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add PIA, first commit

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abelvm 2016-07-12 15:48:38 +02:00
parent e84dc30b77
commit cb3a49594d
8 changed files with 164 additions and 252 deletions
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35
doc/09_voronoi.md
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## Spacial interpolation
Function to construct the [Voronoi Diagram](https://en.wikipedia.org/wiki/Voronoi_diagram) from a dataset of scatter points, clipped to the significant area
PostGIS wil include this in future versions ([doc for dev branch](http://postgis.net/docs/manual-dev/ST_Voronoi.html)) and will perform faster for sure, but in the meantime...
### CDB_Voronoi (geom geometry[], buffer numeric DEFAULT 0.5, tolerance numeric DEFAULT 1e-9)
#### Arguments
| Name | Type | Description |
|------|------|-------------|
| geom | geometry[] | Array of points's geometries |
| buffer | numeric | enlargment ratio for the envelope area used for the restraints|
| tolerance | geometry | The target point to calc the value |
### Returns
| Column Name | Type | Description |
|-------------|------|-------------|
| geom | geometry collection | Collection of polygons of the Voronoi cells|
#### Example Usage
```sql
WITH a AS (
SELECT
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 geomin
)
SELECT
CDB_voronoi(geomin, 0.2, 1e-9) as result
FROM a;
```

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doc/13_PIA.md Normal file
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## Pole of inaccessibility (PIA)
Function to find the [PIA](https://en.wikipedia.org/wiki/Pole_of_inaccessibility) from a given polygon and tolerance, following the quadtree approach by [Vladimir Agafonkin](https://github.com/mourner) described [here](https://github.com/mapbox/polylabel)
### CDB_PIA (polygon geometry, tolerance numeric DEFAULT 1.0)
#### Arguments
| Name | Type | Description |
|------|------|-------------|
| polygon | geometry | Target polygon |
| tolerance | numeric | Threshold to decide to take a cell into account |
### Returns
| Column Name | Type | Description |
|-------------|------|-------------|
| point | geometry| Pole of inaccessibility |
#### Example Usage
```sql
with a as(
select st_geomfromtext('POLYGON((-432540.453078056 4949775.20452642,-432329.947920966 4951361.232584,-431245.028163694 4952223.31516671,-429131.071033529 4951768.00415574,-424622.07505895 4952843.13503987,-423688.327170174 4953499.20752423,-424086.294349759 4954968.38274191,-423068.388925945 4954378.63345336,-423387.653225542 4953355.67417084,-420594.869840519 4953781.00230592,-416026.095299382 4951484.06849063,-412483.018546414 4951024.5410983,-410490.399661215 4954502.24032205,-408186.197521284 4956398.91417441,-407627.262358013 4959300.94633864,-406948.770061627 4959874.85407739,-404949.583326472 4959047.74518163,-402570.908447199 4953743.46829807,-400971.358683991 4952193.11680804,-403533.488084088 4949649.89857885,-406335.177028373 4950193.19571096,-407790.456731515 4952391.46015616,-412060.672398345 4950381.2389307,-410716.93482498 4949156.7509561,-408464.162289794 4943912.8940387,-409350.599394983 4942819.84896006,-408087.791091424 4942451.6711778,-407274.045613725 4940572.4807777,-404446.196589102 4939976.71501489,-402422.964843936 4940450.3670813,-401010.654464241 4939054.8061663,-397647.247369412 4940679.80737878,-395658.413346901 4940528.84765185,-395536.852462953 4938829.79565997,-394268.923462818 4938003.7277717,-393388.720249116 4934757.80596815,-392393.301362444 4934326.71675815,-392573.527618037 4932323.40974412,-393464.640141837 4931903.10653605,-393085.597275686 4931094.7353605,-398426.261165985 4929156.87541607,-398261.174361137 4926238.00816416,-394045.059966834 4925765.18668498,-392982.960705174 4926391.81893628,-393090.272694301 4927176.84692181,-391648.240010564 4924626.06386961,-391889.914625075 4923086.14787613,-394345.177314013 4923235.086036,-395550.878718795 4917812.79243978,-399009.463978251 4912927.7157945,-398948.794855767 4911941.91010796,-398092.636652078 4911806.57392519,-401991.601817112 4911722.9204501,-406225.972607907 4914505.47286319,-411104.994569885 4912569.26941163,-412925.513522316 4913030.3608866,-414630.148884835 4914436.69169949,-414207.691417276 4919205.78028405,-418306.141109809 4917994.9580478,-424184.700779621 4918938.12432889,-426816.961458921 4923664.37379373,-420956.324227126 4923381.98014807,-420186.661267781 4924286.48693378,-420943.411166194 4926812.76394433,-419779.45457046 4928527.43466337,-419768.767899344 4930681.94459216,-421911.668097113 4930432.40620397,-423482.386112205 4933451.28047252,-427272.814773717 4934151.56473242,-427144.908678797 4939731.77191996,-428982.125554848 4940522.84445172,-428986.133056516 4942437.17281266,-431237.792396792 4947309.68284815,-432476.889648814 4947791.74800037,-432540.453078056 4949775.20452642))', 3857) as g
)
SELECT st_astext(CDB_PIA(g)) from a;
```

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src/pg/sql/09_voronoi.sql
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CREATE OR REPLACE FUNCTION CDB_voronoi(
IN geomin geometry[],
IN buffer numeric DEFAULT 0.5,
IN tolerance numeric DEFAULT 1e-9
)
RETURNS geometry AS $$
DECLARE
geomout geometry;
BEGIN
WITH
convexhull_1 as (
SELECT
ST_ConvexHull(ST_Collect(geomin)) as g,
buffer * |/ st_area(ST_ConvexHull(ST_Collect(geomin))) as r
),
clipper as(
SELECT
st_buffer(ST_MinimumBoundingCircle(a.g), buffer*a.r) as g
FROM convexhull_1 a
),
env0 as (
SELECT
(st_dumppoints(st_expand(a.g, buffer*a.r))).geom as e
FROM convexhull_1 a
),
env as (
SELECT
array_agg(env0.e) as e
FROM env0
),
sample AS (
SELECT
ST_Collect(geomin || env.e) as geom
FROM env
),
convexhull as (
SELECT
ST_ConvexHull(ST_Collect(geomin)) as cg
),
tin as (
SELECT
ST_Dump(ST_DelaunayTriangles(geom, tolerance, 0)) as gd
FROM
sample
),
tin_polygons as (
SELECT
(gd).Path as id,
(gd).Geom as pg,
ST_Centroid(ST_MinimumBoundingCircle((gd).Geom, 180)) as ct
FROM tin
),
tin_lines as (
SELECT
id,
ST_ExteriorRing(pg) as lg
FROM tin_polygons
),
tin_nodes as (
SELECT
id,
ST_PointN(lg,1) p1,
ST_PointN(lg,2) p2,
ST_PointN(lg,3) p3
FROM tin_lines
),
tin_edges AS (
SELECT
p.id,
UNNEST(ARRAY[
ST_MakeLine(n.p1,n.p2) ,
ST_MakeLine(n.p2,n.p3) ,
ST_MakeLine(n.p3,n.p1)]) as Edge,
ST_Force_2D(_Find_Circle(n.p1,n.p2,n.p3)) as ct ,
CASE WHEN st_distance(p.ct, ST_ExteriorRing(p.pg)) < tolerance THEN
TRUE
ELSE FALSE END AS ctx,
p.pg,
ST_within(p.ct, convexhull.cg) as ctin
FROM
tin_polygons p,
tin_nodes n,
convexhull
WHERE p.id = n.id
),
voro_nodes as (
SELECT
CASE WHEN x.ctx = TRUE THEN
ST_Centroid(x.edge)
ELSE
x.ct
END as xct,
CASE WHEN y.id is null THEN
CASE WHEN x.ctin = TRUE THEN
ST_SetSRID(ST_MakePoint(
ST_X(x.ct) + ((ST_X(ST_Centroid(x.edge)) - ST_X(x.ct)) * (1+buffer)),
ST_Y(x.ct) + ((ST_Y(ST_Centroid(x.edge)) - ST_Y(x.ct)) * (1+buffer))
), ST_SRID(x.ct))
END
ELSE
y.ct
END as yct
FROM
tin_edges x
LEFT OUTER JOIN
tin_edges y
ON x.id <> y.id AND ST_Equals(x.edge, y.edge)
),
voro_edges as(
SELECT
ST_LineMerge(ST_Collect(ST_MakeLine(xct, yct))) as v
FROM
voro_nodes
),
voro_cells as(
SELECT
ST_Polygonize(
ST_Node(
ST_LineMerge(
ST_Union(v, ST_ExteriorRing(
ST_Convexhull(v)
)
)
)
)
) as g
FROM
voro_edges
),
voro_set as(
SELECT
(st_dump(v.g)).geom as g
FROM voro_cells v
)
SELECT
st_collect(ST_intersection(c.g, v.g))
-- ST_intersection(c.g, v.g)
INTO geomout
FROM
voro_set v,
clipper c;
RETURN geomout;
END;
$$ language plpgsql IMMUTABLE;
/** ----------------------------------------------------------------------------------------
* @function : FindCircle
* @precis : Function that determines if three points form a circle. If so a table containing
* centre and radius is returned. If not, a null table is returned.
* @version : 1.0
* @param : p_pt1 : First point in curve
* @param : p_pt2 : Second point in curve
* @param : p_pt3 : Third point in curve
* @return : geometry : In which X,Y ordinates are the centre X, Y and the Z being the radius of found circle
* or NULL if three points do not form a circle.
* @history : Simon Greener - Feb 2012 - Original coding.
* @copyright : Simon Greener @ 2012
* Licensed under a Creative Commons Attribution-Share Alike 2.5 Australia License. (http://creativecommons.org/licenses/by-sa/2.5/au/)
**/
CREATE OR REPLACE FUNCTION _Find_Circle(p_pt1 geometry, p_pt2 geometry, p_pt3 geometry)
RETURNS geometry AS
$BODY$
DECLARE
v_Centre geometry;
v_radius NUMERIC;
v_CX NUMERIC;
v_CY NUMERIC;
v_dA NUMERIC;
v_dB NUMERIC;
v_dC NUMERIC;
v_dD NUMERIC;
v_dE NUMERIC;
v_dF NUMERIC;
v_dG NUMERIC;
BEGIN
IF ( p_pt1 IS NULL OR p_pt2 IS NULL OR p_pt3 IS NULL ) THEN
RAISE EXCEPTION 'All supplied points must be not null.';
RETURN NULL;
END IF;
IF ( ST_GeometryType(p_pt1) <> 'ST_Point' OR
ST_GeometryType(p_pt1) <> 'ST_Point' OR
ST_GeometryType(p_pt1) <> 'ST_Point' ) THEN
RAISE EXCEPTION 'All supplied geometries must be points.';
RETURN NULL;
END IF;
v_dA := ST_X(p_pt2) - ST_X(p_pt1);
v_dB := ST_Y(p_pt2) - ST_Y(p_pt1);
v_dC := ST_X(p_pt3) - ST_X(p_pt1);
v_dD := ST_Y(p_pt3) - ST_Y(p_pt1);
v_dE := v_dA * (ST_X(p_pt1) + ST_X(p_pt2)) + v_dB * (ST_Y(p_pt1) + ST_Y(p_pt2));
v_dF := v_dC * (ST_X(p_pt1) + ST_X(p_pt3)) + v_dD * (ST_Y(p_pt1) + ST_Y(p_pt3));
v_dG := 2.0 * (v_dA * (ST_Y(p_pt3) - ST_Y(p_pt2)) - v_dB * (ST_X(p_pt3) - ST_X(p_pt2)));
-- If v_dG is zero then the three points are collinear and no finite-radius
-- circle through them exists.
IF ( v_dG = 0 ) THEN
RETURN NULL;
ELSE
v_CX := (v_dD * v_dE - v_dB * v_dF) / v_dG;
v_CY := (v_dA * v_dF - v_dC * v_dE) / v_dG;
v_Radius := SQRT(POWER(ST_X(p_pt1) - v_CX,2) + POWER(ST_Y(p_pt1) - v_CY,2) );
END IF;
RETURN ST_SetSRID(ST_MakePoint(v_CX, v_CY, v_radius),ST_Srid(p_pt1));
END;
$BODY$
LANGUAGE plpgsql VOLATILE STRICT;

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src/pg/sql/13_PIA.sql Normal file
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-- Based on:
-- https://github.com/mapbox/polylabel/blob/master/index.js
-- https://sites.google.com/site/polesofinaccessibility/
-- Requires: https://github.com/CartoDB/cartodb-postgresql
CREATE OR REPLACE FUNCTION CDB_PIA(
IN polygon geometry,
IN tolerance numeric DEFAULT 1.0
)
RETURNS geometry AS $$
DECLARE
env geometry[];
cells geometry[];
best_c geometry;
best_d numeric;
test_d numeric;
test_mx numeric;
test_h numeric;
test_tol numeric;
test_cells geometry[];
width numeric;
height numeric;
h numeric;
i integer;
n integer;
sqr numeric;
p geometry;
BEGIN
sqr := |/2;
-- grid #0 cell size
height := ST_YMax(polygon) - ST_YMin(polygon);
width := ST_XMax(polygon) - ST_XMin(polygon);
SELECT 0.5*LEAST(height, width) INTO h;
-- grid #0
with c1 as(
SELECT CDB_RectangleGrid(polygon, h, h) as cell
)
-- ,c2 as(
-- SELECT cell FROM c1 WHERE ST_Intersects(cell, polygon)
-- )
SELECT array_agg(cell) INTO cells FROM c1;
-- 1st guess: centroid
SELECT _Signed_Dist(polygon, ST_Centroid(Polygon)) INTO best_d;
-- looping the loop
n := array_length(cells,1);
i := 1;
LOOP
EXIT WHEN i > n;
-- cell side size
SELECT ST_XMax(cells[i]) - ST_XMin(cells[i]) INTO test_h;
-- check distance
SELECT _Signed_Dist(polygon, ST_Centroid(cells[i])) INTO test_d;
IF test_d > best_d THEN
best_d := test_d;
best_c := cells[i];
END IF;
-- longest distance within the cell
SELECT test_d + (test_h * sqr) INTO test_mx;
-- if the cell has no chance to contains the desired point, continue
SELECT test_mx - best_d INTO test_tol;
IF test_tol <= tolerance THEN
i := i+1;
CONTINUE;
END IF;
-- resample the cell
with c1 as(
SELECT CDB_RectangleGrid(cells[i], test_h/2, test_h/2) as cell
)
-- , c2 as(
-- SELECT cell FROM c1 WHERE ST_Intersects(cell, polygon)
-- )
SELECT array_agg(cell) INTO test_cells FROM c1;
-- concat the new cells to the former array
cells := cells || test_cells;
-- prepare next iteration
n := array_length(cells,1);
i := i+1;
END LOOP;
RETURN ST_Centroid(best_c);
END;
$$ language plpgsql IMMUTABLE;
-- signed distance point to polygon with holes
-- negative is the point is out the polygon
CREATE OR REPLACE FUNCTION _Signed_Dist(
IN polygon geometry,
IN point geometry
)
RETURNS numeric AS $$
DECLARE
i integer;
within integer;
holes integer;
dist numeric;
BEGIN
dist := 1e999;
SELECT LEAST(dist, ST_distance(point, ST_ExteriorRing(polygon))::numeric) INTO dist;
SELECT CASE WHEN ST_Within(point,polygon) THEN 1 ELSE -1 END INTO within;
SELECT ST_NumInteriorRings(polygon) INTO holes;
IF holes > 0 THEN
FOR i IN 1..holes
LOOP
SELECT LEAST(dist, ST_distance(point, ST_InteriorRingN(polygon, i))::numeric) INTO dist;
END LOOP;
END IF;
dist := dist * within::numeric;
RETURN dist;
END;
$$ language plpgsql IMMUTABLE;

5
src/pg/test/expected/09_voronoi_test.out
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src/pg/test/expected/13_pia_test.out Normal file
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st_astext
-------------------------------------------
POINT(-409081.241940808 4930027.50443989)
(1 row)

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src/pg/test/sql/09_voronoi_test.sql
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WITH a AS (
SELECT
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 geomin
)
SELECT
CDB_voronoi(geomin, 0.2, 1e-9) as result
FROM a;

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src/pg/test/sql/13_pia_test.sql Normal file
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with a as(
select st_geomfromtext('POLYGON((-432540.453078056 4949775.20452642,-432329.947920966 4951361.232584,-431245.028163694 4952223.31516671,-429131.071033529 4951768.00415574,-424622.07505895 4952843.13503987,-423688.327170174 4953499.20752423,-424086.294349759 4954968.38274191,-423068.388925945 4954378.63345336,-423387.653225542 4953355.67417084,-420594.869840519 4953781.00230592,-416026.095299382 4951484.06849063,-412483.018546414 4951024.5410983,-410490.399661215 4954502.24032205,-408186.197521284 4956398.91417441,-407627.262358013 4959300.94633864,-406948.770061627 4959874.85407739,-404949.583326472 4959047.74518163,-402570.908447199 4953743.46829807,-400971.358683991 4952193.11680804,-403533.488084088 4949649.89857885,-406335.177028373 4950193.19571096,-407790.456731515 4952391.46015616,-412060.672398345 4950381.2389307,-410716.93482498 4949156.7509561,-408464.162289794 4943912.8940387,-409350.599394983 4942819.84896006,-408087.791091424 4942451.6711778,-407274.045613725 4940572.4807777,-404446.196589102 4939976.71501489,-402422.964843936 4940450.3670813,-401010.654464241 4939054.8061663,-397647.247369412 4940679.80737878,-395658.413346901 4940528.84765185,-395536.852462953 4938829.79565997,-394268.923462818 4938003.7277717,-393388.720249116 4934757.80596815,-392393.301362444 4934326.71675815,-392573.527618037 4932323.40974412,-393464.640141837 4931903.10653605,-393085.597275686 4931094.7353605,-398426.261165985 4929156.87541607,-398261.174361137 4926238.00816416,-394045.059966834 4925765.18668498,-392982.960705174 4926391.81893628,-393090.272694301 4927176.84692181,-391648.240010564 4924626.06386961,-391889.914625075 4923086.14787613,-394345.177314013 4923235.086036,-395550.878718795 4917812.79243978,-399009.463978251 4912927.7157945,-398948.794855767 4911941.91010796,-398092.636652078 4911806.57392519,-401991.601817112 4911722.9204501,-406225.972607907 4914505.47286319,-411104.994569885 4912569.26941163,-412925.513522316 4913030.3608866,-414630.148884835 4914436.69169949,-414207.691417276 4919205.78028405,-418306.141109809 4917994.9580478,-424184.700779621 4918938.12432889,-426816.961458921 4923664.37379373,-420956.324227126 4923381.98014807,-420186.661267781 4924286.48693378,-420943.411166194 4926812.76394433,-419779.45457046 4928527.43466337,-419768.767899344 4930681.94459216,-421911.668097113 4930432.40620397,-423482.386112205 4933451.28047252,-427272.814773717 4934151.56473242,-427144.908678797 4939731.77191996,-428982.125554848 4940522.84445172,-428986.133056516 4942437.17281266,-431237.792396792 4947309.68284815,-432476.889648814 4947791.74800037,-432540.453078056 4949775.20452642))', 3857) as g
)
SELECT st_astext(CDB_PIA(g)) from a;