abelvm
8 years ago
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## Spacial interpolation
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Function to interpolate a numeric attribute of a point in a 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_SpatialInterpolation (query text, point geometry, method integer DEFAULT 1, p1 integer DEFAULT 0, ps integer DEFAULT 0)
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#### Arguments
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| Name | Type | Description |
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|------|------|-------------|
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| query | text | query that returns at least `the_geom` and a numeric value as `attrib` |
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| point | geometry | The target point to calc the value |
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| method | integer | 0:nearest neighbor, 1: barycentric, 2: IDW|
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| p1 | integer | IDW: limit the number of neighbors, 0->no limit|
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| p2 | integer | IDW: order of distance decay, 0-> order 1|
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### CDB_SpatialInterpolation (geom geometry[], values numeric[], point geometry, method integer DEFAULT 1, p1 integer DEFAULT 0, ps integer DEFAULT 0)
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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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| point | geometry | The target point to calc the value |
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| method | integer | 0:nearest neighbor, 1: barycentric, 2: IDW|
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| p1 | integer | IDW: limit the number of neighbors, 0->no limit|
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| p2 | integer | IDW: order of distance decay, 0-> order 1|
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### Returns
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| Column Name | Type | Description |
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|-------------|------|-------------|
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| value | numeric | Interpolated value at the given point, `-888.888` if the given point is out of the boundaries of the source points set |
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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_agg(the_geom) as geomin,
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array_agg(temp::numeric) as colin
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from table_4804232032
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)
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SELECT CDB_SpatialInterpolation(geomin, colin, CDB_latlng(41.38, 2.15),1) FROM a;
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```
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@ -0,0 +1,127 @@
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-- 0: nearest neighbor
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-- 1: barymetric
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-- 2: IDW
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CREATE OR REPLACE FUNCTION CDB_SpatialInterpolation(
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IN query text,
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IN point geometry,
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IN method integer DEFAULT 1,
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IN p1 numeric DEFAULT 0,
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IN p2 numeric DEFAULT 0
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)
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RETURNS numeric AS
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$$
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DECLARE
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gs geometry[];
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vs numeric[];
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BEGIN
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EXECUTE 'WITH a AS('||query||') SELECT array_agg(the_geom), array_agg(attrib) FROM a' INTO gs, vs;
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RETURN QUERY SELECT CDB_SpatialInterpolation(gs, vs, point, method, p1,p2) FROM a;
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END;
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$$
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language plpgsql IMMUTABLE;
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CREATE OR REPLACE FUNCTION CDB_SpatialInterpolation(
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IN geomin geometry[],
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IN colin numeric[],
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IN point geometry,
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IN method integer DEFAULT 1,
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IN p1 numeric DEFAULT 0,
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IN p2 numeric DEFAULT 0
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)
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RETURNS numeric AS
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$$
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DECLARE
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gs geometry[];
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vs numeric[];
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gs2 geometry[];
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vs2 numeric[];
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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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output := -999.999;
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-- nearest
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IF method = 0 THEN
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WITH a as (SELECT unnest(geomin) as g, unnest(colin) as v)
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SELECT a.v INTO output FROM a ORDER BY point<->a.g LIMIT 1;
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RETURN output;
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-- barymetric
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ELSIF method = 1 THEN
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WITH 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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d as (SELECT v FROM c WHERE ST_Within(point, v))
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SELECT v INTO g FROM d;
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IF g is null THEN
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-- out of the realm of the input data
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RETURN -888.888;
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END IF;
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-- vertex of the selected cell
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WITH a AS (SELECT (ST_DumpPoints(g)).geom AS v)
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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(vertex) 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(vertex) 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(vertex) 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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SELECT ST_area(g), ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point, vertex[2], vertex[3], point]))), ST_area(ST_MakePolygon(ST_MakeLine(ARRAY[point, vertex[1], vertex[3], point]))), 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);
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RETURN output;
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-- IDW
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-- p1: limit the number of neighbors, 0->no limit
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-- p2: order of distance decay, 0-> order 1
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ELSIF method = 2 THEN
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IF p2 = 0 THEN
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p2 := 1;
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END IF;
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WITH a as (SELECT unnest(geomin) as g, unnest(colin) as v),
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b as (SELECT a.g, a.v FROM a ORDER BY point<->a.g)
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SELECT array_agg(b.g), array_agg(b.v) INTO gs, vs FROM b;
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IF p1::integer>0 THEN
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gs2:=gs;
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vs2:=vs;
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FOR i IN 1..p1
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LOOP
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gs2 := gs2 || gs[i];
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vs2 := vs2 || vs[i];
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END LOOP;
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ELSE
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gs2:=gs;
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vs2:=vs;
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END IF;
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WITH a as (SELECT unnest(gs2) as g, unnest(vs2) as v),
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b as (
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SELECT
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(1/ST_distance(point, a.g)^p2::integer) as k,
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(a.v/ST_distance(point, a.g)^p2::integer) as f
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FROM a
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)
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SELECT sum(b.f)/sum(b.k) INTO output FROM b;
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RETURN output;
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END IF;
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RETURN -777.777;
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END;
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$$
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language plpgsql IMMUTABLE;
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@ -0,0 +1,4 @@
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cdb_spatialinterpolation
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--------------------------
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780.79470198683925288365
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(1 row)
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@ -0,0 +1,6 @@
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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] 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 CDB_SpatialInterpolation(g, vals, ST_GeomFromText('POINT(2.154 41.37)'),1) FROM a;
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