django/docs/ref/contrib/gis/geos.txt

========
GEOS API
========

.. module:: django.contrib.gis.geos
    :synopsis: GeoDjango's high-level interface to the GEOS library.

Background
==========

What is GEOS?
-------------

`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.

__ https://trac.osgeo.org/geos/
__ http://sourceforge.net/projects/jts-topo-suite/
__ http://www.opengeospatial.org/standards/sfs
__ http://www.refractions.net/

Features
--------

GeoDjango implements a high-level Python wrapper for the GEOS library, its
features include:

* A BSD-licensed interface to the GEOS geometry routines, implemented purely
  in Python using ``ctypes``.
* Loosely-coupled to GeoDjango.  For example, :class:`GEOSGeometry` objects
  may be used outside of a Django project/application.  In other words,
  no need to have ``DJANGO_SETTINGS_MODULE`` set or use a database, etc.
* Mutability: :class:`GEOSGeometry` objects may be modified.
* Cross-platform and tested; compatible with Windows, Linux, Solaris, and Mac
  OS X platforms.

.. _geos-tutorial:

Tutorial
========

This section contains a brief introduction and tutorial to using
:class:`GEOSGeometry` objects.

Creating a Geometry
-------------------

:class:`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 :class:`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)

All these constructors take the keyword argument ``srid``. For example::

    >>> from django.contrib.gis.geos import GEOSGeometry, LineString, Point
    >>> print(GEOSGeometry('POINT (0 0)', srid=4326))
    SRID=4326;POINT (0 0)
    >>> print(LineString((0, 0), (1, 1), srid=4326))
    SRID=4326;LINESTRING (0 0, 1 1)
    >>> print(Point(0, 0, srid=32140))
    SRID=32140;POINT (0 0)

Finally, there is the :func:`fromfile` factory method which returns a
:class:`GEOSGeometry` object from a file::

    >>> from django.contrib.gis.geos import fromfile
    >>> pnt = fromfile('/path/to/pnt.wkt')
    >>> pnt = fromfile(open('/path/to/pnt.wkt'))

.. _geos-exceptions-in-logfile:

.. admonition:: My logs are filled with GEOS-related errors

    You find many ``TypeError`` or ``AttributeError`` exceptions filling your
    Web server's log files. This generally means that you are creating GEOS
    objects at the top level of some of your Python modules. Then, due to a race
    condition in the garbage collector, your module is garbage collected before
    the GEOS object. To prevent this, create :class:`GEOSGeometry` objects
    inside the local scope of your functions/methods.

Geometries are Pythonic
-----------------------
:class:`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 :class:`Point`::

    >>> pnt = Point(5, 23)
    >>> [coord for coord in pnt]
    [5.0, 23.0]

With any geometry object, the :attr:`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 :class:`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 :class:`Polygon` will return the ring
(a :class:`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] # second-to-last 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))

Geometries support set-like operators::

    >>> from django.contrib.gis.geos import LineString
    >>> ls1 = LineString((0, 0), (2, 2))
    >>> ls2 = LineString((1, 1), (3, 3))
    >>> print(ls1 | ls2)  # equivalent to `ls1.union(ls2)`
    MULTILINESTRING ((0 0, 1 1), (1 1, 2 2), (2 2, 3 3))
    >>> print(ls1 & ls2)  # equivalent to `ls1.intersection(ls2)`
    LINESTRING (1 1, 2 2)
    >>> print(ls1 - ls2)  # equivalent to `ls1.difference(ls2)`
    LINESTRING(0 0, 1 1)
    >>> print(ls1 ^ ls2)  # equivalent to `ls1.sym_difference(ls2)`
    MULTILINESTRING ((0 0, 1 1), (2 2, 3 3))

.. admonition:: Equality operator doesn't check spatial equality

    The :class:`~GEOSGeometry` equality operator uses
    :meth:`~GEOSGeometry.equals_exact`, not :meth:`~GEOSGeometry.equals`, i.e.
    it requires the compared geometries to have the same coordinates in the
    same positions::

        >>> from django.contrib.gis.geos import LineString
        >>> ls1 = LineString((0, 0), (1, 1))
        >>> ls2 = LineString((1, 1), (0, 0))
        >>> ls1.equals(ls2)
        True
        >>> ls1 == ls2
        False

Geometry Objects
================

``GEOSGeometry``
----------------

.. class:: GEOSGeometry(geo_input, srid=None)

    :param geo_input: Geometry input value (string or buffer)
    :param srid: spatial reference identifier
    :type srid: int

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 :class:`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``
=======================  ======================

Properties
~~~~~~~~~~

.. attribute:: GEOSGeometry.coords

    Returns the coordinates of the geometry as a tuple.

.. attribute:: GEOSGeometry.dims

    Returns the dimension of the geometry:

    * ``0`` for :class:`Point`\s and :class:`MultiPoint`\s
    * ``1`` for :class:`LineString`\s and :class:`MultiLineString`\s
    * ``2`` for :class:`Polygon`\s and :class:`MultiPolygon`\s
    * ``-1`` for empty :class:`GeometryCollection`\s
    * the maximum dimension of its elements for non-empty
      :class:`GeometryCollection`\s

.. attribute:: GEOSGeometry.empty

    Returns whether or not the set of points in the geometry is empty.

.. attribute:: GEOSGeometry.geom_type

    Returns a string corresponding to the type of geometry.  For example::

        >>> pnt = GEOSGeometry('POINT(5 23)')
        >>> pnt.geom_type
        'Point'

.. attribute:: GEOSGeometry.geom_typeid

    Returns the GEOS geometry type identification number.  The following table
    shows the value for each geometry type:

    ===========================  ========
    Geometry                     ID
    ===========================  ========
    :class:`Point`               0
    :class:`LineString`          1
    :class:`LinearRing`          2
    :class:`Polygon`             3
    :class:`MultiPoint`          4
    :class:`MultiLineString`     5
    :class:`MultiPolygon`        6
    :class:`GeometryCollection`  7
    ===========================  ========

.. attribute:: GEOSGeometry.num_coords

    Returns the number of coordinates in the geometry.

.. attribute:: GEOSGeometry.num_geom

    Returns the number of geometries in this geometry.  In other words, will
    return 1 on anything but geometry collections.

.. attribute:: GEOSGeometry.hasz

    Returns a boolean indicating whether the geometry is three-dimensional.

.. attribute:: GEOSGeometry.ring

    Returns a boolean indicating whether the geometry is a ``LinearRing``.

.. attribute:: GEOSGeometry.simple

    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 :class:`LineString` object is not simple if it
    intersects itself. Thus, :class:`LinearRing` and :class:`Polygon` objects
    are always simple because they do cannot intersect themselves, by
    definition.

.. attribute:: GEOSGeometry.valid

    Returns a boolean indicating whether the geometry is valid.

.. attribute:: GEOSGeometry.valid_reason

    Returns a string describing the reason why a geometry is invalid.

.. attribute:: GEOSGeometry.srid

    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

Output Properties
~~~~~~~~~~~~~~~~~

The properties in this section export the :class:`GEOSGeometry` object into
a different.  This output may be in the form of a string, buffer, or even
another object.

.. attribute:: GEOSGeometry.ewkt

    Returns the "extended" Well-Known Text of the geometry.  This representation
    is specific to PostGIS and is a superset of the OGC WKT standard. [#fnogc]_
    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.

.. attribute:: GEOSGeometry.hex

    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
    :attr:`GEOSGeometry.hexewkb` property instead).

.. attribute:: GEOSGeometry.hexewkb

    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.

.. attribute:: GEOSGeometry.json

    Returns the GeoJSON representation of the geometry. Note that the result is
    not a complete GeoJSON structure but only the ``geometry`` key content of a
    GeoJSON structure. See also :doc:`/ref/contrib/gis/serializers`.

.. attribute:: GEOSGeometry.geojson

    Alias for :attr:`GEOSGeometry.json`.

.. attribute:: GEOSGeometry.kml

    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.

.. attribute:: GEOSGeometry.ogr

    Returns an :class:`~django.contrib.gis.gdal.OGRGeometry` object
    corresponding to the GEOS geometry.

.. _wkb:

.. attribute:: GEOSGeometry.wkb

    Returns the WKB (Well-Known Binary) representation of this Geometry
    as a Python buffer.  SRID value is not included, use the
    :attr:`GEOSGeometry.ewkb` property instead.

.. _ewkb:

.. attribute:: GEOSGeometry.ewkb

    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.

.. attribute:: GEOSGeometry.wkt

    Returns the Well-Known Text of the geometry (an OGC standard).

    .. versionchanged:: 1.10

        Non-significant zeros are stripped from the output.

__ https://developers.google.com/kml/documentation/

Spatial Predicate Methods
~~~~~~~~~~~~~~~~~~~~~~~~~

All of the following spatial predicate methods take another
:class:`GEOSGeometry` instance (``other``) as a parameter, and
return a boolean.

.. method:: GEOSGeometry.contains(other)

    Returns ``True`` if :meth:`other.within(this) <GEOSGeometry.within>` returns
    ``True``.

.. method:: GEOSGeometry.covers(other)

    .. versionadded:: 1.10

    Returns ``True`` if this geometry covers the specified geometry.

    The ``covers`` predicate has the following equivalent definitions:

    * Every point of the other geometry is a point of this geometry.
    * The DE-9IM Intersection Matrix for the two geometries is
      ``T*****FF*``, ``*T****FF*``, ``***T**FF*``, or ``****T*FF*``.

    If either geometry is empty, returns ``False``.

    This predicate is similar to :meth:`GEOSGeometry.contains`, but is more
    inclusive (i.e. returns ``True`` for more cases). In particular, unlike
    :meth:`~GEOSGeometry.contains` it does not distinguish between points in the
    boundary and in the interior of geometries. For most situations,
    ``covers()`` should be preferred to :meth:`~GEOSGeometry.contains`. As an
    added benefit, ``covers()`` is more amenable to optimization and hence
    should outperform :meth:`~GEOSGeometry.contains`.

.. method:: GEOSGeometry.crosses(other)

    Returns ``True`` if the DE-9IM 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).

.. method:: GEOSGeometry.disjoint(other)

    Returns ``True`` if the DE-9IM intersection matrix for the two geometries
    is ``FF*FF****``.

.. method:: GEOSGeometry.equals(other)

    Returns ``True`` if the DE-9IM intersection matrix for the two geometries
    is ``T*F**FFF*``.

.. method:: GEOSGeometry.equals_exact(other, tolerance=0)

    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.

.. method:: GEOSGeometry.intersects(other)

    Returns ``True`` if :meth:`GEOSGeometry.disjoint` is ``False``.

.. method:: GEOSGeometry.overlaps(other)

    Returns true if the DE-9IM intersection matrix for the two geometries
    is ``T*T***T**`` (for two points or two surfaces) ``1*T***T**``
    (for two curves).

.. method:: GEOSGeometry.relate_pattern(other, pattern)

    Returns ``True`` if the elements in the DE-9IM intersection matrix
    for this geometry and the other matches the given ``pattern`` --
    a string of nine characters from the alphabet: {``T``, ``F``, ``*``, ``0``}.

.. method:: GEOSGeometry.touches(other)

    Returns ``True`` if the DE-9IM intersection matrix for the two geometries
    is ``FT*******``, ``F**T*****`` or ``F***T****``.

.. method:: GEOSGeometry.within(other)

    Returns ``True`` if the DE-9IM intersection matrix for the two geometries
    is ``T*F**F***``.

Topological Methods
~~~~~~~~~~~~~~~~~~~

.. method:: GEOSGeometry.buffer(width, quadsegs=8)

    Returns a :class:`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).

.. method:: GEOSGeometry.difference(other)

    Returns a :class:`GEOSGeometry` representing the points making up this
    geometry that do not make up other.

.. method:: GEOSGeometry.interpolate(distance)
.. method:: GEOSGeometry.interpolate_normalized(distance)

    Given a distance (float), returns the point (or closest point) within the
    geometry (:class:`LineString` or :class:`MultiLineString`) at that distance.
    The normalized version takes the distance as a float between 0 (origin) and
    1 (endpoint).

    Reverse of :meth:`GEOSGeometry.project`.

.. method:: GEOSGeometry.intersection(other)

    Returns a :class:`GEOSGeometry` representing the points shared by this
    geometry and other.

.. method:: GEOSGeometry.project(point)
.. method:: GEOSGeometry.project_normalized(point)

    Returns the distance (float) from the origin of the geometry
    (:class:`LineString` or :class:`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 :meth:`GEOSGeometry.interpolate`.

.. method:: GEOSGeometry.relate(other)

    Returns the DE-9IM intersection matrix (a string) representing the
    topological relationship between this geometry and the other.

.. method:: GEOSGeometry.simplify(tolerance=0.0, preserve_topology=False)

    Returns a new :class:`GEOSGeometry`, simplified to the specified tolerance
    using the Douglas-Peucker algorithm. A higher tolerance value implies
    fewer points in the output. If no tolerance is provided, it defaults to 0.

    By default, this function does not preserve topology. For example,
    :class:`Polygon` objects can be split, be collapsed into lines, or
    disappear. :class:`Polygon` holes can be created or disappear, and lines may
    cross. By specifying ``preserve_topology=True``, the result will have the
    same dimension and number of components as the input; this is significantly
    slower, however.

.. method:: GEOSGeometry.sym_difference(other)

    Returns a :class:`GEOSGeometry` combining the points in this geometry
    not in other, and the points in other not in this geometry.

.. method:: GEOSGeometry.union(other)

    Returns a :class:`GEOSGeometry` representing all the points in this
    geometry and the other.

Topological Properties
~~~~~~~~~~~~~~~~~~~~~~

.. attribute:: GEOSGeometry.boundary

    Returns the boundary as a newly allocated Geometry object.

.. attribute:: GEOSGeometry.centroid

    Returns a :class:`Point` object representing the geometric center of
    the geometry.  The point is not guaranteed to be on the interior
    of the geometry.

.. attribute:: GEOSGeometry.convex_hull

    Returns the smallest :class:`Polygon` that contains all the points in
    the geometry.

.. attribute:: GEOSGeometry.envelope

    Returns a :class:`Polygon` that represents the bounding envelope of
    this geometry. Note that it can also return a :class:`Point` if the input
    geometry is a point.

.. attribute:: GEOSGeometry.point_on_surface

    Computes and returns a :class:`Point` guaranteed to be on the interior
    of this geometry.

.. attribute:: GEOSGeometry.unary_union

    .. versionadded:: 1.10

    Computes the union of all the elements of this geometry.

    The result obeys the following contract:

    * Unioning a set of :class:`LineString`\s has the effect of fully noding and
      dissolving the linework.

    * Unioning a set of :class:`Polygon`\s will always return a :class:`Polygon`
      or :class:`MultiPolygon` geometry (unlike :meth:`GEOSGeometry.union`,
      which may return geometries of lower dimension if a topology collapse
      occurs).

Other Properties & Methods
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. attribute:: GEOSGeometry.area

    This property returns the area of the Geometry.

.. attribute:: GEOSGeometry.extent

    This property returns the extent of this geometry as a 4-tuple,
    consisting of ``(xmin, ymin, xmax, ymax)``.

.. method:: GEOSGeometry.clone()

    This method returns a :class:`GEOSGeometry` that is a clone of the original.

.. method:: GEOSGeometry.distance(geom)

    Returns the distance between the closest points on this geometry and the
    given ``geom`` (another :class:`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.

.. attribute:: GEOSGeometry.length

    Returns the length of this geometry (e.g., 0 for a :class:`Point`,
    the length of a :class:`LineString`, or the circumference of
    a :class:`Polygon`).

.. attribute:: GEOSGeometry.prepared

    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 :ref:`prepared-geometries` documentation for more information.

.. attribute:: GEOSGeometry.srs

    Returns a :class:`~django.contrib.gis.gdal.SpatialReference` object
    corresponding to the SRID of the geometry or ``None``.

.. method:: GEOSGeometry.transform(ct, clone=False)

    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
    :class:`~django.contrib.gis.gdal.SpatialReference` object, or a
    :class:`~django.contrib.gis.gdal.CoordTransform` object. By default, the
    geometry is transformed in-place 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::

        Raises :class:`~django.contrib.gis.geos.GEOSException` if GDAL is not
        available or if the geometry's SRID is ``None`` or less than 0. It
        doesn't impose any constraints on the geometry's SRID if called with a
        :class:`~django.contrib.gis.gdal.CoordTransform` object.

        .. versionchanged:: 1.10

            In previous versions, it required the geometry's SRID to be a
            positive integer even if it was called with a
            :class:`~django.contrib.gis.gdal.CoordTransform` object.

``Point``
---------

.. class:: Point(x=None, y=None, z=None, srid=None)

    ``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])

    Empty ``Point`` objects may be instantiated by passing no arguments or an
    empty sequence. The following are equivalent::

        >>> pnt = Point()
        >>> pnt = Point([])

    .. versionchanged:: 1.10

        In previous versions, an empty ``Point`` couldn't be instantiated.

``LineString``
--------------

.. class:: LineString(*args, **kwargs)

    ``LineString`` objects are instantiated using arguments that are either a
    sequence of coordinates or :class:`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 :class:`Point` objects::

        >>> ls = LineString( ((0, 0), (1, 1)) )
        >>> ls = LineString( [Point(0, 0), Point(1, 1)] )

    Empty ``LineString`` objects may be instantiated by passing no arguments
    or an empty sequence. The following are equivalent::

        >>> ls = LineString()
        >>> ls = LineString([])

    .. versionchanged:: 1.10

        In previous versions, an empty ``LineString`` couldn't be instantiated.

    .. attribute:: closed

        .. versionadded:: 1.10

        Returns whether or not this ``LineString`` is closed.

``LinearRing``
--------------

.. class:: LinearRing(*args, **kwargs)

    ``LinearRing`` objects are constructed in the exact same way as
    :class:`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``
-----------

.. class:: Polygon(*args, **kwargs)

    ``Polygon`` objects may be instantiated by passing in parameters that
    represent the rings of the polygon.  The parameters must either be
    :class:`LinearRing` instances, or a sequence that may be used to construct a
    :class:`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))

    .. versionchanged:: 1.10

        In previous versions, an empty ``Polygon`` couldn't be instantiated.

    .. classmethod:: from_bbox(bbox)

        Returns a polygon object from the given bounding-box, a 4-tuple
        comprising ``(xmin, ymin, xmax, ymax)``.

    .. attribute:: num_interior_rings

        Returns the number of interior rings in this geometry.

.. admonition:: Comparing Polygons

    Note that it is possible to compare ``Polygon`` objects directly with ``<``
    or ``>``, but as the comparison is made through Polygon's
    :class:`LineString`, it does not mean much (but is consistent and quick).
    You can always force the comparison with the :attr:`~GEOSGeometry.area`
    property::

        >>> if poly_1.area > poly_2.area:
        >>>     pass

Geometry Collections
====================

``MultiPoint``
--------------

.. class:: MultiPoint(*args, **kwargs)

    ``MultiPoint`` objects may be instantiated by passing in :class:`Point`
    objects as arguments, or a single sequence of :class:`Point` objects::

        >>> mp = MultiPoint(Point(0, 0), Point(1, 1))
        >>> mp = MultiPoint( (Point(0, 0), Point(1, 1)) )

    .. versionchanged:: 1.10

        In previous versions, an empty ``MultiPoint`` couldn't be instantiated.

``MultiLineString``
-------------------

.. class:: MultiLineString(*args, **kwargs)

    ``MultiLineString`` objects may be instantiated by passing in
    :class:`LineString` objects as arguments, or a single sequence of
    :class:`LineString` objects::

        >>> ls1 = LineString((0, 0), (1, 1))
        >>> ls2 = LineString((2, 2), (3, 3))
        >>> mls = MultiLineString(ls1, ls2)
        >>> mls = MultiLineString([ls1, ls2])

    .. versionchanged:: 1.10

        In previous versions, an empty ``MultiLineString`` couldn't be
        instantiated.

    .. attribute:: merged

        Returns a :class:`LineString` representing the line merge of
        all the components in this ``MultiLineString``.

    .. attribute:: closed

        .. versionadded:: 1.10

        Returns ``True`` if and only if all elements are closed. Requires GEOS 3.5.

``MultiPolygon``
----------------

.. class:: MultiPolygon(*args, **kwargs)

    ``MultiPolygon`` objects may be instantiated by passing :class:`Polygon`
    objects as arguments, or a single sequence of :class:`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])

    .. versionchanged:: 1.10

        In previous versions, an empty ``MultiPolygon`` couldn't be
        instantiated.

    .. attribute:: cascaded_union

        .. deprecated:: 1.10

            Use the :attr:`GEOSGeometry.unary_union` property instead.

        Returns a :class:`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. [#fncascadedunion]_

``GeometryCollection``
----------------------

.. class:: GeometryCollection(*args, **kwargs)

    ``GeometryCollection`` objects may be instantiated by passing in other
    :class:`GEOSGeometry` as arguments, or a single sequence of
    :class:`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))

    .. versionchanged:: 1.10

        In previous versions, an empty ``GeometryCollection`` couldn't be
        instantiated.

.. _prepared-geometries:

Prepared Geometries
===================

In order to obtain a prepared geometry, just access the
:attr:`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 <https://trac.osgeo.org/geos/wiki/PreparedGeometry>`_.

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

``PreparedGeometry``
--------------------

.. class:: PreparedGeometry

    All methods on ``PreparedGeometry`` take an ``other`` argument, which
    must be a :class:`GEOSGeometry` instance.

    .. method:: contains(other)

    .. method:: contains_properly(other)

    .. method:: covers(other)

    .. method:: crosses(other)

    .. method:: disjoint(other)

    .. method:: intersects(other)

    .. method:: overlaps(other)

    .. method:: touches(other)

    .. method:: within(other)

Geometry Factories
==================

.. function:: fromfile(file_h)

    :param file_h: input file that contains spatial data
    :type file_h: a Python ``file`` object or a string path to the file
    :rtype: a :class:`GEOSGeometry` corresponding to the spatial data in the file

    Example::

        >>> from django.contrib.gis.geos import fromfile
        >>> g = fromfile('/home/bob/geom.wkt')

.. function:: fromstr(string, srid=None)

    :param string: string that contains spatial data
    :type string: string
    :param srid: spatial reference identifier
    :type srid: int
    :rtype: a :class:`GEOSGeometry` corresponding to the spatial data in the string

    ``fromstr(string, srid)`` is equivalent to
    :class:`GEOSGeometry(string, srid) <GEOSGeometry>`.

    Example::

        >>> from django.contrib.gis.geos import fromstr
        >>> pnt = fromstr('POINT(-90.5 29.5)', srid=4326)

I/O Objects
===========

Reader Objects
--------------

The reader I/O classes simply return a :class:`GEOSGeometry` instance from the
WKB and/or WKT input given to their ``read(geom)`` method.

.. class:: WKBReader

    Example::

        >>> from django.contrib.gis.geos import WKBReader
        >>> wkb_r = WKBReader()
        >>> wkb_r.read('0101000000000000000000F03F000000000000F03F')
        <Point object at 0x103a88910>

.. class:: WKTReader

    Example::

        >>> from django.contrib.gis.geos import WKTReader
        >>> wkt_r = WKTReader()
        >>> wkt_r.read('POINT(1 1)')
        <Point object at 0x103a88b50>

Writer Objects
--------------

All writer objects have a ``write(geom)`` method that returns either the
WKB or WKT of the given geometry.  In addition, :class:`WKBWriter` objects
also have properties that may be used to change the byte order, and or
include the SRID value (in other words, EWKB).

.. class:: WKBWriter(dim=2)

    ``WKBWriter`` provides the most control over its output.  By default it
    returns OGC-compliant 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. See the
    :attr:`WKBWriter.outdim` documentation for more details about the ``dim``
    argument.

    .. versionchanged:: 1.10

        The ability to pass the ``dim`` argument to the constructor was added.

    .. method:: WKBWriter.write(geom)

    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)
        <read-only buffer for 0x103a898f0, size -1, offset 0 at 0x103a89930>

    .. method:: WKBWriter.write_hex(geom)

    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'

    .. attribute:: WKBWriter.byteorder

    This property may be set to change the byte-order 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'

    .. attribute:: WKBWriter.outdim

    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'

    .. attribute:: WKBWriter.srid

    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'

.. class:: WKTWriter(dim=2, trim=False, precision=None)

    This class allows outputting the WKT representation of a geometry. See the
    :attr:`WKBWriter.outdim`, :attr:`trim`, and :attr:`precision` attributes for
    details about the constructor arguments.

    .. versionchanged:: 1.10

        The ability to pass the ``dim``, ``trim``, and ``precision`` arguments
        to the constructor was added.

    .. method:: WKTWriter.write(geom)

    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)'

    .. attribute:: WKTWriter.outdim

        See :attr:`WKBWriter.outdim`.

    .. attribute:: WKTWriter.trim

    .. versionadded:: 1.10

    This property is used to enable or disable trimming of
    unnecessary decimals.

        >>> from django.contrib.gis.geos import Point, WKTWriter
        >>> pnt = Point(1, 1)
        >>> wkt_w = WKTWriter()
        >>> wkt_w.trim
        False
        >>> wkt_w.write(pnt)
        'POINT (1.0000000000000000 1.0000000000000000)'
        >>> wkt_w.trim = True
        >>> wkt_w.write(pnt)
        'POINT (1 1)'

    .. attribute:: WKTWriter.precision

    .. versionadded:: 1.10

    This property controls the rounding precision of coordinates;
    if set to ``None`` rounding is disabled.

        >>> from django.contrib.gis.geos import Point, WKTWriter
        >>> pnt = Point(1.44, 1.66)
        >>> wkt_w = WKTWriter()
        >>> print(wkt_w.precision)
        None
        >>> wkt_w.write(pnt)
        'POINT (1.4399999999999999 1.6599999999999999)'
        >>> wkt_w.precision = 0
        >>> wkt_w.write(pnt)
        'POINT (1 2)'
        >>> wkt_w.precision = 1
        >>> wkt_w.write(pnt)
        'POINT (1.4 1.7)'

.. rubric:: Footnotes
.. [#fnogc] *See* `PostGIS EWKB, EWKT and Canonical Forms <http://postgis.net/docs/using_postgis_dbmanagement.html#EWKB_EWKT>`_, PostGIS documentation at Ch. 4.1.2.
.. [#fncascadedunion] For more information, read Paul Ramsey's blog post about `(Much) Faster Unions in PostGIS 1.4 <http://blog.cleverelephant.ca/2009/01/must-faster-unions-in-postgis-14.html>`_ and Martin Davis' blog post on `Fast polygon merging in JTS using Cascaded Union <http://lin-ear-th-inking.blogspot.com/2007/11/fast-polygon-merging-in-jts-using.html>`_.

Settings
========

.. setting:: GEOS_LIBRARY_PATH

``GEOS_LIBRARY_PATH``
---------------------

A string specifying the location of the GEOS C library.  Typically,
this setting is only used if the GEOS C library is in a non-standard
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``.

Exceptions
==========

.. exception:: GEOSException

    The base GEOS exception, indicates a GEOS-related error.