GEOS stands for Geometry Engine  Open Source, and is a C++ library, ported from the Java Topology Suite. GEOS implements the OpenGIS Simple Features for SQL spatial predicate functions and spatial operators. GEOS, now an OSGeo project, was initially developed and maintained by Refractions Research of Victoria, Canada.
GeoDjango implements a highlevel Python wrapper for the GEOS library, its features include:
This section contains a brief introduction and tutorial to using GEOSGeometry objects.
GEOSGeometry objects may be created in a few ways. The first is to simply instantiate the object on some spatial input – the following are examples of creating the same geometry from WKT, HEX, WKB, and GeoJSON:
>>> from django.contrib.gis.geos import GEOSGeometry
>>> pnt = GEOSGeometry('POINT(5 23)') # WKT
>>> pnt = GEOSGeometry('010100000000000000000014400000000000003740') # HEX
>>> pnt = GEOSGeometry(buffer('\x01\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x14@\x00\x00\x00\x00\x00\x007@'))
>>> pnt = GEOSGeometry('{ "type": "Point", "coordinates": [ 5.000000, 23.000000 ] }') # GeoJSON
Another option is to use the constructor for the specific geometry type that you wish to create. For example, a Point object may be created by passing in the X and Y coordinates into its constructor:
>>> from django.contrib.gis.geos import Point
>>> pnt = Point(5, 23)
Finally, there are fromstr() and fromfile() factory methods, which return a GEOSGeometry object from an input string or a file:
>>> from django.contrib.gis.geos import fromstr, fromfile
>>> pnt = fromstr('POINT(5 23)')
>>> pnt = fromfile('/path/to/pnt.wkt')
>>> pnt = fromfile(open('/path/to/pnt.wkt'))
GEOSGeometry objects are ‘Pythonic’, in other words components may be accessed, modified, and iterated over using standard Python conventions. For example, you can iterate over the coordinates in a Point:
>>> pnt = Point(5, 23)
>>> [coord for coord in pnt]
[5.0, 23.0]
With any geometry object, the GEOSGeometry.coords property may be used to get the geometry coordinates as a Python tuple:
>>> pnt.coords
(5.0, 23.0)
You can get/set geometry components using standard Python indexing techniques. However, what is returned depends on the geometry type of the object. For example, indexing on a LineString returns a coordinate tuple:
>>> from django.contrib.gis.geos import LineString
>>> line = LineString((0, 0), (0, 50), (50, 50), (50, 0), (0, 0))
>>> line[0]
(0.0, 0.0)
>>> line[2]
(50.0, 0.0)
Whereas indexing on a Polygon will return the ring (a LinearRing object) corresponding to the index:
>>> from django.contrib.gis.geos import Polygon
>>> poly = Polygon( ((0.0, 0.0), (0.0, 50.0), (50.0, 50.0), (50.0, 0.0), (0.0, 0.0)) )
>>> poly[0]
<LinearRing object at 0x1044395b0>
>>> poly[0][2] # secondtolast coordinate of external ring
(50.0, 0.0)
In addition, coordinates/components of the geometry may added or modified, just like a Python list:
>>> line[0] = (1.0, 1.0)
>>> line.pop()
(0.0, 0.0)
>>> line.append((1.0, 1.0))
>>> line.coords
((1.0, 1.0), (0.0, 50.0), (50.0, 50.0), (50.0, 0.0), (1.0, 1.0))
Parameters: 


This is the base class for all GEOS geometry objects. It initializes on the given geo_input argument, and then assumes the proper geometry subclass (e.g., GEOSGeometry('POINT(1 1)') will create a Point object).
The following input formats, along with their corresponding Python types, are accepted:
Format  Input Type 

WKT / EWKT  str or unicode 
HEX / HEXEWKB  str or unicode 
WKB / EWKB  buffer 
GeoJSON  str or unicode 
Note
The new 3D/4D WKT notation with an intermediary Z or M (like POINT Z (3, 4, 5)) is only supported with GEOS 3.3.0 or later.
Returns the coordinates of the geometry as a tuple.
Returns whether or not the set of points in the geometry is empty.
Returns a string corresponding to the type of geometry. For example:
>>> pnt = GEOSGeometry('POINT(5 23)')
>>> pnt.geom_type
'Point'
Returns the GEOS geometry type identification number. The following table shows the value for each geometry type:
Geometry  ID 

Point  0 
LineString  1 
LinearRing  2 
Polygon  3 
MultiPoint  4 
MultiLineString  5 
MultiPolygon  6 
GeometryCollection  7 
Returns the number of coordinates in the geometry.
Returns the number of geometries in this geometry. In other words, will return 1 on anything but geometry collections.
Returns a boolean indicating whether the geometry is threedimensional.
Returns a boolean indicating whether the geometry is a LinearRing.
Returns a boolean indicating whether the geometry is ‘simple’. A geometry is simple if and only if it does not intersect itself (except at boundary points). For example, a LineString object is not simple if it intersects itself. Thus, LinearRing and Polygon objects are always simple because they do cannot intersect themselves, by definition.
Returns a boolean indicating whether the geometry is valid.
Returns a string describing the reason why a geometry is invalid.
Property that may be used to retrieve or set the SRID associated with the geometry. For example:
>>> pnt = Point(5, 23)
>>> print(pnt.srid)
None
>>> pnt.srid = 4326
>>> pnt.srid
4326
The properties in this section export the GEOSGeometry object into a different. This output may be in the form of a string, buffer, or even another object.
Returns the “extended” WellKnown Text of the geometry. This representation is specific to PostGIS and is a super set of the OGC WKT standard. [1] Essentially the SRID is prepended to the WKT representation, for example SRID=4326;POINT(5 23).
Note
The output from this property does not include the 3dm, 3dz, and 4d information that PostGIS supports in its EWKT representations.
Returns the WKB of this Geometry in hexadecimal form. Please note that the SRID value is not included in this representation because it is not a part of the OGC specification (use the GEOSGeometry.hexewkb property instead).
Returns the EWKB of this Geometry in hexadecimal form. This is an extension of the WKB specification that includes the SRID value that are a part of this geometry.
Returns the GeoJSON representation of the geometry.
Note
Requires GDAL.
Alias for GEOSGeometry.json.
Returns a KML (Keyhole Markup Language) representation of the geometry. This should only be used for geometries with an SRID of 4326 (WGS84), but this restriction is not enforced.
Returns an OGRGeometry object corresponding to the GEOS geometry.
Note
Requires GDAL.
Returns the WKB (WellKnown Binary) representation of this Geometry as a Python buffer. SRID value is not included, use the GEOSGeometry.ewkb property instead.
Return the EWKB representation of this Geometry as a Python buffer. This is an extension of the WKB specification that includes any SRID value that are a part of this geometry.
Returns the WellKnown Text of the geometry (an OGC standard).
All of the following spatial predicate methods take another GEOSGeometry instance (other) as a parameter, and return a boolean.
Returns True if GEOSGeometry.within() is False.
Returns True if the DE9IM intersection matrix for the two Geometries is T*T****** (for a point and a curve,a point and an area or a line and an area) 0******** (for two curves).
Returns True if the DE9IM intersection matrix for the two geometries is FF*FF****.
Returns True if the DE9IM intersection matrix for the two geometries is T*F**FFF*.
Returns true if the two geometries are exactly equal, up to a specified tolerance. The tolerance value should be a floating point number representing the error tolerance in the comparison, e.g., poly1.equals_exact(poly2, 0.001) will compare equality to within one thousandth of a unit.
Returns True if GEOSGeometry.disjoint() is False.
Returns true if the DE9IM intersection matrix for the two geometries is T*T***T** (for two points or two surfaces) 1*T***T** (for two curves).
Returns True if the elements in the DE9IM intersection matrix for this geometry and the other matches the given pattern – a string of nine characters from the alphabet: {T, F, *, 0}.
Returns True if the DE9IM intersection matrix for the two geometries is FT*******, F**T***** or F***T****.
Returns True if the DE9IM intersection matrix for the two geometries is T*F**F***.
Returns a GEOSGeometry that represents all points whose distance from this geometry is less than or equal to the given width. The optional quadsegs keyword sets the number of segments used to approximate a quarter circle (defaults is 8).
Returns a GEOSGeometry representing the points making up this geometry that do not make up other.
Given a distance (float), returns the point (or closest point) within the geometry (LineString or MultiLineString) at that distance. The normalized version takes the distance as a float between 0 (origin) and 1 (endpoint).
Reverse of GEOSGeometry.project().
Returns a GEOSGeometry representing the points shared by this geometry and other.
Returns the distance (float) from the origin of the geometry (LineString or MultiLineString) to the point projected on the geometry (that is to a point of the line the closest to the given point). The normalized version returns the distance as a float between 0 (origin) and 1 (endpoint).
Reverse of GEOSGeometry.interpolate().
Returns the DE9IM intersection matrix (a string) representing the topological relationship between this geometry and the other.
Returns a new GEOSGeometry, simplified using the DouglasPeucker algorithm to the specified tolerance. A higher tolerance value implies less points in the output. If no tolerance is tolerance provided, it defaults to 0.
By default, this function does not preserve topology  e.g., Polygon objects can be split, collapsed into lines or disappear. Polygon holes can be created or disappear, and lines can cross. By specifying preserve_topology=True, the result will have the same dimension and number of components as the input, however, this is significantly slower.
Returns a GEOSGeometry combining the points in this geometry not in other, and the points in other not in this geometry.
Returns a GEOSGeometry representing all the points in this geometry and the other.
Returns the boundary as a newly allocated Geometry object.
Returns a Point object representing the geometric center of the geometry. The point is not guaranteed to be on the interior of the geometry.
Returns the smallest Polygon that contains all the points in the geometry.
Returns a Polygon that represents the bounding envelope of this geometry.
Computes and returns a Point guaranteed to be on the interior of this geometry.
This property returns the area of the Geometry.
This property returns the extent of this geometry as a 4tuple, consisting of (xmin, ymin, xmax, ymax).
This method returns a GEOSGeometry that is a clone of the original.
Returns the distance between the closest points on this geometry and the given geom (another GEOSGeometry object).
Note
GEOS distance calculations are linear – in other words, GEOS does not perform a spherical calculation even if the SRID specifies a geographic coordinate system.
Returns the length of this geometry (e.g., 0 for a Point, the length of a LineString, or the circumference of a Polygon).
Returns a GEOS PreparedGeometry for the contents of this geometry. PreparedGeometry objects are optimized for the contains, intersects, covers, crosses, disjoint, overlaps, touches and within operations. Refer to the Prepared Geometries documentation for more information.
Returns a SpatialReference object corresponding to the SRID of the geometry or None.
Note
Requires GDAL.
Transforms the geometry according to the given coordinate transformation parameter (ct), which may be an integer SRID, spatial reference WKT string, a PROJ.4 string, a SpatialReference object, or a CoordTransform object. By default, the geometry is transformed inplace and nothing is returned. However if the clone keyword is set, then the geometry is not modified and a transformed clone of the geometry is returned instead.
Note
Requires GDAL.
Note
Prior to 1.3, this method would silently noop if GDAL was not available. Now, a GEOSException is raised as application code relying on this behavior is in error. In addition, use of this method when the SRID is None or less than 0 now also generates a GEOSException.
Point objects are instantiated using arguments that represent the component coordinates of the point or with a single sequence coordinates. For example, the following are equivalent:
>>> pnt = Point(5, 23)
>>> pnt = Point([5, 23])
LineString objects are instantiated using arguments that are either a sequence of coordinates or Point objects. For example, the following are equivalent:
>>> ls = LineString((0, 0), (1, 1))
>>> ls = LineString(Point(0, 0), Point(1, 1))
In addition, LineString objects may also be created by passing in a single sequence of coordinate or Point objects:
>>> ls = LineString( ((0, 0), (1, 1)) )
>>> ls = LineString( [Point(0, 0), Point(1, 1)] )
LinearRing objects are constructed in the exact same way as LineString objects, however the coordinates must be closed, in other words, the first coordinates must be the same as the last coordinates. For example:
>>> ls = LinearRing((0, 0), (0, 1), (1, 1), (0, 0))
Notice that (0, 0) is the first and last coordinate – if they were not equal, an error would be raised.
Polygon objects may be instantiated by passing in one or more parameters that represent the rings of the polygon. The parameters must either be LinearRing instances, or a sequence that may be used to construct a LinearRing:
>>> ext_coords = ((0, 0), (0, 1), (1, 1), (1, 0), (0, 0))
>>> int_coords = ((0.4, 0.4), (0.4, 0.6), (0.6, 0.6), (0.6, 0.4), (0.4, 0.4))
>>> poly = Polygon(ext_coords, int_coords)
>>> poly = Polygon(LinearRing(ext_coords), LinearRing(int_coords))
Returns a polygon object from the given boundingbox, a 4tuple comprising (xmin, ymin, xmax, ymax).
Returns the number of interior rings in this geometry.
Comparing Polygons
Note that it is possible to compare Polygon objects directly with < or >, but as the comparison is made through Polygon’s LineString, it does not mean much (but is consistent and quick). You can always force the comparison with the area property:
>>> if poly_1.area > poly_2.area:
>>> pass
MultiLineString objects may be instantiated by passing in one or more LineString objects as arguments, or a single sequence of LineString objects:
>>> ls1 = LineString((0, 0), (1, 1))
>>> ls2 = LineString((2, 2), (3, 3))
>>> mls = MultiLineString(ls1, ls2)
>>> mls = MultiLineString([ls1, ls2])
Returns a LineString representing the line merge of all the components in this MultiLineString.
MultiPolygon objects may be instantiated by passing one or more Polygon objects as arguments, or a single sequence of Polygon objects:
>>> p1 = Polygon( ((0, 0), (0, 1), (1, 1), (0, 0)) )
>>> p2 = Polygon( ((1, 1), (1, 2), (2, 2), (1, 1)) )
>>> mp = MultiPolygon(p1, p2)
>>> mp = MultiPolygon([p1, p2])
Returns a Polygon that is the union of all of the component polygons in this collection. The algorithm employed is significantly more efficient (faster) than trying to union the geometries together individually. [2]
GeometryCollection objects may be instantiated by passing in one or more other GEOSGeometry as arguments, or a single sequence of GEOSGeometry objects:
>>> poly = Polygon( ((0, 0), (0, 1), (1, 1), (0, 0)) )
>>> gc = GeometryCollection(Point(0, 0), MultiPoint(Point(0, 0), Point(1, 1)), poly)
>>> gc = GeometryCollection((Point(0, 0), MultiPoint(Point(0, 0), Point(1, 1)), poly))
In order to obtain a prepared geometry, just access the GEOSGeometry.prepared property. Once you have a PreparedGeometry instance its spatial predicate methods, listed below, may be used with other GEOSGeometry objects. An operation with a prepared geometry can be orders of magnitude faster – the more complex the geometry that is prepared, the larger the speedup in the operation. For more information, please consult the GEOS wiki page on prepared geometries.
For example:
>>> from django.contrib.gis.geos import Point, Polygon
>>> poly = Polygon.from_bbox((0, 0, 5, 5))
>>> prep_poly = poly.prepared
>>> prep_poly.contains(Point(2.5, 2.5))
True
All methods on PreparedGeometry take an other argument, which must be a GEOSGeometry instance.
Note
GEOS 3.3 is required to use this predicate.
Note
GEOS 3.3 is required to use this predicate.
Note
GEOS 3.3 is required to use this predicate.
Note
GEOS 3.3 is required to use this predicate.
Note
GEOS 3.3 is required to use this predicate.
Parameters:  file_h (a Python file object or a string path to the file) – input file that contains spatial data 

Return type:  a GEOSGeometry corresponding to the spatial data in the file 
Example:
>>> from django.contrib.gis.geos import fromfile
>>> g = fromfile('/home/bob/geom.wkt')
Parameters:  

Return type:  a GEOSGeometry corresponding to the spatial data in the string 
Example:
>>> from django.contrib.gis.geos import fromstr
>>> pnt = fromstr('POINT(90.5 29.5)', srid=4326)
The reader I/O classes simply return a GEOSGeometry instance from the WKB and/or WKT input given to their read(geom) method.
Example:
>>> from django.contrib.gis.geos import WKBReader
>>> wkb_r = WKBReader()
>>> wkb_r.read('0101000000000000000000F03F000000000000F03F')
<Point object at 0x103a88910>
Example:
>>> from django.contrib.gis.geos import WKTReader
>>> wkt_r = WKTReader()
>>> wkt_r.read('POINT(1 1)')
<Point object at 0x103a88b50>
All writer objects have a write(geom) method that returns either the WKB or WKT of the given geometry. In addition, WKBWriter objects also have properties that may be used to change the byte order, and or include the SRID value (in other words, EWKB).
WKBWriter provides the most control over its output. By default it returns OGCcompliant WKB when its write method is called. However, it has properties that allow for the creation of EWKB, a superset of the WKB standard that includes additional information.
Returns the WKB of the given geometry as a Python buffer object. Example:
>>> from django.contrib.gis.geos import Point, WKBWriter
>>> pnt = Point(1, 1)
>>> wkb_w = WKBWriter()
>>> wkb_w.write(pnt)
<readonly buffer for 0x103a898f0, size 1, offset 0 at 0x103a89930>
Returns WKB of the geometry in hexadecimal. Example:
>>> from django.contrib.gis.geos import Point, WKBWriter
>>> pnt = Point(1, 1)
>>> wkb_w = WKBWriter()
>>> wkb_w.write_hex(pnt)
'0101000000000000000000F03F000000000000F03F'
This property may be set to change the byteorder of the geometry representation.
Byteorder Value  Description 

0  Big Endian (e.g., compatible with RISC systems) 
1  Little Endian (e.g., compatible with x86 systems) 
Example:
>>> from django.contrib.gis.geos import Point, WKBWriter
>>> wkb_w = WKBWriter()
>>> pnt = Point(1, 1)
>>> wkb_w.write_hex(pnt)
'0101000000000000000000F03F000000000000F03F'
>>> wkb_w.byteorder = 0
'00000000013FF00000000000003FF0000000000000'
This property may be set to change the output dimension of the geometry representation. In other words, if you have a 3D geometry then set to 3 so that the Z value is included in the WKB.
Outdim Value  Description 

2  The default, output 2D WKB. 
3  Output 3D WKB. 
Example:
>>> from django.contrib.gis.geos import Point, WKBWriter
>>> wkb_w = WKBWriter()
>>> wkb_w.outdim
2
>>> pnt = Point(1, 1, 1)
>>> wkb_w.write_hex(pnt) # By default, no Z value included:
'0101000000000000000000F03F000000000000F03F'
>>> wkb_w.outdim = 3 # Tell writer to include Z values
>>> wkb_w.write_hex(pnt)
'0101000080000000000000F03F000000000000F03F000000000000F03F'
Set this property with a boolean to indicate whether the SRID of the geometry should be included with the WKB representation. Example:
>>> from django.contrib.gis.geos import Point, WKBWriter
>>> wkb_w = WKBWriter()
>>> pnt = Point(1, 1, srid=4326)
>>> wkb_w.write_hex(pnt) # By default, no SRID included:
'0101000000000000000000F03F000000000000F03F'
>>> wkb_w.srid = True # Tell writer to include SRID
>>> wkb_w.write_hex(pnt)
'0101000020E6100000000000000000F03F000000000000F03F'
Returns the WKT of the given geometry. Example:
>>> from django.contrib.gis.geos import Point, WKTWriter
>>> pnt = Point(1, 1)
>>> wkt_w = WKTWriter()
>>> wkt_w.write(pnt)
'POINT (1.0000000000000000 1.0000000000000000)'
Footnotes
[1]  See PostGIS EWKB, EWKT and Canonical Forms, PostGIS documentation at Ch. 4.1.2. 
[2]  For more information, read Paul Ramsey’s blog post about (Much) Faster Unions in PostGIS 1.4 and Martin Davis’ blog post on Fast polygon merging in JTS using Cascaded Union. 
A string specifying the location of the GEOS C library. Typically, this setting is only used if the GEOS C library is in a nonstandard location (e.g., /home/bob/lib/libgeos_c.so).
Note
The setting must be the full path to the C shared library; in other words you want to use libgeos_c.so, not libgeos.so.
Jul 10, 2014