Geometry ======== Shapely geometry classes, such as ``shapely.Point``, are the central data types in Shapely. Each geometry class extends the ``shapely.Geometry`` base class, which is a container of the underlying GEOS geometry object, to provide geometry type-specific attributes and behavior. The ``Geometry`` object keeps track of the underlying GEOS geometry and lets the python garbage collector free its memory when it is not used anymore. Geometry objects are immutable. This means that after constructed, they cannot be changed in place. Every Shapely operation will result in a new object being returned. Geometry types ~~~~~~~~~~~~~~ .. currentmodule:: shapely .. autosummary:: :toctree: reference/ Point LineString LinearRing Polygon MultiPoint MultiLineString MultiPolygon GeometryCollection Construction ~~~~~~~~~~~~ Geometries can be constructed directly using Shapely geometry classes: .. code:: python >>> from shapely import Point, LineString >>> Point(5.2, 52.1) >>> LineString([(0, 0), (1, 2)]) Geometries can also be constructed from a WKT (Well-Known Text) or WKB (Well-Known Binary) representation: .. code:: python >>> from shapely import from_wkb, from_wkt >>> from_wkt("POINT (5.2 52.1)") >>> from_wkb(b"\x01\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\xf0?\x00\x00\x00\x00\x00\x00\xf0?") A more efficient way of constructing geometries is by making use of the (vectorized) functions described in :ref:`ref-creation`. Pickling ~~~~~~~~ Geometries can be serialized using pickle: >>> import pickle >>> from shapely import Point >>> pickled = pickle.dumps(Point(1, 1)) >>> pickle.loads(pickled) .. warning:: Pickling will convert linearrings to linestrings. See :func:`shapely.to_wkb` for a complete list of limitations. Hashing ~~~~~~~ Geometries can be used as elements in sets or as keys in dictionaries. Python uses a technique called *hashing* for lookups in these datastructures. Shapely generates this hash from the WKB representation. Therefore, geometries are equal if and only if their WKB representations are equal. .. code:: python >>> from shapely import Point >>> point_1 = Point(5.2, 52.1) >>> point_2 = Point(1, 1) >>> point_3 = Point(5.2, 52.1) >>> {point_1, point_2, point_3} {, } .. warning:: Due to limitations of WKB, linearrings will equal linestrings if they contain the exact same points. See :func:`shapely.to_wkb`. Comparing two geometries directly is also supported. This is the same as using :func:`shapely.equals_exact` with a ``tolerance`` value of zero. >>> point_1 == point_2 False >>> point_1 == point_3 True >>> point_1 != point_2 True Formatting ~~~~~~~~~~ Geometries can be formatted to strings using properties, functions, or a Python format specification. The most convenient is to use ``.wkb_hex`` and ``.wkt`` properties. .. code:: python >>> from shapely import Point, to_wkb, to_wkt, to_geojson >>> pt = Point(-169.910918, -18.997564) >>> pt.wkb_hex 0101000000CF6A813D263D65C0BDAAB35A60FF32C0 >>> pt.wkt POINT (-169.910918 -18.997564) More output options can be found using using :func:`~shapely.to_wkb`, :func:`~shapely.to_wkt`, and :func:`~shapely.to_geojson` functions. .. code:: python >>> to_wkb(pt, hex=True, byte_order=0) 0000000001C0653D263D816ACFC032FF605AB3AABD >>> to_wkt(pt, rounding_precision=3) POINT (-169.911 -18.998) >>> print(to_geojson(pt, indent=2)) { "type": "Point", "coordinates": [ -169.910918, -18.997564 ] } A format specification may also be used to control the format and precision. .. code:: python >>> print(f"Cave near {pt:.3f}") Cave near POINT (-169.911 -18.998) >>> print(f"or hex-encoded as {pt:x}") or hex-encoded as 0101000000cf6a813d263d65c0bdaab35a60ff32c0 Shapely has a format specification inspired from Python's :ref:`python:formatspec`, described next. Semantic for format specification --------------------------------- .. productionlist:: format-spec format_spec: [0][.`precision`][`type`] precision: `digit`+ digit: "0"..."9" type: "f" | "F" | "g" | "G" | "x" | "X" Format types ``'f'`` and ``'F'`` are to use a fixed-point notation, which is activated by setting GEOS' trim option off. The upper case variant converts ``nan`` to ``NAN`` and ``inf`` to ``INF``. Format types ``'g'`` and ``'G'`` are to use a "general format", where unnecessary digits are trimmed. This notation is activated by setting GEOS' trim option on. The upper case variant is similar to ``'F'``, and may also display an upper-case ``"E"`` if scientific notation is required. Note that this representation may be different for GEOS 3.10.0 and later, which does not use scientific notation. For numeric outputs ``'f'`` and ``'g'``, the precision is optional, and if not specified, rounding precision will be disabled showing full precision. Format types ``'x'`` and ``'X'`` show a hex-encoded string representation of WKB or Well-Known Binary, with the case of the output matched the case of the format type character. .. _canonical-form: Canonical form -------------- When operations are applied on geometries the result is returned according to some conventions. In most cases, geometries will be returned in "mild" canonical form. There is no goal to keep this form stable, so it is expected to change in future versions of GEOS: - the coordinates of exterior rings follow a clockwise orientation and interior rings have a counter-clockwise orientation. This is the opposite of the OGC specifications because the choice was made before this was included in the standard. - the starting point of rings can be changed in the output, but the exact order is undefined and should not be relied upon - the order of geometry types in a collection can be changed, but the order is undefined When :func:`~shapely.normalize` is used, the "strict" canonical form is applied. This type of normalization is meant to be stable, so changes to it will be avoided if possible: - the coordinates of exterior rings follow a clockwise orientation and interior rings have a counter-clockwise orientation - the starting point of rings is lower left - elements in collections are ordered by geometry type: by descending dimension and multi-types first (MultiPolygon, Polygon, MultiLineString, LineString, MultiPoint, Point). Multiple elements from the same type are ordered from right to left and from top to bottom. It is important to note that input geometries do not have to follow these conventions.