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doc/19_contour.md
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doc/19_contour.md
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## Contour maps
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Function to generate a contour map from an scatter dataset of points, using one of three methos:
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* [Nearest neighbor](https://en.wikipedia.org/wiki/Nearest-neighbor_interpolation)
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* [Barycentric](https://en.wikipedia.org/wiki/Barycentric_coordinate_system)
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* [IDW](https://en.wikipedia.org/wiki/Inverse_distance_weighting)
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### CDB_Contour (geom geometry[], values numeric[], resolution integer, buffer numeric, method, classmethod integer, steps integer)
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#### Arguments
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| Name | Type | Description |
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|------|------|-------------|
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| geom | geometry[] | Array of points's geometries |
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| values | numeric[] | Array of points' values for the param under study|
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| resolution | integer | Size in meters of the cells in the grid|
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| buffer | numeric | Value between 0 and 1 for spatial buffer of the set of points
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| method | integer | 0:nearest neighbor, 1: barycentric, 2: IDW|
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| classmethod | integer | 0:equals, 1: heads&tails, 2:jenks, 3:quantiles |
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| steps | integer | Number of steps in the classification|
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### Returns
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Returns a table object
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| Name | Type | Description |
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|------|------|-------------|
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| the_geom | geometry | Geometries of the classified contour map|
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| avg_value | numeric | Avg value of the area|
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| min_value | numeric | Min value of the area|
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| max_value | numeric | Max value of the areal|
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| bin | integer | Index of the class of the area|
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#### Example Usage
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```sql
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WITH a AS (
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SELECT
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ARRAY[800, 700, 600, 500, 400, 300, 200, 100]::numeric[] AS vals,
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ARRAY[ST_GeomFromText('POINT(2.1744 41.403)'),ST_GeomFromText('POINT(2.1228 41.380)'),ST_GeomFromText('POINT(2.1511 41.374)'),ST_GeomFromText('POINT(2.1528 41.413)'),ST_GeomFromText('POINT(2.165 41.391)'),ST_GeomFromText('POINT(2.1498 41.371)'),ST_GeomFromText('POINT(2.1533 41.368)'),ST_GeomFromText('POINT(2.131386 41.41399)')] AS g
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)
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SELECT
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foo.*
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FROM
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a,
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CDB_contour(a.g, a.vals, 500, 0.0, 1,3,5) foo;
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```
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191
src/pg/sql/19_contour.sql
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src/pg/sql/19_contour.sql
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CREATE OR REPLACE FUNCTION CDB_Contour(
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IN geomin geometry[],
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IN colin numeric[],
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IN resolution integer,
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IN buffer numeric,
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IN intmethod integer,
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IN classmethod integer,
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IN steps integer
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)
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RETURNS TABLE(
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the_geom geometry,
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bin integer,
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min_value numeric,
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max_value numeric,
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avg_value numeric
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) AS $$
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DECLARE
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cell numeric;
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tin geometry[];
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BEGIN
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-- calc the cell size in web mercator units
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WITH center as (
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SELECT ST_centroid(ST_Collect(geomin)) as c
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)
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SELECT
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round(resolution / cos(ST_y(c) * pi()/180))
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INTO cell
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FROM center;
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-- raise notice 'Resol: %', cell;
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-- we don't have iterative barycentric interpolation in CDB_interpolation,
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-- and it's a costy function, so let's make a custom one here till
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-- we update the code
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-- tin := ARRAY[]::geometry[];
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IF intmethod=1 THEN
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WITH
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a as (SELECT unnest(geomin) AS e),
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b as (SELECT ST_DelaunayTriangles(ST_Collect(a.e),0.001, 0) AS t FROM a),
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c as (SELECT (ST_Dump(t)).geom as v FROM b)
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SELECT array_agg(v) INTO tin FROM c;
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END IF;
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-- Delaunay stuff performed just ONCE!!
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-- magic
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RETURN QUERY
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WITH
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convexhull as (
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SELECT
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ST_ConvexHull(ST_Collect(geomin)) as g,
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buffer * |/ st_area(ST_ConvexHull(ST_Collect(geomin)))/PI() as r
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),
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envelope as (
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SELECT
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st_expand(a.g, a.r) as e
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FROM convexhull a
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),
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envelope3857 as(
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SELECT
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ST_Transform(e, 3857) as geom
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FROM envelope
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),
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grid as(
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SELECT
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ST_Transform(CDB_RectangleGrid(geom, cell, cell), 4326) as geom
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FROM envelope3857
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),
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interp as(
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SELECT
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geom,
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CASE
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WHEN intmethod=1 THEN cdb_crankshaft._interp_in_tin(geomin, colin, tin, ST_Centroid(geom))
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ELSE db_crankshaft.CDB_SpatialInterpolation(geomin, colin, ST_Centroid(geom), intmethod)
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END as val
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FROM grid
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),
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classes as(
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SELECT CASE
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WHEN classmethod = 0 THEN
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CDB_EqualIntervalBins(array_agg(val), steps)
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WHEN classmethod = 1 THEN
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CDB_HeadsTailsBins(array_agg(val), steps)
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WHEN classmethod = 2 THEN
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CDB_JenksBins(array_agg(val), steps)
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ELSE
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CDB_QuantileBins(array_agg(val), steps)
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END as b
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FROM interp
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where val is not null
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),
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classified as(
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SELECT
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i.*,
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width_bucket(i.val, c.b) as bucket
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FROM interp i left join classes c
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ON 1=1
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),
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classified2 as(
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SELECT
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geom,
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val,
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CASE
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WHEN bucket = steps THEN bucket - 1
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ELSE bucket
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END as b
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FROM classified
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),
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final as(
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SELECT
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st_union(geom) as the_geom,
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b as bin,
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min(val) as min_value,
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max(val) as max_value,
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avg(val) as avg_value
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FROM classified2
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GROUP BY bin
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)
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SELECT
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*
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FROM final
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where final.bin is not null
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;
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END;
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$$ language plpgsql;
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-- =====================================================================
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-- Interp in grid, so we can use barycentric with a precalculated tin (NNI)
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-- =====================================================================
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CREATE OR REPLACE FUNCTION cdb_crankshaft._interp_in_tin(
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IN geomin geometry[],
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IN colin numeric[],
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IN tin geometry[],
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IN point geometry
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)
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RETURNS numeric AS
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$$
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DECLARE
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g geometry;
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vertex geometry[];
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sg numeric;
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sa numeric;
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sb numeric;
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sc numeric;
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va numeric;
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vb numeric;
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vc numeric;
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output numeric;
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BEGIN
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-- get the cell the point is within
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WITH
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a as (SELECT unnest(tin) as v),
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b as (SELECT v FROM a WHERE ST_Within(point, v))
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SELECT v INTO g FROM b;
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-- if we're out of the data realm,
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-- return null
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IF g is null THEN
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RETURN null;
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END IF;
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-- vertex of the selected cell
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WITH a AS (
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SELECT (ST_DumpPoints(g)).geom AS v
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)
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SELECT array_agg(v) INTO vertex FROM a;
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-- retrieve the value of each vertex
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WITH a AS(SELECT unnest(geomin) as geo, unnest(colin) as c)
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SELECT c INTO va FROM a WHERE ST_Equals(geo, vertex[1]);
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WITH a AS(SELECT unnest(geomin) as geo, unnest(colin) as c)
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SELECT c INTO vb FROM a WHERE ST_Equals(geo, vertex[2]);
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WITH a AS(SELECT unnest(geomin) as geo, unnest(colin) as c)
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SELECT c INTO vc FROM a WHERE ST_Equals(geo, vertex[3]);
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-- calc the areas
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SELECT
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ST_area(g),
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ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point, vertex[2], vertex[3], point]))),
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ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point, vertex[1], vertex[3], point]))),
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ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point,vertex[1],vertex[2], point]))) INTO sg, sa, sb, sc;
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output := (coalesce(sa,0) * coalesce(va,0) + coalesce(sb,0) * coalesce(vb,0) + coalesce(sc,0) * coalesce(vc,0)) / coalesce(sg,1);
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RETURN output;
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END;
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$$
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language plpgsql;
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2
src/pg/test/expected/19_contour_test.out
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2
src/pg/test/expected/19_contour_test.out
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SET client_min_messages TO WARNING;
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\set ECHO none
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14
src/pg/test/sql/19_contour_test.sql
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14
src/pg/test/sql/19_contour_test.sql
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SET client_min_messages TO WARNING;
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\set ECHO none
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\pset format unaligned
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WITH a AS (
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SELECT
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ARRAY[800, 700, 600, 500, 400, 300, 200, 100]::numeric[] AS vals,
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ARRAY[ST_GeomFromText('POINT(2.1744 41.403)'),ST_GeomFromText('POINT(2.1228 41.380)'),ST_GeomFromText('POINT(2.1511 41.374)'),ST_GeomFromText('POINT(2.1528 41.413)'),ST_GeomFromText('POINT(2.165 41.391)'),ST_GeomFromText('POINT(2.1498 41.371)'),ST_GeomFromText('POINT(2.1533 41.368)'),ST_GeomFromText('POINT(2.131386 41.41399)')] AS g
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)
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SELECT
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foo.*
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FROM
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a,
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CDB_contour(a.g, a.vals, 500, 0.0, 1,3,5) foo;
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