SFCGAL is a C++ wrapper library around CGAL that provides advanced 2D and 3D functions. For robustness, geometry coordinates have an exact rational number representation. Installation instructions of the library can be found on SFCGAL home page http://www.sfcgal.org. To load the functions create extension postgis_sfcgal. Some SFCGAL functions replace standard ones (ST_Intersects, ST_Intersection, ST_Difference, ST_Union, ST_Area and ST_Distance), to switch between standard functions and SFCGAL function use: SET postgis.backend = sfcgal; and SET postgis.backend = geos; postgis_sfcgal_version Returns the version of SFCGAL in use text postgis_sfcgal_version Availability: 2.1.0 &sfcgal_required; &Z_support; &P_support; &T_support; ST_Extrude Extrude a surface to a related volume geometry ST_Extrude geometry geom float x float y float z Availability: 2.1.0 &sfcgal_required; &Z_support; &P_support; &T_support; 3D images were generated using the PostGIS and rendering in HTML using X3Dom HTML Javascript redering library. SELECT ST_Buffer(ST_GeomFromText('POINT(100 90)'), 50, 'quad_segs=2'),0,0,30); Original octagon formed from buffering point ST_Extrude(ST_Buffer(ST_GeomFromText('POINT(100 90)'), 50, 'quad_segs=2'),0,0,30); Hexagon extruded 30 units along Z produces a PolyhedralSurfaceZ SELECT ST_GeomFromText('LINESTRING(50 50, 100 90, 95 150)') Original linestring SELECT ST_Extrude( ST_GeomFromText('LINESTRING(50 50, 100 90, 95 150)'),0,0,10)); LineString Extruded along Z produces a PolyhedralSurfaceZ ST_StraightSkeleton Compute a straight skeleton from a geometry geometry ST_StraightSkeleton geometry geom Availability: 2.1.0 &sfcgal_required; &Z_support; &P_support; &T_support; SELECT ST_StraightSkeleton(ST_GeomFromText('POLYGON (( 190 190, 10 190, 10 10, 190 10, 190 20, 160 30, 60 30, 60 130, 190 140, 190 190 ))')); Original polygon Straight Skeleton of polygon ST_ApproximateMedialAxis Compute the approximate medial axis of an areal geometry. geometry ST_ApproximateMedialAxis geometry geom Return an approximate medial axis for the areal input based on its straight skeleton. Uses an SFCGAL specific API when built against a capable version (1.2.0+). Otherwise the function is just a wrapper around ST_StraightSkeleton (slower case). Availability: 2.2.0 &sfcgal_required; &Z_support; &P_support; &T_support; SELECT ST_ApproximateMedialAxis(ST_GeomFromText('POLYGON (( 190 190, 10 190, 10 10, 190 10, 190 20, 160 30, 60 30, 60 130, 190 140, 190 190 ))')); A polygon and its approximate medial axis ST_IsPlanar Check if a surface is or not planar boolean ST_IsPlanar geometry geom Availability: 2.2.0: This was documented in 2.1.0 but got accidentally left out in 2.1 release. &sfcgal_required; &Z_support; &P_support; &T_support; ST_Orientation Determine surface orientation integer ST_Orientation geometry geom The function only applies to polygons. It returns -1 if the polygon is counterclockwise oriented and 1 if the polygon is clockwise oriented. Availability: 2.1.0 &sfcgal_required; &Z_support; ST_ForceLHR Force LHR orientation geometry ST_ForceLHR geometry geom Availability: 2.1.0 &sfcgal_required; &Z_support; &P_support; &T_support; ST_MinkowskiSum Performs Minkowski sum geometry ST_MinkowskiSum geometry geom1 geometry geom2 This function performs a 2D minkowski sum of a point, line or polygon with a polygon. A minkowski sum of two geometries A and B is the set of all points that are the sum of any point in A and B. Minkowski sums are often used in motion planning and computer-aided design. More details on Wikipedia Minkowski addition. The first parameter can be any 2D geometry (point, linestring, polygon). If a 3D geometry is passed, it will be converted to 2D by forcing Z to 0, leading to possible cases of invalidity. The second parameter must be a 2D polygon. Implementation utilizes CGAL 2D Minkowskisum. Availability: 2.1.0 &sfcgal_required; Minkowski Sum of Linestring and circle polygon where Linestring cuts thru the circle Before Summing After summing SELECT ST_MinkowskiSum(line, circle)) FROM (SELECT ST_MakeLine(ST_MakePoint(10, 10),ST_MakePoint(100, 100)) As line, ST_Buffer(ST_GeomFromText('POINT(50 50)'), 30) As circle) As foo; -- wkt -- MULTIPOLYGON(((30 59.9999999999999,30.5764415879031 54.1472903395161,32.2836140246614 48.5194970290472,35.0559116309237 43.3328930094119,38.7867965644036 38.7867965644035,43.332893009412 35.0559116309236,48.5194970290474 32.2836140246614,54.1472903395162 30.5764415879031,60.0000000000001 30,65.8527096604839 30.5764415879031,71.4805029709527 32.2836140246614,76.6671069905881 35.0559116309237,81.2132034355964 38.7867965644036,171.213203435596 128.786796564404,174.944088369076 133.332893009412,177.716385975339 138.519497029047,179.423558412097 144.147290339516,180 150,179.423558412097 155.852709660484,177.716385975339 161.480502970953,174.944088369076 166.667106990588,171.213203435596 171.213203435596,166.667106990588 174.944088369076, 161.480502970953 177.716385975339,155.852709660484 179.423558412097,150 180,144.147290339516 179.423558412097,138.519497029047 177.716385975339,133.332893009412 174.944088369076,128.786796564403 171.213203435596,38.7867965644035 81.2132034355963,35.0559116309236 76.667106990588,32.2836140246614 71.4805029709526,30.5764415879031 65.8527096604838,30 59.9999999999999))) Minkowski Sum of a polygon and multipoint Before Summing After summing: polygon is duplicated and translated to position of points SELECT ST_MinkowskiSum(mp, poly) FROM (SELECT 'MULTIPOINT(25 50,70 25)'::geometry As mp, 'POLYGON((130 150, 20 40, 50 60, 125 100, 130 150))'::geometry As poly ) As foo -- wkt -- MULTIPOLYGON( ((70 115,100 135,175 175,225 225,70 115)), ((120 65,150 85,225 125,275 175,120 65)) ) ST_3DIntersection Perform 3D intersection geometry ST_3DIntersection geometry geom1 geometry geom2 Availability: 2.1.0 &sfcgal_required; &Z_support; &P_support; &T_support; SELECT ST_AsText(ST_3DIntersection(linestring, polygon)) As wkt FROM ST_GeomFromText('LINESTRING Z (2 2 6,1.5 1.5 7,1 1 8,0.5 0.5 8,0 0 10)') AS linestring CROSS JOIN ST_GeomFromText('POLYGON((0 0 8, 0 1 8, 1 1 8, 1 0 8, 0 0 8))') AS polygon; wkt -------------------------------- LINESTRING Z (1 1 8,0.5 0.5 8) Cube (closed Polyhedral Surface) and Polygon Z SELECT ST_AsText(ST_3DIntersection( ST_GeomFromText('POLYHEDRALSURFACE Z( ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)), ((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)), ((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)), ((1 1 0, 1 1 1, 1 0 1, 1 0 0, 1 1 0)), ((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0)), ((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)) )'), 'POLYGON Z ((0 0 0, 0 0 0.5, 0 0.5 0.5, 0 0.5 0, 0 0 0))'::geometry)) TIN Z (((0 0 0,0 0 0.5,0 0.5 0.5,0 0 0)),((0 0.5 0,0 0 0,0 0.5 0.5,0 0.5 0))) Intersection of 2 solids that result in volumetric intersection is also a solid (ST_Dimension returns 3) SELECT ST_AsText(ST_3DIntersection( ST_Extrude(ST_Buffer('POINT(10 20)'::geometry,10,1),0,0,30), ST_Extrude(ST_Buffer('POINT(10 20)'::geometry,10,1),2,0,10) )); POLYHEDRALSURFACE Z (((13.3333333333333 13.3333333333333 10,20 20 0,20 20 10,13.3333333333333 13.3333333333333 10)), ((20 20 10,16.6666666666667 23.3333333333333 10,13.3333333333333 13.3333333333333 10,20 20 10)), ((20 20 0,16.6666666666667 23.3333333333333 10,20 20 10,20 20 0)), ((13.3333333333333 13.3333333333333 10,10 10 0,20 20 0,13.3333333333333 13.3333333333333 10)), ((16.6666666666667 23.3333333333333 10,12 28 10,13.3333333333333 13.3333333333333 10,16.6666666666667 23.3333333333333 10)), ((20 20 0,9.99999999999995 30 0,16.6666666666667 23.3333333333333 10,20 20 0)), ((10 10 0,9.99999999999995 30 0,20 20 0,10 10 0)),((13.3333333333333 13.3333333333333 10,12 12 10,10 10 0,13.3333333333333 13.3333333333333 10)), ((12 28 10,12 12 10,13.3333333333333 13.3333333333333 10,12 28 10)), ((16.6666666666667 23.3333333333333 10,9.99999999999995 30 0,12 28 10,16.6666666666667 23.3333333333333 10)), ((10 10 0,0 20 0,9.99999999999995 30 0,10 10 0)), ((12 12 10,11 11 10,10 10 0,12 12 10)),((12 28 10,11 11 10,12 12 10,12 28 10)), ((9.99999999999995 30 0,11 29 10,12 28 10,9.99999999999995 30 0)),((0 20 0,2 20 10,9.99999999999995 30 0,0 20 0)), ((10 10 0,2 20 10,0 20 0,10 10 0)),((11 11 10,2 20 10,10 10 0,11 11 10)),((12 28 10,11 29 10,11 11 10,12 28 10)), ((9.99999999999995 30 0,2 20 10,11 29 10,9.99999999999995 30 0)),((11 11 10,11 29 10,2 20 10,11 11 10))) ST_3DDifference Perform 3D difference geometry ST_3DDifference geometry geom1 geometry geom2 Availability: 2.2.0 &sfcgal_required; &Z_support; &P_support; &T_support; ST_3DUnion Perform 3D union geometry ST_3DUnion geometry geom1 geometry geom2 Availability: 2.2.0 &sfcgal_required; &Z_support; &P_support; &T_support; ST_3DArea Computes area of 3D surface geometries. Will return 0 for solids. floatST_3DArea geometry geom1 Availability: 2.1.0 &sfcgal_required; &Z_support; &P_support; &T_support; Note: By default a PolyhedralSurface built from WKT is a surface geometry, not solid. It therefore has surface area. Once converted to a solid, no area. SELECT ST_3DArea(geom) As cube_surface_area, ST_3DArea(ST_MakeSolid(geom)) As solid_surface_area FROM (SELECT 'POLYHEDRALSURFACE( ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)), ((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)), ((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)), ((1 1 0, 1 1 1, 1 0 1, 1 0 0, 1 1 0)), ((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0)), ((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)) )'::geometry) As f(geom); cube_surface_area | solid_surface_area -------------------+-------------------- 6 | 0 , , , ST_Tesselate Perform surface Tesselation of a polygon or polyhedralsurface and returns as a TIN or collection of TINS geometry ST_Tesselate geometry geom Takes as input a surface such a MULTI(POLYGON) or POLYHEDRALSURFACE and returns a TIN representation via the process of tesselation using triangles. Availability: 2.1.0 &sfcgal_required; &Z_support; &P_support; &T_support; SELECT ST_GeomFromText('POLYHEDRALSURFACE Z( ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)), ((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)), ((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)), ((1 1 0, 1 1 1, 1 0 1, 1 0 0, 1 1 0)), ((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0)), ((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)) )'); Original Cube SELECT ST_Tesselate(ST_GeomFromText('POLYHEDRALSURFACE Z( ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)), ((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)), ((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)), ((1 1 0, 1 1 1, 1 0 1, 1 0 0, 1 1 0)), ((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0)), ((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)) )')); ST_AsText output: TIN Z (((0 0 0,0 0 1,0 1 1,0 0 0)),((0 1 0,0 0 0,0 1 1,0 1 0)), ((0 0 0,0 1 0,1 1 0,0 0 0)), ((1 0 0,0 0 0,1 1 0,1 0 0)),((0 0 1,1 0 0,1 0 1,0 0 1)), ((0 0 1,0 0 0,1 0 0,0 0 1)), ((1 1 0,1 1 1,1 0 1,1 1 0)),((1 0 0,1 1 0,1 0 1,1 0 0)), ((0 1 0,0 1 1,1 1 1,0 1 0)),((1 1 0,0 1 0,1 1 1,1 1 0)), ((0 1 1,1 0 1,1 1 1,0 1 1)),((0 1 1,0 0 1,1 0 1,0 1 1))) Tesselated Cube with triangles colored SELECT 'POLYGON (( 10 190, 10 70, 80 70, 80 130, 50 160, 120 160, 120 190, 10 190 ))'::geometry; Original polygon SELECT ST_Tesselate('POLYGON (( 10 190, 10 70, 80 70, 80 130, 50 160, 120 160, 120 190, 10 190 ))'::geometry); ST_AsText output TIN(((80 130,50 160,80 70,80 130)),((50 160,10 190,10 70,50 160)), ((80 70,50 160,10 70,80 70)),((120 160,120 190,50 160,120 160)), ((120 190,10 190,50 160,120 190))) Tesselated Polygon ST_Volume Computes the volume of a 3D solid. If applied to surface (even closed) geometries will return 0. float ST_Volume geometry geom1 Availability: 2.2.0 &sfcgal_required; &Z_support; &P_support; &T_support; When closed surfaces are created with WKT, they are treated as areal rather than solid. To make them solid, you need to use . Areal geometries have no volume. Here is an example to demonstrate. SELECT ST_Volume(geom) As cube_surface_vol, ST_Volume(ST_MakeSolid(geom)) As solid_surface_vol FROM (SELECT 'POLYHEDRALSURFACE( ((0 0 0, 0 0 1, 0 1 1, 0 1 0, 0 0 0)), ((0 0 0, 0 1 0, 1 1 0, 1 0 0, 0 0 0)), ((0 0 0, 1 0 0, 1 0 1, 0 0 1, 0 0 0)), ((1 1 0, 1 1 1, 1 0 1, 1 0 0, 1 1 0)), ((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0)), ((0 0 1, 1 0 1, 1 1 1, 0 1 1, 0 0 1)) )'::geometry) As f(geom); cube_surface_vol | solid_surface_vol ------------------+------------------- 0 | 1 , , ST_MakeSolid Cast the geometry into a solid. No check is performed. To obtain a valid solid, the input geometry must be a closed Polyhedral Surface or a closed TIN. geometryST_MakeSolid geometry geom1 Availability: 2.2.0 &sfcgal_required; &Z_support; &P_support; &T_support; ST_IsSolid Test if the geometry is a solid. No validity check is performed. booleanST_IsSolid geometry geom1 Availability: 2.2.0 &sfcgal_required; &Z_support; &P_support; &T_support;