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doc/09_voronoi.md
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38
doc/09_voronoi.md
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## Voronoi
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Function to construct the [Voronoi Diagram](https://en.wikipedia.org/wiki/Voronoi_diagram) from a dataset of scatter points, clipped to the significant area
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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...
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### CDB_Voronoi (geom geometry[], buffer numeric DEFAULT 0.5, tolerance numeric DEFAULT 1e-9)
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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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| buffer | numeric | enlargment ratio for the envelope area used for the restraints|
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| tolerance | numeric | Delaunay tolerance, optional |
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### Returns
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| Column Name | Type | Description |
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|-------------|------|-------------|
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| geom | geometry collection | Collection of polygons of the Voronoi cells|
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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[ST_GeomFromText('POINT(2.1744 41.403)', 4326),ST_GeomFromText('POINT(2.1228 41.380)', 4326),ST_GeomFromText('POINT(2.1511 41.374)', 4326),ST_GeomFromText('POINT(2.1528 41.413)', 4326),ST_GeomFromText('POINT(2.165 41.391)', 4326),ST_GeomFromText('POINT(2.1498 41.371)', 4326),ST_GeomFromText('POINT(2.1533 41.368)', 4326),ST_GeomFromText('POINT(2.131386 41.41399)', 4326)] AS geomin
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)
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SELECT
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st_transform(
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(st_dump(CDB_voronoi(geomin, 0.2, 1e-9)
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)).geom
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, 3857) as the_geom_webmercator
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FROM a;
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```
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236
src/pg/sql/09_voronoi.sql
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src/pg/sql/09_voronoi.sql
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-- =============================================================================================
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--
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-- CDB_Voronoi
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--
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-- =============================================================================================
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CREATE OR REPLACE FUNCTION CDB_voronoi(
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IN geomin geometry[],
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IN buffer numeric DEFAULT 0.5,
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IN tolerance numeric DEFAULT 1e-9
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)
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RETURNS geometry AS $$
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DECLARE
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geomout geometry;
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BEGIN
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-- we need to make the geometry calculations in (pseudo)meters!!!
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with a as (
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SELECT unnest(geomin) as g1
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),
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b as(
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SELECT st_transform(g1, 3857) g2 from a
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)
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SELECT array_agg(g2) INTO geomin from b;
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WITH
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convexhull_1 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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clipper as(
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SELECT
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st_buffer(ST_MinimumBoundingCircle(a.g), buffer*a.r) as g
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FROM convexhull_1 a
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),
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env0 as (
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SELECT
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(st_dumppoints(st_expand(a.g, buffer*a.r))).geom as e
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FROM convexhull_1 a
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),
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env as (
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SELECT
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array_agg(env0.e) as e
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FROM env0
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),
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sample AS (
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SELECT
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ST_Collect(geomin || env.e) as geom
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FROM env
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),
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convexhull as (
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SELECT
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ST_ConvexHull(ST_Collect(geomin)) as cg
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),
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tin as (
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SELECT
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ST_Dump(ST_DelaunayTriangles(geom, tolerance, 0)) as gd
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FROM
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sample
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),
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tin_polygons as (
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SELECT
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(gd).Path as id,
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(gd).Geom as pg,
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ST_Centroid(ST_MinimumBoundingCircle((gd).Geom, 180)) as ct
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FROM tin
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),
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tin_lines as (
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SELECT
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id,
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ST_ExteriorRing(pg) as lg
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FROM tin_polygons
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),
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tin_nodes as (
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SELECT
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id,
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ST_PointN(lg,1) p1,
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ST_PointN(lg,2) p2,
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ST_PointN(lg,3) p3
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FROM tin_lines
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),
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tin_edges AS (
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SELECT
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p.id,
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UNNEST(ARRAY[
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ST_MakeLine(n.p1,n.p2) ,
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ST_MakeLine(n.p2,n.p3) ,
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ST_MakeLine(n.p3,n.p1)]) as Edge,
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ST_Force2D(cdb_crankshaft._Find_Circle(n.p1,n.p2,n.p3)) as ct,
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CASE WHEN st_distance(p.ct, ST_ExteriorRing(p.pg)) < tolerance THEN
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TRUE
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ELSE FALSE END AS ctx,
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p.pg,
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ST_within(p.ct, convexhull.cg) as ctin
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FROM
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tin_polygons p,
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tin_nodes n,
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convexhull
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WHERE p.id = n.id
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),
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voro_nodes as (
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SELECT
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CASE WHEN x.ctx = TRUE THEN
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ST_Centroid(x.edge)
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ELSE
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x.ct
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END as xct,
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CASE WHEN y.id is null THEN
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CASE WHEN x.ctin = TRUE THEN
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ST_SetSRID(ST_MakePoint(
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ST_X(x.ct) + ((ST_X(ST_Centroid(x.edge)) - ST_X(x.ct)) * (1+buffer)),
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ST_Y(x.ct) + ((ST_Y(ST_Centroid(x.edge)) - ST_Y(x.ct)) * (1+buffer))
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), ST_SRID(x.ct))
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END
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ELSE
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y.ct
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END as yct
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FROM
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tin_edges x
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LEFT OUTER JOIN
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tin_edges y
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ON x.id <> y.id AND ST_Equals(x.edge, y.edge)
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),
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voro_edges as(
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SELECT
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ST_LineMerge(ST_Collect(ST_MakeLine(xct, yct))) as v
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FROM
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voro_nodes
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),
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voro_cells as(
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SELECT
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ST_Polygonize(
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ST_Node(
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ST_LineMerge(
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ST_Union(v, ST_ExteriorRing(
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ST_Convexhull(v)
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)
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)
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)
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)
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) as g
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FROM
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voro_edges
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),
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voro_set as(
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SELECT
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(st_dump(v.g)).geom as g
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FROM voro_cells v
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),
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clipped_voro as(
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SELECT
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ST_intersection(c.g, v.g) as g
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FROM
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voro_set v,
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clipper c
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WHERE
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ST_GeometryType(v.g) = 'ST_Polygon'
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)
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SELECT
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st_collect(
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ST_Transform(
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ST_ConvexHull(g),
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4326
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)
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)
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INTO geomout
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FROM
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clipped_voro;
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RETURN geomout;
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END;
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$$ language plpgsql IMMUTABLE;
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/** ----------------------------------------------------------------------------------------
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* @function : FindCircle
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* @precis : Function that determines if three points form a circle. If so a table containing
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* centre and radius is returned. If not, a null table is returned.
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* @version : 1.0.1
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* @param : p_pt1 : First point in curve
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* @param : p_pt2 : Second point in curve
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* @param : p_pt3 : Third point in curve
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* @return : geometry : In which X,Y ordinates are the centre X, Y and the Z being the radius of found circle
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* or NULL if three points do not form a circle.
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* @history : Simon Greener - Feb 2012 - Original coding.
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* Rafa de la Torre - Aug 2016 - Small fix for type checking
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* @copyright : Simon Greener @ 2012
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* Licensed under a Creative Commons Attribution-Share Alike 2.5 Australia License. (http://creativecommons.org/licenses/by-sa/2.5/au/)
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**/
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CREATE OR REPLACE FUNCTION _Find_Circle(
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IN p_pt1 geometry,
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IN p_pt2 geometry,
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IN p_pt3 geometry)
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RETURNS geometry AS
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$BODY$
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DECLARE
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v_Centre geometry;
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v_radius NUMERIC;
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v_CX NUMERIC;
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v_CY NUMERIC;
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v_dA NUMERIC;
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v_dB NUMERIC;
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v_dC NUMERIC;
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v_dD NUMERIC;
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v_dE NUMERIC;
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v_dF NUMERIC;
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v_dG NUMERIC;
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BEGIN
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IF ( p_pt1 IS NULL OR p_pt2 IS NULL OR p_pt3 IS NULL ) THEN
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RAISE EXCEPTION 'All supplied points must be not null.';
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RETURN NULL;
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END IF;
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IF ( ST_GeometryType(p_pt1) <> 'ST_Point' OR
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ST_GeometryType(p_pt2) <> 'ST_Point' OR
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ST_GeometryType(p_pt3) <> 'ST_Point' ) THEN
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RAISE EXCEPTION 'All supplied geometries must be points.';
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RETURN NULL;
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END IF;
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v_dA := ST_X(p_pt2) - ST_X(p_pt1);
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v_dB := ST_Y(p_pt2) - ST_Y(p_pt1);
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v_dC := ST_X(p_pt3) - ST_X(p_pt1);
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v_dD := ST_Y(p_pt3) - ST_Y(p_pt1);
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v_dE := v_dA * (ST_X(p_pt1) + ST_X(p_pt2)) + v_dB * (ST_Y(p_pt1) + ST_Y(p_pt2));
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v_dF := v_dC * (ST_X(p_pt1) + ST_X(p_pt3)) + v_dD * (ST_Y(p_pt1) + ST_Y(p_pt3));
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v_dG := 2.0 * (v_dA * (ST_Y(p_pt3) - ST_Y(p_pt2)) - v_dB * (ST_X(p_pt3) - ST_X(p_pt2)));
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-- If v_dG is zero then the three points are collinear and no finite-radius
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-- circle through them exists.
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IF ( v_dG = 0 ) THEN
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RETURN NULL;
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ELSE
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v_CX := (v_dD * v_dE - v_dB * v_dF) / v_dG;
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v_CY := (v_dA * v_dF - v_dC * v_dE) / v_dG;
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v_Radius := SQRT(POWER(ST_X(p_pt1) - v_CX,2) + POWER(ST_Y(p_pt1) - v_CY,2) );
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END IF;
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RETURN ST_SetSRID(ST_MakePoint(v_CX, v_CY, v_radius),ST_Srid(p_pt1));
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END;
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$BODY$
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LANGUAGE plpgsql VOLATILE STRICT;
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7
src/pg/test/expected/09_voronoi_test.out
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7
src/pg/test/expected/09_voronoi_test.out
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SET client_min_messages TO WARNING;
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\set ECHO none
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avg_area
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----------------------
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0.000178661700690617
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(1 row)
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15
src/pg/test/sql/09_voronoi_test.sql
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src/pg/test/sql/09_voronoi_test.sql
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SET client_min_messages TO WARNING;
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\set ECHO none
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WITH a AS (
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SELECT
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ARRAY[ST_GeomFromText('POINT(2.1744 41.403)', 4326),ST_GeomFromText('POINT(2.1228 41.380)', 4326),ST_GeomFromText('POINT(2.1511 41.374)', 4326),ST_GeomFromText('POINT(2.1528 41.413)', 4326),ST_GeomFromText('POINT(2.165 41.391)', 4326),ST_GeomFromText('POINT(2.1498 41.371)', 4326),ST_GeomFromText('POINT(2.1533 41.368)', 4326),ST_GeomFromText('POINT(2.131386 41.41399)', 4326)] AS geomin
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),
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b as(
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SELECT
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(st_dump(cdb_crankshaft.CDB_voronoi(geomin, 0.2, 1e-9))).geom as result
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FROM a
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)
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SELECT
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avg(st_area(result)) as avg_area
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FROM b;
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