Merge pull request #84 from CartoDB/add-PIA

Add Pole of Inaccessibility [13]
2016-08-30 12:12:53 +02:00
parent 23a576939b 2b75da1db2
commit e071d323d4
4 changed files with 170 additions and 0 deletions
--- a/doc/13_PIA.md
+++ b/doc/13_PIA.md
@@ -0,0 +1,33 @@
+## 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
+),
+b as (
+    select ST_Transform(g, 4326) as g from a
+)
+SELECT st_astext(CDB_PIA(g)) from b;
+```
--- a/src/pg/sql/13_PIA.sql
+++ b/src/pg/sql/13_PIA.sql
@@ -0,0 +1,123 @@
+-- Based on:
+-- https://github.com/mapbox/polylabel/blob/master/index.js
+-- https://sites.google.com/site/polesofinaccessibility/
+-- Requires: https://github.com/CartoDB/cartodb-postgresql
+
+-- 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 $$
+DECLARE
+    env geometry[];
+    cells geometry[];
+    cell geometry;
+    best_c geometry;
+    best_d numeric;
+    test_d numeric;
+    test_mx numeric;
+    test_h numeric;
+    test_cells geometry[];
+    width numeric;
+    height numeric;
+    h numeric;
+    i integer;
+    n integer;
+    sqr numeric;
+    p geometry;
+BEGIN
+    sqr := |/2;
+    polygon := ST_Transform(polygon, 3857);
+
+    -- grid #0 cell size
+    height := ST_YMax(polygon) - ST_YMin(polygon);
+    width := ST_XMax(polygon) - ST_XMin(polygon);
+    h := 0.5*LEAST(height, width);
+
+    -- grid #0
+    with c1 as(
+        SELECT cdb_crankshaft.CDB_RectangleGrid(polygon, h, h) as c
+    )
+    SELECT array_agg(c) INTO cells FROM c1;
+
+    -- 1st guess: centroid
+    best_d := cdb_crankshaft._Signed_Dist(polygon, ST_Centroid(Polygon));
+
+    -- looping the loop
+    n := array_length(cells,1);
+    i := 1;
+    LOOP
+
+        EXIT WHEN i > n;
+
+        cell := cells[i];
+        i := i+1;
+
+        -- cell side size, it's square
+        test_h := ST_XMax(cell) - ST_XMin(cell) ;
+
+        -- check distance
+        test_d := cdb_crankshaft._Signed_Dist(polygon, ST_Centroid(cell));
+        IF test_d > best_d THEN
+            best_d := test_d;
+            best_c := cells[i];
+        END IF;
+
+        -- longest distance within the cell
+        test_mx := test_d + (test_h/2 * sqr);
+
+        -- if the cell has no chance to contains the desired point, continue
+        CONTINUE WHEN test_mx - best_d <= tolerance;
+
+        -- resample the cell
+        with c1 as(
+            SELECT cdb_crankshaft.CDB_RectangleGrid(cell, test_h/2, test_h/2) as c
+        )
+        SELECT array_agg(c) INTO test_cells FROM c1;
+
+        -- concat the new cells to the former array
+        cells := cells || test_cells;
+
+        -- prepare next iteration
+        n := array_length(cells,1);
+
+    END LOOP;
+
+    RETURN ST_transform(ST_Centroid(best_c), 4326);
+
+END;
+$$ 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;
--- a/src/pg/test/expected/13_pia_test.out
+++ b/src/pg/test/expected/13_pia_test.out
@@ -0,0 +1,7 @@
+SET client_min_messages TO WARNING;
+\set ECHO none
+                 st_astext                 
+-------------------------------------------
+ POINT(-3.67484492582767 40.4395084885993)
+(1 row)
+
--- a/src/pg/test/sql/13_pia_test.sql
+++ b/src/pg/test/sql/13_pia_test.sql
@@ -0,0 +1,7 @@
+SET client_min_messages TO WARNING;
+\set ECHO none
+
+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_crankshaft.CDB_PIA(g)) from a;