-- considered tiles.
EXECUTE Format('
WITH RECURSIVE t(x, y, z, e) AS (
WITH ext AS (SELECT _cdb_estimated_extent(%6$s) as g),
base AS (
SELECT (-floor(log(2, (greatest(ST_XMax(ext.g)-ST_XMin(ext.g), ST_YMax(ext.g)-ST_YMin(ext.g))/(%4$s*%5$s))::numeric)))::integer z
FROM ext
),
lim AS (
SELECT
FLOOR((ST_XMin(ext.g)+CDB_XYZ_Resolution(0)*128)/(CDB_XYZ_Resolution(base.z)*256))::integer x0,
FLOOR((ST_XMax(ext.g)+CDB_XYZ_Resolution(0)*128)/(CDB_XYZ_Resolution(base.z)*256))::integer x1,
FLOOR((CDB_XYZ_Resolution(0)*128-ST_YMin(ext.g))/(CDB_XYZ_Resolution(base.z)*256))::integer y1,
FLOOR((CDB_XYZ_Resolution(0)*128-ST_YMax(ext.g))/(CDB_XYZ_Resolution(base.z)*256))::integer y0
FROM ext, base
),
seed AS (
SELECT xt, yt, base.z, (
SELECT count(*) FROM %1$s
WHERE the_geom_webmercator && CDB_XYZ_Extent(xt, yt, base.z)
) e
FROM base, lim, generate_series(lim.x0, lim.x1) xt, generate_series(lim.y0, lim.y1) yt
)
SELECT * from seed
UNION ALL
SELECT x*2 + xx, y*2 + yy, t.z+1, (
SELECT count(*) FROM %1$s
WHERE the_geom_webmercator && CDB_XYZ_Extent(x*2 + xx, y*2 + yy, t.z+1)
)
FROM t, base, (VALUES (0, 0), (0, 1), (1, 1), (1, 0)) AS c(xx, yy)
WHERE t.e > %2$s AND t.z < (base.z + %3$s)
)
SELECT MAX(e/ST_Area(CDB_XYZ_Extent(x,y,z))) FROM t where e > 0;
', reloid::text, min_features, nz, n, c, reloid::oid)
INTO fd;
RETURN fd;
END
$$ LANGUAGE PLPGSQL STABLE;
-- Experimental default strategy to assign a reference base Z level
-- to a cartodbfied table. The resulting Z level represents the
-- minimum scale level at which the table data can be rendered
-- without overcrowded results or loss of detail.
-- Parameters:
-- reloid: oid of the input table. It must be a cartodbfy'ed table.
-- Return value: Z level as an integer
CREATE OR REPLACE FUNCTION _CDB_Feature_Density_Ref_Z_Strategy(reloid REGCLASS)
RETURNS INTEGER
AS $$
DECLARE
lim FLOAT8 := 500; -- TODO: determine/parameterize this
nz integer := 4;
fd FLOAT8;
c FLOAT8;
BEGIN
-- Compute fd as an estimation of the (maximum) number
-- of features per unit of tile area (in webmercator squared meters)
SELECT _CDB_Feature_Density(reloid, nz) INTO fd;
-- lim maximum number of (desiderable) features per tile
-- we have c = 2*Pi*R = CDB_XYZ_Resolution(-8) (earth circumference)
-- ta(z): tile area = power(c*power(2,z), 2) = c*c*power(2,2*z)
-- => fd*ta(z) if the average number of features per tile at level z
-- find minimum z so that fd*ta(z) <= lim
-- compute a rough 'feature density' value
SELECT CDB_XYZ_Resolution(-8) INTO c;
RETURN ceil(log(2.0, (c*c*fd/lim)::numeric)/2);
END;
$$ LANGUAGE PLPGSQL STABLE;
-- Overview table name for a given Z level and base dataset or overview table
-- Scope: private.
-- Parameters:
-- ref reference table (can be the base table of the dataset or an existing
-- overview) from which the overview is being generated.
-- ref_z Z level of the reference table
-- overview_z Z level of the overview to be named, must be smaller than ref_z
-- Return value: the name to be used for the overview. The name is always
-- unqualified (does not include a schema name).
CREATE OR REPLACE FUNCTION _CDB_Overview_Name(ref REGCLASS, ref_z INTEGER, overview_z INTEGER)
RETURNS TEXT
AS $$
DECLARE
schema_name TEXT;
base TEXT;
suffix TEXT;
is_overview BOOLEAN;
BEGIN
SELECT * FROM _cdb_split_table_name(ref) INTO schema_name, base;
SELECT _CDB_OverviewBaseTableName(base) INTO base;
RETURN _CDB_OverviewTableName(base, overview_z);
END
$$ LANGUAGE PLPGSQL IMMUTABLE;
-- Sampling reduction method.
-- Valid for any kind of geometry.
-- Scope: private.
-- reloid original table (can be the base table of the dataset or an existing
-- overview) from which the overview is being generated.
-- ref_z Z level assigned to the original table
-- overview_z Z level of the overview to be generated, must be smaller than ref_z
-- Return value: Name of the generated overview table
CREATE OR REPLACE FUNCTION _CDB_Sampling_Reduce_Strategy(reloid REGCLASS, ref_z INTEGER, overview_z INTEGER)
RETURNS REGCLASS
AS $$
DECLARE
overview_rel TEXT;
fraction FLOAT8;
base_name TEXT;
class_info RECORD;
num_samples INTEGER;
BEGIN
overview_rel := _CDB_Overview_Name(reloid, ref_z, overview_z);
fraction := power(2, 2*(overview_z - ref_z));
-- FIXME: handle schema name for overview_rel if reloid requires it
EXECUTE Format('DROP TABLE IF EXISTS %I CASCADE;', overview_rel);
-- Estimate number of rows
SELECT reltuples, relpages FROM pg_class INTO STRICT class_info
WHERE oid = reloid::oid;
IF class_info.relpages < 2 OR fraction > 0.5 THEN
-- We'll avoid possible CDB_RandomTids problems
EXECUTE Format('
CREATE TABLE %I AS SELECT * FROM %s WHERE random() < %s;
', overview_rel, reloid, fraction);
ELSE
num_samples := ceil(class_info.reltuples*fraction);
EXECUTE Format('
CREATE TABLE %1$I AS SELECT * FROM %2$s
WHERE ctid = ANY (
ARRAY[
(SELECT CDB_RandomTids(''%2$s'', %3$s))
]
);
', overview_rel, reloid, num_samples);
END IF;
RETURN overview_rel;
END;
$$ LANGUAGE PLPGSQL;
-- Register new overview table (post-creation chores)
-- Scope: private
-- Parameters:
-- dataset: oid of the input dataset table, It must be a cartodbfy'ed table.
-- overview_table: oid of the overview table to be registered.
-- overview_z: intended Z level for the overview table
-- This function is declared SECURITY DEFINER so it executes with the privileges
-- of the function creator to have a chance to alter the privileges of the
-- overview table to match those of the dataset. It will only perform any change
-- if the overview table belgons to the same scheme as the dataset and it
-- matches the scheme naming for overview tables.
CREATE OR REPLACE FUNCTION _CDB_Register_Overview(dataset REGCLASS, overview_table REGCLASS, overview_z INTEGER)
RETURNS VOID
AS $$
DECLARE
sql TEXT;
table_owner TEXT;
dataset_scheme TEXT;
dataset_name TEXT;
overview_scheme TEXT;
overview_name TEXT;
BEGIN
-- This function will only register a table as an overview table if it matches
-- the overviews naming scheme for the dataset and z level and the table belongs
-- to the same scheme as the the dataset
SELECT * FROM _cdb_split_table_name(dataset) INTO dataset_scheme, dataset_name;
SELECT * FROM _cdb_split_table_name(overview_table) INTO overview_scheme, overview_name;
IF dataset_scheme = overview_scheme AND
overview_name = _CDB_OverviewTableName(dataset_name, overview_z) THEN
-- preserve the owner of the base table
SELECT u.usename
FROM pg_catalog.pg_class c JOIN pg_catalog.pg_user u ON (c.relowner=u.usesysid)
WHERE c.relname = dataset::text
INTO table_owner;
EXECUTE Format('ALTER TABLE IF EXISTS %s OWNER TO %I;', overview_table::text, table_owner);
-- preserve the table privileges
UPDATE pg_class c_to
SET relacl = c_from.relacl
FROM pg_class c_from
WHERE c_from.oid = dataset
AND c_to.oid = overview_table;
PERFORM _CDB_Add_Indexes(overview_table);
-- TODO: If metadata about existing overviews is to be stored
-- it should be done here (CDB_Overviews would consume such metadata)
END IF;
END
$$ LANGUAGE PLPGSQL SECURITY DEFINER;
-- Dataset attributes (column names other than the
-- CartoDB primary key and geometry columns) which should be aggregated
-- in aggregated overviews.
-- Scope: private.
-- Parameters
-- reloid: oid of the input table. It must be a cartodbfy'ed table.
-- Return value: set of attribute names
CREATE OR REPLACE FUNCTION _CDB_Aggregable_Attributes(reloid REGCLASS)
RETURNS SETOF information_schema.sql_identifier
AS $$
SELECT c FROM CDB_ColumnNames(reloid) c, _CDB_Columns() cdb
WHERE c NOT IN (
cdb.pkey, cdb.geomcol, cdb.mercgeomcol
)
$$ LANGUAGE SQL STABLE;
-- List of dataset attributes to be aggregated in aggregated overview
-- as a comma-separated SQL expression.
-- Scope: private.
-- Parameters
-- reloid: oid of the input table. It must be a cartodbfy'ed table.
-- Return value: SQL subexpression as text
CREATE OR REPLACE FUNCTION _CDB_Aggregable_Attributes_Expression(reloid REGCLASS)
RETURNS TEXT
AS $$
DECLARE
attr_list TEXT;
BEGIN
SELECT string_agg(s.c, ',') FROM (
SELECT * FROM _CDB_Aggregable_Attributes(reloid) c
) AS s INTO attr_list;
RETURN attr_list;
END
$$ LANGUAGE PLPGSQL STABLE;
-- SQL Aggregation expression for a datase attribute
-- Scope: private.
-- Parameters
-- reloid: oid of the input table. It must be a cartodbfy'ed table.
-- column_name: column to be aggregated
-- table_alias: (optional) table qualifier for the column to be aggregated
-- Return SQL subexpression as text with aggregated attribute aliased
-- with its original name.
CREATE OR REPLACE FUNCTION _CDB_Attribute_Aggregation_Expression(reloid REGCLASS, column_name TEXT, table_alias TEXT DEFAULT '')
RETURNS TEXT
AS $$
DECLARE
column_type TEXT;
qualified_column TEXT;
BEGIN
IF table_alias <> '' THEN
qualified_column := Format('%I.%I', table_alias, column_name);
ELSE
qualified_column := Format('%I', column_name);
END IF;
column_type := CDB_ColumnType(reloid, column_name);
CASE column_type
WHEN 'double precision', 'real', 'integer', 'bigint' THEN
RETURN Format('AVG(%s)::' || column_type, qualified_column);
WHEN 'text' THEN
-- TODO: we could define a new aggregate function that returns distinct
-- separated values with a limit, adding ellipsis if more values existed
-- e.g. with '/' as separator and a limit of three:
-- 'A', 'B', 'A', 'C', 'D' => 'A/B/C/...'
-- Other ideas: if value is unique then use it, otherwise use something
-- like '*' or '(varies)' or '(multiple values)', or NULL
-- Using 'string_agg(' || qualified_column || ',''/'')'
-- here causes
RETURN 'CASE count(*) WHEN 1 THEN MIN(' || qualified_column || ') ELSE NULL END::' || column_type;
ELSE
RETURN 'CASE count(*) WHEN 1 THEN MIN(' || qualified_column || ') ELSE NULL END::' || column_type;
END CASE;
END
$$ LANGUAGE PLPGSQL IMMUTABLE;
-- List of dataset aggregated attributes as a comma-separated SQL expression.
-- Scope: private.
-- Parameters
-- reloid: oid of the input table. It must be a cartodbfy'ed table.
-- table_alias: (optional) table qualifier for the columns to be aggregated
-- Return value: SQL subexpression as text
CREATE OR REPLACE FUNCTION _CDB_Aggregated_Attributes_Expression(reloid REGCLASS, table_alias TEXT DEFAULT '')
RETURNS TEXT
AS $$
DECLARE
attr_list TEXT;
BEGIN
SELECT string_agg(_CDB_Attribute_Aggregation_Expression(reloid, s.c, table_alias) || Format(' AS %s', s.c), ',')
FROM (
SELECT * FROM _CDB_Aggregable_Attributes(reloid) c
) AS s INTO attr_list;
RETURN attr_list;
END
$$ LANGUAGE PLPGSQL STABLE;
-- Array of geometry types detected in a cartodbfied table
-- For effciency only look at a limited number of rwos.
-- Parameters
-- reloid: oid of the input table. It must be a cartodbfy'ed table.
-- Return value: array of geometry type names
CREATE OR REPLACE FUNCTION _CDB_GeometryTypes(reloid REGCLASS)
RETURNS TEXT[]
AS $$
DECLARE
gtypes TEXT[];
BEGIN
EXECUTE Format('
SELECT array_agg(DISTINCT ST_GeometryType(the_geom)) FROM (
SELECT the_geom FROM %s
WHERE (the_geom is not null) LIMIT 10
) as geom_types
', reloid)
INTO gtypes;
RETURN gtypes;
END
$$ LANGUAGE PLPGSQL STABLE;
-- Experimental Overview reduction method for point datasets.
-- It clusters the points using a grid, then aggregates the point in each
-- cluster into a point at the centroid of the clustered records.
-- Scope: private.
-- Parameters:
-- reloid original table (can be the base table of the dataset or an existing
-- overview) from which the overview is being generated.
-- ref_z Z level assigned to the original table
-- overview_z Z level of the overview to be generated, must be smaller than ref_z
-- Return value: Name of the generated overview table
CREATE OR REPLACE FUNCTION _CDB_GridCluster_Reduce_Strategy(reloid REGCLASS, ref_z INTEGER, overview_z INTEGER)
RETURNS REGCLASS
AS $$
DECLARE
overview_rel TEXT;
reduction FLOAT8;
base_name TEXT;
grid_px FLOAT8 = 7.5; -- Grid size in pixels at Z level overview_z
grid_m FLOAT8;
aggr_attributes TEXT;
attributes TEXT;
columns TEXT;
gtypes TEXT[];
BEGIN
SELECT _CDB_GeometryTypes(reloid) INTO gtypes;
IF array_upper(gtypes, 1) <> 1 OR gtypes[1] <> 'ST_Point' THEN
-- This strategy only supports datasets with point geomety
RETURN NULL;
RETURN 'x';
END IF;
--TODO: check applicability: geometry type, minimum number of points...
overview_rel := _CDB_Overview_Name(reloid, ref_z, overview_z);
-- compute grid cell size using the overview_z dimension...
SELECT CDB_XYZ_Resolution(overview_z)*grid_px INTO grid_m;
attributes := _CDB_Aggregable_Attributes_Expression(reloid);
aggr_attributes := _CDB_Aggregated_Attributes_Expression(reloid);
IF attributes <> '' THEN
attributes := ', ' || attributes;
END IF;
IF aggr_attributes <> '' THEN
aggr_attributes := aggr_attributes || ', ';
END IF;
-- compute the resulting columns in the same order as in the base table
-- cartodb_id,
-- ST_Transform(ST_SetSRID(ST_MakePoint(sx/n, sy/n), 3857), 4326) AS the_geom,
-- ST_SetSRID(ST_MakePoint(sx/n, sy/n), 3857) AS the_geom_webmercator
-- %4$s
WITH cols AS (
SELECT
CASE c
WHEN 'cartodb_id' THEN 'cartodb_id'
WHEN 'the_geom' THEN
'ST_Transform(ST_SetSRID(ST_MakePoint(sx/n, sy/n), 3857), 4326) AS the_geom'
WHEN 'the_geom_webmercator' THEN
'ST_SetSRID(ST_MakePoint(sx/n, sy/n), 3857) AS the_geom_webmercator'
ELSE c
END AS column
FROM CDB_ColumnNames(reloid) c
)
SELECT string_agg(s.column, ',') FROM (
SELECT * FROM cols
) AS s INTO columns;
-- FIXME: handle schema name for overview_rel if reloid requires it
EXECUTE Format('DROP TABLE IF EXISTS %I CASCADE;', overview_rel);
-- Now we cluster the data using a grid of size grid_m
-- and selecte the centroid (average coordinates) of each cluster.
-- If we had a selected numeric attribute of interest we could use it
-- as a weight for the average coordinates.
EXECUTE Format('
CREATE TABLE %3$I AS
WITH clusters AS (
SELECT
%5$s
count(*) AS n,
SUM(ST_X(f.the_geom_webmercator)) AS sx,
SUM(ST_Y(f.the_geom_webmercator)) AS sy,
Floor(ST_X(f.the_geom_webmercator)/%2$s)::int AS gx,
Floor(ST_Y(f.the_geom_webmercator)/%2$s)::int AS gy,
MIN(cartodb_id) AS cartodb_id
FROM %1$s f
GROUP BY gx, gy
)
SELECT %6$s FROM clusters
', reloid::text, grid_m, overview_rel, attributes, aggr_attributes, columns);
RETURN overview_rel;
END;
$$ LANGUAGE PLPGSQL;
-- Create overview tables for a dataset.
-- Scope: public
-- Parameters:
-- reloid: oid of the input table. It must be a cartodbfy'ed table with
-- vector features.
-- refscale_strategy: function that computes the reference Z of the dataset
-- reduce_strategy: function that generates overviews from a base table
-- or higher level overview. The overview tables
-- created by the strategy must have the same columns
-- as the base table and in the same order.
-- Return value: Array with the names of the generated overview tables
CREATE OR REPLACE FUNCTION CDB_CreateOverviews(
reloid REGCLASS,
refscale_strategy regproc DEFAULT '_CDB_Feature_Density_Ref_Z_Strategy'::regproc,
reduce_strategy regproc DEFAULT '_CDB_GridCluster_Reduce_Strategy'::regproc
)
RETURNS text[]
AS $$
DECLARE
ref_z integer;
overviews_z integer[];
base_z integer;
base_rel REGCLASS;
overview_z integer;
overview_tables REGCLASS[];
overviews_step integer := 1;
BEGIN
-- Determine the referece zoom level
EXECUTE 'SELECT ' || quote_ident(refscale_strategy::text) || Format('(''%s'');', reloid) INTO ref_z;
-- Determine overlay zoom levels
-- TODO: should be handled by the refscale_strategy?
overview_z := ref_z - 1;
WHILE overview_z >= 0 LOOP
SELECT array_append(overviews_z, overview_z) INTO overviews_z;
overview_z := overview_z - overviews_step;
END LOOP;
-- Create overlay tables
base_z := ref_z;
base_rel := reloid;
FOREACH overview_z IN ARRAY overviews_z LOOP
EXECUTE 'SELECT ' || quote_ident(reduce_strategy::text) || Format('(''%s'', %s, %s);', base_rel, base_z, overview_z) INTO base_rel;
IF base_rel IS NULL THEN
EXIT;
END IF;
base_z := overview_z;
PERFORM _CDB_Register_Overview(reloid, base_rel, base_z);
SELECT array_append(overview_tables, base_rel) INTO overview_tables;
END LOOP;
RETURN overview_tables;
END;
$$ LANGUAGE PLPGSQL;

View File

@@ -5,24 +5,9 @@
CREATE OR REPLACE FUNCTION CDB_XYZ_Resolution(z INTEGER)
RETURNS FLOAT8
AS $$
DECLARE
earth_circumference FLOAT8;
tile_size INTEGER;
full_resolution FLOAT8;
BEGIN
-- Earth equatorial circumference in meters (according to wikipedia)
earth_circumference := 40075017;
-- Size of each tile in pixels (1:1 aspect ratio)
tile_size := 256;
full_resolution := earth_circumference/tile_size;
RETURN full_resolution / (power(2,z));
END
$$ LANGUAGE 'plpgsql' IMMUTABLE STRICT;
-- circumference divided by 256 is z0 resolution, then divide by 2^z
SELECT 40075017.0 / 256 / power(2, z);
$$ LANGUAGE SQL IMMUTABLE STRICT;
-- }
-- {

View File

@@ -1,10 +1,9 @@
CREATE OR REPLACE FUNCTION cartodb.CDB_ZoomFromScale(scaleDenominator numeric) RETURNS int AS $$
BEGIN
CASE
WHEN scaleDenominator > 1000000000 THEN RETURN 0;
WHEN scaleDenominator <= 1000000000 AND scaleDenominator > 500000000 THEN RETURN 1;
WHEN scaleDenominator <= 500000000 AND scaleDenominator > 200000000 THEN RETURN 2;
WHEN scaleDenominator <= 200000000 AND scaleDenominator > 100000000 THEN RETURN 3;
WHEN scaleDenominator > 500000000 THEN RETURN 0;
WHEN scaleDenominator <= 500000000 AND scaleDenominator > 200000000 THEN RETURN 1;
WHEN scaleDenominator <= 200000000 AND scaleDenominator > 100000000 THEN RETURN 2;
WHEN scaleDenominator <= 100000000 AND scaleDenominator > 50000000 THEN RETURN 3;
WHEN scaleDenominator <= 50000000 AND scaleDenominator > 25000000 THEN RETURN 4;
WHEN scaleDenominator <= 25000000 AND scaleDenominator > 12500000 THEN RETURN 5;

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@@ -0,0 +1 @@
../scripts-available/CDB_Overviews.sql

View File

@@ -0,0 +1,33 @@
SET client_min_messages TO error;
\set VERBOSITY default
\i test/overviews/fixtures.sql
SELECT _CDB_Aggregable_Attributes_Expression('base_bare_t'::regclass);
SELECT _CDB_Aggregated_Attributes_Expression('base_bare_t'::regclass);
SELECT _CDB_Aggregated_Attributes_Expression('base_bare_t'::regclass, 'tab');
SELECT CDB_CreateOverviews('base_bare_t'::regclass);
SELECT count(*) FROM _vovw_5_base_bare_t;
SELECT _CDB_Aggregable_Attributes_Expression('base_t'::regclass);
SELECT _CDB_Aggregated_Attributes_Expression('base_t'::regclass);
SELECT _CDB_Aggregated_Attributes_Expression('base_t'::regclass, 'tab');
SELECT CDB_CreateOverviews('base_t'::regclass);
SELECT count(*) FROM _vovw_5_base_t;
SELECT CDB_CreateOverviews('polyg_t'::regclass);
SELECT CDB_Overviews('base_t'::regclass);
SELECT CDB_Overviews(ARRAY['base_t'::regclass, 'base_bare_t'::regclass]);
SELECT CDB_Overviews('polyg_t'::regclass);
SELECT CDB_DropOverviews('base_bare_t'::regclass);
SELECT CDB_DropOverviews('base_t'::regclass);
SELECT count(*) FROM _vovw_5_base_t;
DROP TABLE base_bare_t;
DROP TABLE base_t;
DROP TABLE polyg_t;

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@@ -0,0 +1,44 @@
SET
CREATE TABLE
INSERT 0 1114
CREATE TABLE
INSERT 0 1114
CREATE TABLE
INSERT 0 5
{_vovw_5_base_bare_t,_vovw_4_base_bare_t,_vovw_3_base_bare_t,_vovw_2_base_bare_t,_vovw_1_base_bare_t,_vovw_0_base_bare_t}
125
number,int_number,name,start
AVG(number)::double precision AS number,AVG(int_number)::integer AS int_number,CASE count(*) WHEN 1 THEN MIN(name) ELSE NULL END::text AS name,CASE count(*) WHEN 1 THEN MIN(start) ELSE NULL END::date AS start
AVG(tab.number)::double precision AS number,AVG(tab.int_number)::integer AS int_number,CASE count(*) WHEN 1 THEN MIN(tab.name) ELSE NULL END::text AS name,CASE count(*) WHEN 1 THEN MIN(tab.start) ELSE NULL END::date AS start
{_vovw_5_base_t,_vovw_4_base_t,_vovw_3_base_t,_vovw_2_base_t,_vovw_1_base_t,_vovw_0_base_t}
125
(base_t,0,_vovw_0_base_t)
(base_t,1,_vovw_1_base_t)
(base_t,2,_vovw_2_base_t)
(base_t,3,_vovw_3_base_t)
(base_t,4,_vovw_4_base_t)
(base_t,5,_vovw_5_base_t)
(base_bare_t,0,_vovw_0_base_bare_t)
(base_bare_t,1,_vovw_1_base_bare_t)
(base_bare_t,2,_vovw_2_base_bare_t)
(base_bare_t,3,_vovw_3_base_bare_t)
(base_bare_t,4,_vovw_4_base_bare_t)
(base_bare_t,5,_vovw_5_base_bare_t)
(base_t,0,_vovw_0_base_t)
(base_t,1,_vovw_1_base_t)
(base_t,2,_vovw_2_base_t)
(base_t,3,_vovw_3_base_t)
(base_t,4,_vovw_4_base_t)
(base_t,5,_vovw_5_base_t)
ERROR: relation "_vovw_5_base_t" does not exist
LINE 1: SELECT count(*) FROM _vovw_5_base_t;
^
DROP TABLE
DROP TABLE
DROP TABLE

2242
test/overviews/fixtures.sql Normal file

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@@ -0,0 +1,43 @@
# Ruby script to generate test/overviews/fixtures.sql for testing overviews
# Generated tables:
# * base_bare_t -- points without attributes (only PK, geometries)
NUM_CLUSTERS = 128
MAX_PER_CLUSTER = 16
CLUSTER_RADIUS = 1E-3
MIN_X = -10.0
MAX_X = 10.0
MIN_Y = 30.0
MAX_Y = 40.0
ATTRIBUTES = "number double precision, int_number integer, name text, start date"
id = 0
POINTS = (0...NUM_CLUSTERS).map{
x = MIN_X + rand()*(MAX_X - MIN_X)
y = MIN_Y + rand()*(MAX_Y - MIN_Y)
(0..rand(MAX_PER_CLUSTER)).map{
id += 1
{
id: id,
x: (x + rand()*CLUSTER_RADIUS).round(6),
y: (y + rand()*CLUSTER_RADIUS).round(6)
}
}
}.flatten
values = POINTS.map{ |point|
"#{point[:id]}, 'SRID=4326;POINT(#{point[:x]} #{point[:y]})'::geometry, ST_Transform('SRID=4326;POINT(#{point[:x]} #{point[:y]})'::geometry, 3857)"
}
File.open('fixtures.sql', 'w') do |sql|
sql.puts "-- bare table with no attribute columns"
sql.puts "CREATE TABLE base_bare_t (cartodb_id integer, the_geom geometry, the_geom_webmercator geometry);"
sql.puts "INSERT INTO base_bare_t VALUES"
sql.puts values.map{|v| "(#{v})"}.join(",\n") + ";"
sql.puts "-- table with attributes"
sql.puts "CREATE TABLE base_t (cartodb_id integer, the_geom geometry, the_geom_webmercator geometry, #{ATTRIBUTES});"
sql.puts "INSERT INTO base_t VALUES"
sql.puts values.map{|v| "(#{v})"}.join(",\n") + ";"
end