# 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.

## Construction#

Geometries can be constructed directly using Shapely geometry classes:

```>>> from shapely import Point, LineString
>>> Point(5.2, 52.1)
<POINT (5.2 52.1)>
>>> LineString([(0, 0), (1, 2)])
<LINESTRING (0 0, 1 2)>
```

Geometries can also be constructed from a WKT (Well-Known Text) or WKB (Well-Known Binary) representation:

```>>> from shapely import from_wkb, from_wkt
>>> from_wkt("POINT (5.2 52.1)")
<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?")
<POINT (1 1)>
```

A more efficient way of constructing geometries is by making use of the (vectorized) functions described in `shapely.creation`.

## Pickling#

Geometries can be serialized using pickle:

```>>> import pickle
>>> from shapely import Point
>>> pickled = pickle.dumps(Point(1, 1))
<POINT (1 1)>
```

Warning

Pickling will convert linearrings to linestrings. See `shapely.io.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.

```>>> 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}
{<POINT (1 1)>, <POINT (5.2 52.1)>}
```

Warning

Due to limitations of WKB, linearrings will equal linestrings if they contain the exact same points. See `shapely.io.to_wkb()`.

Comparing two geometries directly is also supported. This is the same as using `shapely.predicates.equals_exact()` with a `tolerance` value of zero.

```>>> point_1 == point_2
False
>>> point_1 == point_3
True
>>> point_1 != point_2
True
```

## Geometry types#

Geometry classes and factories

class GeometryCollection(geoms=None)#

Bases: `shapely.geometry.base.BaseMultipartGeometry`

A collection of one or more geometries that may contain more than one type of geometry.

Parameters
geomslist

A list of shapely geometry instances, which may be of varying geometry types.

Examples

Create a GeometryCollection with a Point and a LineString

```>>> from shapely import LineString, Point
>>> p = Point(51, -1)
>>> l = LineString([(52, -1), (49, 2)])
>>> gc = GeometryCollection([p, l])
```
Attributes
geomssequence

A sequence of Shapely geometry instances

Methods

 `almost_equals`(other[, decimal]) True if geometries are equal at all coordinates to a specified decimal place. `buffer`(distance[, resolution, quadsegs, ...]) Get a geometry that represents all points within a distance of this geometry. `contains`(other) Returns True if the geometry contains the other, else False `covered_by`(other) Returns True if the geometry is covered by the other, else False `covers`(other) Returns True if the geometry covers the other, else False `crosses`(other) Returns True if the geometries cross, else False `difference`(other) Returns the difference of the geometries `disjoint`(other) Returns True if geometries are disjoint, else False `distance`(other) Unitless distance to other geometry (float) `equals`(other) Returns True if geometries are equal, else False. `equals_exact`(other, tolerance) True if geometries are equal to within a specified tolerance. `hausdorff_distance`(other) Unitless hausdorff distance to other geometry (float) `interpolate`(distance[, normalized]) Return a point at the specified distance along a linear geometry `intersection`(other) Returns the intersection of the geometries `intersects`(other) Returns True if geometries intersect, else False `line_interpolate_point`(distance[, normalized]) Return a point at the specified distance along a linear geometry `line_locate_point`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point Converts geometry to normal form (or canonical form). `overlaps`(other) Returns True if geometries overlap, else False Returns a point guaranteed to be within the object, cheaply. `project`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point `relate`(other) Returns the DE-9IM intersection matrix for the two geometries (string) `relate_pattern`(other, pattern) Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False Returns a point guaranteed to be within the object, cheaply. Returns a copy of this geometry with the order of coordinates reversed. `segmentize`(tolerance) Adds vertices to line segments based on tolerance. `simplify`(tolerance[, preserve_topology]) Returns a simplified geometry produced by the Douglas-Peucker algorithm `svg`([scale_factor, color]) Returns a group of SVG elements for the multipart geometry. Returns the symmetric difference of the geometries (Shapely geometry) `touches`(other) Returns True if geometries touch, else False `union`(other) Returns the union of the geometries (Shapely geometry) `within`(other) Returns True if geometry is within the other, else False
 geometryType
__eq__(value, /)#

Return self==value.

__ge__(value, /)#

Return self>=value.

property __geo_interface__#

Dictionary representation of the geometry

__gt__(value, /)#

Return self>value.

__hash__(/)#

Return hash(self).

__le__(value, /)#

Return self<=value.

__lt__(value, /)#

Return self<value.

__ne__(value, /)#

Return self!=value.

static __new__(self, geoms=None)#
__or__(other)#

Return self|value.

__reduce__()#

Helper for pickle.

__repr__()#

Return repr(self).

__str__()#

Return str(self).

almost_equals(other, decimal=6)#

True if geometries are equal at all coordinates to a specified decimal place.

Deprecated since version 1.8.0: The ‘almost_equals()’ method is deprecated and will be removed in Shapely 2.0 because the name is confusing. The ‘equals_exact()’ method should be used instead.

Refers to approximate coordinate equality, which requires coordinates to be approximately equal and in the same order for all components of a geometry.

Because of this it is possible for “equals()” to be True for two geometries and “almost_equals()” to be False.

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property area#

Unitless area of the geometry (float)

property boundary#

Returns a lower dimension geometry that bounds the object

The boundary of a polygon is a line, the boundary of a line is a collection of points. The boundary of a point is an empty (null) collection.

property bounds#

Returns minimum bounding region (minx, miny, maxx, maxy)

buffer(distance, resolution=16, quadsegs=None, cap_style=1, join_style=1, mitre_limit=5.0, single_sided=False)#

Get a geometry that represents all points within a distance of this geometry.

A positive distance produces a dilation, a negative distance an erosion. A very small or zero distance may sometimes be used to “tidy” a polygon.

Parameters
distancefloat

The distance to buffer around the object.

resolutionint, optional

The resolution of the buffer around each vertex of the object.

Sets the number of line segments used to approximate an angle fillet. Note: the use of a quadsegs parameter is deprecated and will be gone from the next major release.

cap_styleint, optional

The styles of caps are: CAP_STYLE.round (1), CAP_STYLE.flat (2), and CAP_STYLE.square (3).

join_styleint, optional

The styles of joins between offset segments are: JOIN_STYLE.round (1), JOIN_STYLE.mitre (2), and JOIN_STYLE.bevel (3).

mitre_limitfloat, optional

The mitre limit ratio is used for very sharp corners. The mitre ratio is the ratio of the distance from the corner to the end of the mitred offset corner. When two line segments meet at a sharp angle, a miter join will extend the original geometry. To prevent unreasonable geometry, the mitre limit allows controlling the maximum length of the join corner. Corners with a ratio which exceed the limit will be beveled.

single_sidebool, optional

The side used is determined by the sign of the buffer distance:

a positive distance indicates the left-hand side a negative distance indicates the right-hand side

The single-sided buffer of point geometries is the same as the regular buffer. The End Cap Style for single-sided buffers is always ignored, and forced to the equivalent of CAP_FLAT.

Returns
Geometry

Notes

The return value is a strictly two-dimensional geometry. All Z coordinates of the original geometry will be ignored.

Examples

```>>> from shapely.wkt import loads
>>> g = loads('POINT (0.0 0.0)')
```

16-gon approx of a unit radius circle:

```>>> g.buffer(1.0).area
3.1365484905459...
```

128-gon approximation:

```>>> g.buffer(1.0, 128).area
3.141513801144...
```

triangle approximation:

```>>> g.buffer(1.0, 3).area
3.0
>>> list(g.buffer(1.0, cap_style=CAP_STYLE.square).exterior.coords)
[(1.0, 1.0), (1.0, -1.0), (-1.0, -1.0), (-1.0, 1.0), (1.0, 1.0)]
>>> g.buffer(1.0, cap_style=CAP_STYLE.square).area
4.0
```
property centroid#

Returns the geometric center of the object

contains(other)#

Returns True if the geometry contains the other, else False

property convex_hull#

Imagine an elastic band stretched around the geometry: that’s a convex hull, more or less

The convex hull of a three member multipoint, for example, is a triangular polygon.

property coords#

covered_by(other)#

Returns True if the geometry is covered by the other, else False

covers(other)#

Returns True if the geometry covers the other, else False

crosses(other)#

Returns True if the geometries cross, else False

difference(other)#

Returns the difference of the geometries

disjoint(other)#

Returns True if geometries are disjoint, else False

distance(other)#

Unitless distance to other geometry (float)

property envelope#

A figure that envelopes the geometry

equals(other)#

Returns True if geometries are equal, else False.

This method considers point-set equality (or topological equality), and is equivalent to (self.within(other) & self.contains(other)).

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals(
...     LineString([(0, 0), (1, 1), (2, 2)])
... )
True
```
equals_exact(other, tolerance)#

True if geometries are equal to within a specified tolerance.

Parameters
otherBaseGeometry

The other geometry object in this comparison.

tolerancefloat

Absolute tolerance in the same units as coordinates.

This method considers coordinate equality, which requires
coordinates to be equal and in the same order for all components
of a geometry.
Because of this it is possible for “equals()” to be True for two
geometries and “equals_exact()” to be False.
Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property geom_type#

Name of the geometry’s type, such as ‘Point’

property has_z#

True if the geometry’s coordinate sequence(s) have z values (are 3-dimensional)

hausdorff_distance(other)#

Unitless hausdorff distance to other geometry (float)

interpolate(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of line_interpolate_point.

intersection(other)#

Returns the intersection of the geometries

intersects(other)#

Returns True if geometries intersect, else False

property is_closed#

True if the geometry is closed, else False

Applicable only to 1-D geometries.

property is_empty#

True if the set of points in this geometry is empty, else False

property is_ring#

True if the geometry is a closed ring, else False

property is_simple#

True if the geometry is simple, meaning that any self-intersections are only at boundary points, else False

property is_valid#

True if the geometry is valid (definition depends on sub-class), else False

property length#

Unitless length of the geometry (float)

line_interpolate_point(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of interpolate.

line_locate_point(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of project.

property minimum_clearance#

Unitless distance by which a node could be moved to produce an invalid geometry (float)

property minimum_rotated_rectangle#

Returns the general minimum bounding rectangle of the geometry. Can possibly be rotated. If the convex hull of the object is a degenerate (line or point) this same degenerate is returned.

normalize()#

Converts geometry to normal form (or canonical form).

This method orders the coordinates, rings of a polygon and parts of multi geometries consistently. Typically useful for testing purposes (for example in combination with equals_exact).

Examples

```>>> from shapely import MultiLineString
>>> line = MultiLineString([[(0, 0), (1, 1)], [(3, 3), (2, 2)]])
>>> line.normalize()
<MULTILINESTRING ((2 2, 3 3), (0 0, 1 1))>
```
overlaps(other)#

Returns True if geometries overlap, else False

point_on_surface()#

Returns a point guaranteed to be within the object, cheaply.

Alias of representative_point.

project(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of line_locate_point.

relate(other)#

Returns the DE-9IM intersection matrix for the two geometries (string)

relate_pattern(other, pattern)#

Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False

representative_point()#

Returns a point guaranteed to be within the object, cheaply.

Alias of point_on_surface.

reverse()#

Returns a copy of this geometry with the order of coordinates reversed.

If the geometry is a polygon with interior rings, the interior rings are also reversed.

Points are unchanged.

`is_ccw`

Checks if a geometry is clockwise.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (1, 2)]).reverse()
<LINESTRING (1 2, 0 0)>
>>> Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]).reverse()
<POLYGON ((0 0, 0 1, 1 1, 1 0, 0 0))>
```
segmentize(tolerance)#

Adds vertices to line segments based on tolerance.

Additional vertices will be added to every line segment in an input geometry so that segments are no greater than tolerance. New vertices will evenly subdivide each segment.

Only linear components of input geometries are densified; other geometries are returned unmodified.

Parameters
tolerancefloat or array_like

Additional vertices will be added so that all line segments are no greater than this value. Must be greater than 0.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (0, 10)]).segmentize(tolerance=5)
<LINESTRING (0 0, 0 5, 0 10)>
>>> Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]).segmentize(tolerance=5)
<POLYGON ((0 0, 5 0, 10 0, 10 5, 10 10, 5 10, 0 10, 0 5, 0 0))>
```
simplify(tolerance, preserve_topology=True)#

Returns a simplified geometry produced by the Douglas-Peucker algorithm

Coordinates of the simplified geometry will be no more than the tolerance distance from the original. Unless the topology preserving option is used, the algorithm may produce self-intersecting or otherwise invalid geometries.

svg(scale_factor=1.0, color=None)#

Returns a group of SVG elements for the multipart geometry.

Parameters
scale_factorfloat

Multiplication factor for the SVG stroke-width. Default is 1.

colorstr, optional

Hex string for stroke or fill color. Default is to use “#66cc99” if geometry is valid, and “#ff3333” if invalid.

symmetric_difference(other)#

Returns the symmetric difference of the geometries (Shapely geometry)

touches(other)#

Returns True if geometries touch, else False

union(other)#

Returns the union of the geometries (Shapely geometry)

within(other)#

Returns True if geometry is within the other, else False

property wkb#

WKB representation of the geometry

property wkb_hex#

WKB hex representation of the geometry

property wkt#

WKT representation of the geometry

property xy#

Separate arrays of X and Y coordinate values

class LineString(coordinates=None)#

Bases: `shapely.geometry.base.BaseGeometry`

A geometry type composed of one or more line segments.

A LineString is a one-dimensional feature and has a non-zero length but zero area. It may approximate a curve and need not be straight. Unlike a LinearRing, a LineString is not closed.

Parameters
coordinatessequence

A sequence of (x, y, [,z]) numeric coordinate pairs or triples, or an array-like with shape (N, 2) or (N, 3). Also can be a sequence of Point objects.

Examples

Create a LineString with two segments

```>>> a = LineString([[0, 0], [1, 0], [1, 1]])
>>> a.length
2.0
```
Attributes
`area`

Unitless area of the geometry (float)

`boundary`

Returns a lower dimension geometry that bounds the object

`bounds`

Returns minimum bounding region (minx, miny, maxx, maxy)

`centroid`

Returns the geometric center of the object

`convex_hull`

Imagine an elastic band stretched around the geometry: that’s a

`coords`

`envelope`

A figure that envelopes the geometry

`geom_type`

Name of the geometry’s type, such as ‘Point’

`has_z`

True if the geometry’s coordinate sequence(s) have z values (are

`is_closed`

True if the geometry is closed, else False

`is_empty`

True if the set of points in this geometry is empty, else False

`is_ring`

True if the geometry is a closed ring, else False

`is_simple`

True if the geometry is simple, meaning that any self-intersections

`is_valid`

True if the geometry is valid (definition depends on sub-class),

`length`

Unitless length of the geometry (float)

`minimum_clearance`

Unitless distance by which a node could be moved to produce an invalid geometry (float)

`minimum_rotated_rectangle`

Returns the general minimum bounding rectangle of the geometry.

type
`wkb`

WKB representation of the geometry

`wkb_hex`

WKB hex representation of the geometry

`wkt`

WKT representation of the geometry

`xy`

Separate arrays of X and Y coordinate values

Methods

 `almost_equals`(other[, decimal]) True if geometries are equal at all coordinates to a specified decimal place. `buffer`(distance[, resolution, quadsegs, ...]) Get a geometry that represents all points within a distance of this geometry. `contains`(other) Returns True if the geometry contains the other, else False `covered_by`(other) Returns True if the geometry is covered by the other, else False `covers`(other) Returns True if the geometry covers the other, else False `crosses`(other) Returns True if the geometries cross, else False `difference`(other) Returns the difference of the geometries `disjoint`(other) Returns True if geometries are disjoint, else False `distance`(other) Unitless distance to other geometry (float) `equals`(other) Returns True if geometries are equal, else False. `equals_exact`(other, tolerance) True if geometries are equal to within a specified tolerance. `hausdorff_distance`(other) Unitless hausdorff distance to other geometry (float) `interpolate`(distance[, normalized]) Return a point at the specified distance along a linear geometry `intersection`(other) Returns the intersection of the geometries `intersects`(other) Returns True if geometries intersect, else False `line_interpolate_point`(distance[, normalized]) Return a point at the specified distance along a linear geometry `line_locate_point`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point Converts geometry to normal form (or canonical form). `overlaps`(other) Returns True if geometries overlap, else False `parallel_offset`(distance[, side, ...]) Returns a LineString or MultiLineString geometry at a distance from the object on its right or its left side. Returns a point guaranteed to be within the object, cheaply. `project`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point `relate`(other) Returns the DE-9IM intersection matrix for the two geometries (string) `relate_pattern`(other, pattern) Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False Returns a point guaranteed to be within the object, cheaply. Returns a copy of this geometry with the order of coordinates reversed. `segmentize`(tolerance) Adds vertices to line segments based on tolerance. `simplify`(tolerance[, preserve_topology]) Returns a simplified geometry produced by the Douglas-Peucker algorithm `svg`([scale_factor, stroke_color, opacity]) Returns SVG polyline element for the LineString geometry. Returns the symmetric difference of the geometries (Shapely geometry) `touches`(other) Returns True if geometries touch, else False `union`(other) Returns the union of the geometries (Shapely geometry) `within`(other) Returns True if geometry is within the other, else False
 geometryType
__eq__(value, /)#

Return self==value.

__ge__(value, /)#

Return self>=value.

property __geo_interface__#

Dictionary representation of the geometry

__gt__(value, /)#

Return self>value.

__hash__(/)#

Return hash(self).

__le__(value, /)#

Return self<=value.

__lt__(value, /)#

Return self<value.

__ne__(value, /)#

Return self!=value.

static __new__(self, coordinates=None)#
__or__(other)#

Return self|value.

__reduce__()#

Helper for pickle.

__repr__()#

Return repr(self).

__str__()#

Return str(self).

almost_equals(other, decimal=6)#

True if geometries are equal at all coordinates to a specified decimal place.

Deprecated since version 1.8.0: The ‘almost_equals()’ method is deprecated and will be removed in Shapely 2.0 because the name is confusing. The ‘equals_exact()’ method should be used instead.

Refers to approximate coordinate equality, which requires coordinates to be approximately equal and in the same order for all components of a geometry.

Because of this it is possible for “equals()” to be True for two geometries and “almost_equals()” to be False.

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property area#

Unitless area of the geometry (float)

property boundary#

Returns a lower dimension geometry that bounds the object

The boundary of a polygon is a line, the boundary of a line is a collection of points. The boundary of a point is an empty (null) collection.

property bounds#

Returns minimum bounding region (minx, miny, maxx, maxy)

buffer(distance, resolution=16, quadsegs=None, cap_style=1, join_style=1, mitre_limit=5.0, single_sided=False)#

Get a geometry that represents all points within a distance of this geometry.

A positive distance produces a dilation, a negative distance an erosion. A very small or zero distance may sometimes be used to “tidy” a polygon.

Parameters
distancefloat

The distance to buffer around the object.

resolutionint, optional

The resolution of the buffer around each vertex of the object.

Sets the number of line segments used to approximate an angle fillet. Note: the use of a quadsegs parameter is deprecated and will be gone from the next major release.

cap_styleint, optional

The styles of caps are: CAP_STYLE.round (1), CAP_STYLE.flat (2), and CAP_STYLE.square (3).

join_styleint, optional

The styles of joins between offset segments are: JOIN_STYLE.round (1), JOIN_STYLE.mitre (2), and JOIN_STYLE.bevel (3).

mitre_limitfloat, optional

The mitre limit ratio is used for very sharp corners. The mitre ratio is the ratio of the distance from the corner to the end of the mitred offset corner. When two line segments meet at a sharp angle, a miter join will extend the original geometry. To prevent unreasonable geometry, the mitre limit allows controlling the maximum length of the join corner. Corners with a ratio which exceed the limit will be beveled.

single_sidebool, optional

The side used is determined by the sign of the buffer distance:

a positive distance indicates the left-hand side a negative distance indicates the right-hand side

The single-sided buffer of point geometries is the same as the regular buffer. The End Cap Style for single-sided buffers is always ignored, and forced to the equivalent of CAP_FLAT.

Returns
Geometry

Notes

The return value is a strictly two-dimensional geometry. All Z coordinates of the original geometry will be ignored.

Examples

```>>> from shapely.wkt import loads
>>> g = loads('POINT (0.0 0.0)')
```

16-gon approx of a unit radius circle:

```>>> g.buffer(1.0).area
3.1365484905459...
```

128-gon approximation:

```>>> g.buffer(1.0, 128).area
3.141513801144...
```

triangle approximation:

```>>> g.buffer(1.0, 3).area
3.0
>>> list(g.buffer(1.0, cap_style=CAP_STYLE.square).exterior.coords)
[(1.0, 1.0), (1.0, -1.0), (-1.0, -1.0), (-1.0, 1.0), (1.0, 1.0)]
>>> g.buffer(1.0, cap_style=CAP_STYLE.square).area
4.0
```
property centroid#

Returns the geometric center of the object

contains(other)#

Returns True if the geometry contains the other, else False

property convex_hull#

Imagine an elastic band stretched around the geometry: that’s a convex hull, more or less

The convex hull of a three member multipoint, for example, is a triangular polygon.

property coords#

covered_by(other)#

Returns True if the geometry is covered by the other, else False

covers(other)#

Returns True if the geometry covers the other, else False

crosses(other)#

Returns True if the geometries cross, else False

difference(other)#

Returns the difference of the geometries

disjoint(other)#

Returns True if geometries are disjoint, else False

distance(other)#

Unitless distance to other geometry (float)

property envelope#

A figure that envelopes the geometry

equals(other)#

Returns True if geometries are equal, else False.

This method considers point-set equality (or topological equality), and is equivalent to (self.within(other) & self.contains(other)).

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals(
...     LineString([(0, 0), (1, 1), (2, 2)])
... )
True
```
equals_exact(other, tolerance)#

True if geometries are equal to within a specified tolerance.

Parameters
otherBaseGeometry

The other geometry object in this comparison.

tolerancefloat

Absolute tolerance in the same units as coordinates.

This method considers coordinate equality, which requires
coordinates to be equal and in the same order for all components
of a geometry.
Because of this it is possible for “equals()” to be True for two
geometries and “equals_exact()” to be False.
Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property geom_type#

Name of the geometry’s type, such as ‘Point’

property has_z#

True if the geometry’s coordinate sequence(s) have z values (are 3-dimensional)

hausdorff_distance(other)#

Unitless hausdorff distance to other geometry (float)

interpolate(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of line_interpolate_point.

intersection(other)#

Returns the intersection of the geometries

intersects(other)#

Returns True if geometries intersect, else False

property is_closed#

True if the geometry is closed, else False

Applicable only to 1-D geometries.

property is_empty#

True if the set of points in this geometry is empty, else False

property is_ring#

True if the geometry is a closed ring, else False

property is_simple#

True if the geometry is simple, meaning that any self-intersections are only at boundary points, else False

property is_valid#

True if the geometry is valid (definition depends on sub-class), else False

property length#

Unitless length of the geometry (float)

line_interpolate_point(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of interpolate.

line_locate_point(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of project.

property minimum_clearance#

Unitless distance by which a node could be moved to produce an invalid geometry (float)

property minimum_rotated_rectangle#

Returns the general minimum bounding rectangle of the geometry. Can possibly be rotated. If the convex hull of the object is a degenerate (line or point) this same degenerate is returned.

normalize()#

Converts geometry to normal form (or canonical form).

This method orders the coordinates, rings of a polygon and parts of multi geometries consistently. Typically useful for testing purposes (for example in combination with equals_exact).

Examples

```>>> from shapely import MultiLineString
>>> line = MultiLineString([[(0, 0), (1, 1)], [(3, 3), (2, 2)]])
>>> line.normalize()
<MULTILINESTRING ((2 2, 3 3), (0 0, 1 1))>
```
overlaps(other)#

Returns True if geometries overlap, else False

parallel_offset(distance, side='right', resolution=16, join_style=1, mitre_limit=5.0)#

Returns a LineString or MultiLineString geometry at a distance from the object on its right or its left side.

The side parameter may be ‘left’ or ‘right’ (default is ‘right’). The resolution of the buffer around each vertex of the object increases by increasing the resolution keyword parameter or third positional parameter. Vertices of right hand offset lines will be ordered in reverse.

The join style is for outside corners between line segments. Accepted values are JOIN_STYLE.round (1), JOIN_STYLE.mitre (2), and JOIN_STYLE.bevel (3).

The mitre ratio limit is used for very sharp corners. It is the ratio of the distance from the corner to the end of the mitred offset corner. When two line segments meet at a sharp angle, a miter join will extend far beyond the original geometry. To prevent unreasonable geometry, the mitre limit allows controlling the maximum length of the join corner. Corners with a ratio which exceed the limit will be beveled.

point_on_surface()#

Returns a point guaranteed to be within the object, cheaply.

Alias of representative_point.

project(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of line_locate_point.

relate(other)#

Returns the DE-9IM intersection matrix for the two geometries (string)

relate_pattern(other, pattern)#

Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False

representative_point()#

Returns a point guaranteed to be within the object, cheaply.

Alias of point_on_surface.

reverse()#

Returns a copy of this geometry with the order of coordinates reversed.

If the geometry is a polygon with interior rings, the interior rings are also reversed.

Points are unchanged.

`is_ccw`

Checks if a geometry is clockwise.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (1, 2)]).reverse()
<LINESTRING (1 2, 0 0)>
>>> Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]).reverse()
<POLYGON ((0 0, 0 1, 1 1, 1 0, 0 0))>
```
segmentize(tolerance)#

Adds vertices to line segments based on tolerance.

Additional vertices will be added to every line segment in an input geometry so that segments are no greater than tolerance. New vertices will evenly subdivide each segment.

Only linear components of input geometries are densified; other geometries are returned unmodified.

Parameters
tolerancefloat or array_like

Additional vertices will be added so that all line segments are no greater than this value. Must be greater than 0.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (0, 10)]).segmentize(tolerance=5)
<LINESTRING (0 0, 0 5, 0 10)>
>>> Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]).segmentize(tolerance=5)
<POLYGON ((0 0, 5 0, 10 0, 10 5, 10 10, 5 10, 0 10, 0 5, 0 0))>
```
simplify(tolerance, preserve_topology=True)#

Returns a simplified geometry produced by the Douglas-Peucker algorithm

Coordinates of the simplified geometry will be no more than the tolerance distance from the original. Unless the topology preserving option is used, the algorithm may produce self-intersecting or otherwise invalid geometries.

svg(scale_factor=1.0, stroke_color=None, opacity=None)#

Returns SVG polyline element for the LineString geometry.

Parameters
scale_factorfloat

Multiplication factor for the SVG stroke-width. Default is 1.

stroke_colorstr, optional

Hex string for stroke color. Default is to use “#66cc99” if geometry is valid, and “#ff3333” if invalid.

opacityfloat

Float number between 0 and 1 for color opacity. Default value is 0.8

symmetric_difference(other)#

Returns the symmetric difference of the geometries (Shapely geometry)

touches(other)#

Returns True if geometries touch, else False

union(other)#

Returns the union of the geometries (Shapely geometry)

within(other)#

Returns True if geometry is within the other, else False

property wkb#

WKB representation of the geometry

property wkb_hex#

WKB hex representation of the geometry

property wkt#

WKT representation of the geometry

property xy#

Separate arrays of X and Y coordinate values

Example:

```>>> x, y = LineString([(0, 0), (1, 1)]).xy
>>> list(x)
[0.0, 1.0]
>>> list(y)
[0.0, 1.0]
```
class LinearRing(coordinates=None)#

A geometry type composed of one or more line segments that forms a closed loop.

A LinearRing is a closed, one-dimensional feature. A LinearRing that crosses itself or touches itself at a single point is invalid and operations on it may fail.

Parameters
coordinatessequence

A sequence of (x, y [,z]) numeric coordinate pairs or triples, or an array-like with shape (N, 2) or (N, 3). Also can be a sequence of Point objects.

Notes

Rings are automatically closed. There is no need to specify a final coordinate pair identical to the first.

Examples

Construct a square ring.

```>>> ring = LinearRing( ((0, 0), (0, 1), (1 ,1 ), (1 , 0)) )
>>> ring.is_closed
True
>>> list(ring.coords)
[(0.0, 0.0), (0.0, 1.0), (1.0, 1.0), (1.0, 0.0), (0.0, 0.0)]
>>> ring.length
4.0
```
Attributes
`area`

Unitless area of the geometry (float)

`boundary`

Returns a lower dimension geometry that bounds the object

`bounds`

Returns minimum bounding region (minx, miny, maxx, maxy)

`centroid`

Returns the geometric center of the object

`convex_hull`

Imagine an elastic band stretched around the geometry: that’s a

`coords`

`envelope`

A figure that envelopes the geometry

`geom_type`

Name of the geometry’s type, such as ‘Point’

`has_z`

True if the geometry’s coordinate sequence(s) have z values (are

`is_ccw`

True is the ring is oriented counter clock-wise

`is_closed`

True if the geometry is closed, else False

`is_empty`

True if the set of points in this geometry is empty, else False

`is_ring`

True if the geometry is a closed ring, else False

`is_simple`

True if the geometry is simple, meaning that any self-intersections

`is_valid`

True if the geometry is valid (definition depends on sub-class),

`length`

Unitless length of the geometry (float)

`minimum_clearance`

Unitless distance by which a node could be moved to produce an invalid geometry (float)

`minimum_rotated_rectangle`

Returns the general minimum bounding rectangle of the geometry.

type
`wkb`

WKB representation of the geometry

`wkb_hex`

WKB hex representation of the geometry

`wkt`

WKT representation of the geometry

`xy`

Separate arrays of X and Y coordinate values

Methods

 `almost_equals`(other[, decimal]) True if geometries are equal at all coordinates to a specified decimal place. `buffer`(distance[, resolution, quadsegs, ...]) Get a geometry that represents all points within a distance of this geometry. `contains`(other) Returns True if the geometry contains the other, else False `covered_by`(other) Returns True if the geometry is covered by the other, else False `covers`(other) Returns True if the geometry covers the other, else False `crosses`(other) Returns True if the geometries cross, else False `difference`(other) Returns the difference of the geometries `disjoint`(other) Returns True if geometries are disjoint, else False `distance`(other) Unitless distance to other geometry (float) `equals`(other) Returns True if geometries are equal, else False. `equals_exact`(other, tolerance) True if geometries are equal to within a specified tolerance. `hausdorff_distance`(other) Unitless hausdorff distance to other geometry (float) `interpolate`(distance[, normalized]) Return a point at the specified distance along a linear geometry `intersection`(other) Returns the intersection of the geometries `intersects`(other) Returns True if geometries intersect, else False `line_interpolate_point`(distance[, normalized]) Return a point at the specified distance along a linear geometry `line_locate_point`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point Converts geometry to normal form (or canonical form). `overlaps`(other) Returns True if geometries overlap, else False `parallel_offset`(distance[, side, ...]) Returns a LineString or MultiLineString geometry at a distance from the object on its right or its left side. Returns a point guaranteed to be within the object, cheaply. `project`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point `relate`(other) Returns the DE-9IM intersection matrix for the two geometries (string) `relate_pattern`(other, pattern) Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False Returns a point guaranteed to be within the object, cheaply. Returns a copy of this geometry with the order of coordinates reversed. `segmentize`(tolerance) Adds vertices to line segments based on tolerance. `simplify`(tolerance[, preserve_topology]) Returns a simplified geometry produced by the Douglas-Peucker algorithm `svg`([scale_factor, stroke_color, opacity]) Returns SVG polyline element for the LineString geometry. Returns the symmetric difference of the geometries (Shapely geometry) `touches`(other) Returns True if geometries touch, else False `union`(other) Returns the union of the geometries (Shapely geometry) `within`(other) Returns True if geometry is within the other, else False
 geometryType
__eq__(value, /)#

Return self==value.

__ge__(value, /)#

Return self>=value.

property __geo_interface__#

Dictionary representation of the geometry

__gt__(value, /)#

Return self>value.

__hash__(/)#

Return hash(self).

__le__(value, /)#

Return self<=value.

__lt__(value, /)#

Return self<value.

__ne__(value, /)#

Return self!=value.

static __new__(self, coordinates=None)#
__or__(other)#

Return self|value.

__reduce__()#

WKB doesn’t differentiate between LineString and LinearRing so we need to move the coordinate sequence into the correct geometry type

__repr__()#

Return repr(self).

__str__()#

Return str(self).

almost_equals(other, decimal=6)#

True if geometries are equal at all coordinates to a specified decimal place.

Deprecated since version 1.8.0: The ‘almost_equals()’ method is deprecated and will be removed in Shapely 2.0 because the name is confusing. The ‘equals_exact()’ method should be used instead.

Refers to approximate coordinate equality, which requires coordinates to be approximately equal and in the same order for all components of a geometry.

Because of this it is possible for “equals()” to be True for two geometries and “almost_equals()” to be False.

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property area#

Unitless area of the geometry (float)

property boundary#

Returns a lower dimension geometry that bounds the object

The boundary of a polygon is a line, the boundary of a line is a collection of points. The boundary of a point is an empty (null) collection.

property bounds#

Returns minimum bounding region (minx, miny, maxx, maxy)

buffer(distance, resolution=16, quadsegs=None, cap_style=1, join_style=1, mitre_limit=5.0, single_sided=False)#

Get a geometry that represents all points within a distance of this geometry.

A positive distance produces a dilation, a negative distance an erosion. A very small or zero distance may sometimes be used to “tidy” a polygon.

Parameters
distancefloat

The distance to buffer around the object.

resolutionint, optional

The resolution of the buffer around each vertex of the object.

Sets the number of line segments used to approximate an angle fillet. Note: the use of a quadsegs parameter is deprecated and will be gone from the next major release.

cap_styleint, optional

The styles of caps are: CAP_STYLE.round (1), CAP_STYLE.flat (2), and CAP_STYLE.square (3).

join_styleint, optional

The styles of joins between offset segments are: JOIN_STYLE.round (1), JOIN_STYLE.mitre (2), and JOIN_STYLE.bevel (3).

mitre_limitfloat, optional

The mitre limit ratio is used for very sharp corners. The mitre ratio is the ratio of the distance from the corner to the end of the mitred offset corner. When two line segments meet at a sharp angle, a miter join will extend the original geometry. To prevent unreasonable geometry, the mitre limit allows controlling the maximum length of the join corner. Corners with a ratio which exceed the limit will be beveled.

single_sidebool, optional

The side used is determined by the sign of the buffer distance:

a positive distance indicates the left-hand side a negative distance indicates the right-hand side

The single-sided buffer of point geometries is the same as the regular buffer. The End Cap Style for single-sided buffers is always ignored, and forced to the equivalent of CAP_FLAT.

Returns
Geometry

Notes

The return value is a strictly two-dimensional geometry. All Z coordinates of the original geometry will be ignored.

Examples

```>>> from shapely.wkt import loads
>>> g = loads('POINT (0.0 0.0)')
```

16-gon approx of a unit radius circle:

```>>> g.buffer(1.0).area
3.1365484905459...
```

128-gon approximation:

```>>> g.buffer(1.0, 128).area
3.141513801144...
```

triangle approximation:

```>>> g.buffer(1.0, 3).area
3.0
>>> list(g.buffer(1.0, cap_style=CAP_STYLE.square).exterior.coords)
[(1.0, 1.0), (1.0, -1.0), (-1.0, -1.0), (-1.0, 1.0), (1.0, 1.0)]
>>> g.buffer(1.0, cap_style=CAP_STYLE.square).area
4.0
```
property centroid#

Returns the geometric center of the object

contains(other)#

Returns True if the geometry contains the other, else False

property convex_hull#

Imagine an elastic band stretched around the geometry: that’s a convex hull, more or less

The convex hull of a three member multipoint, for example, is a triangular polygon.

property coords#

covered_by(other)#

Returns True if the geometry is covered by the other, else False

covers(other)#

Returns True if the geometry covers the other, else False

crosses(other)#

Returns True if the geometries cross, else False

difference(other)#

Returns the difference of the geometries

disjoint(other)#

Returns True if geometries are disjoint, else False

distance(other)#

Unitless distance to other geometry (float)

property envelope#

A figure that envelopes the geometry

equals(other)#

Returns True if geometries are equal, else False.

This method considers point-set equality (or topological equality), and is equivalent to (self.within(other) & self.contains(other)).

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals(
...     LineString([(0, 0), (1, 1), (2, 2)])
... )
True
```
equals_exact(other, tolerance)#

True if geometries are equal to within a specified tolerance.

Parameters
otherBaseGeometry

The other geometry object in this comparison.

tolerancefloat

Absolute tolerance in the same units as coordinates.

This method considers coordinate equality, which requires
coordinates to be equal and in the same order for all components
of a geometry.
Because of this it is possible for “equals()” to be True for two
geometries and “equals_exact()” to be False.
Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property geom_type#

Name of the geometry’s type, such as ‘Point’

property has_z#

True if the geometry’s coordinate sequence(s) have z values (are 3-dimensional)

hausdorff_distance(other)#

Unitless hausdorff distance to other geometry (float)

interpolate(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of line_interpolate_point.

intersection(other)#

Returns the intersection of the geometries

intersects(other)#

Returns True if geometries intersect, else False

property is_ccw#

True is the ring is oriented counter clock-wise

property is_closed#

True if the geometry is closed, else False

Applicable only to 1-D geometries.

property is_empty#

True if the set of points in this geometry is empty, else False

property is_ring#

True if the geometry is a closed ring, else False

property is_simple#

True if the geometry is simple, meaning that any self-intersections are only at boundary points, else False

property is_valid#

True if the geometry is valid (definition depends on sub-class), else False

property length#

Unitless length of the geometry (float)

line_interpolate_point(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of interpolate.

line_locate_point(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of project.

property minimum_clearance#

Unitless distance by which a node could be moved to produce an invalid geometry (float)

property minimum_rotated_rectangle#

Returns the general minimum bounding rectangle of the geometry. Can possibly be rotated. If the convex hull of the object is a degenerate (line or point) this same degenerate is returned.

normalize()#

Converts geometry to normal form (or canonical form).

This method orders the coordinates, rings of a polygon and parts of multi geometries consistently. Typically useful for testing purposes (for example in combination with equals_exact).

Examples

```>>> from shapely import MultiLineString
>>> line = MultiLineString([[(0, 0), (1, 1)], [(3, 3), (2, 2)]])
>>> line.normalize()
<MULTILINESTRING ((2 2, 3 3), (0 0, 1 1))>
```
overlaps(other)#

Returns True if geometries overlap, else False

parallel_offset(distance, side='right', resolution=16, join_style=1, mitre_limit=5.0)#

Returns a LineString or MultiLineString geometry at a distance from the object on its right or its left side.

The side parameter may be ‘left’ or ‘right’ (default is ‘right’). The resolution of the buffer around each vertex of the object increases by increasing the resolution keyword parameter or third positional parameter. Vertices of right hand offset lines will be ordered in reverse.

The join style is for outside corners between line segments. Accepted values are JOIN_STYLE.round (1), JOIN_STYLE.mitre (2), and JOIN_STYLE.bevel (3).

The mitre ratio limit is used for very sharp corners. It is the ratio of the distance from the corner to the end of the mitred offset corner. When two line segments meet at a sharp angle, a miter join will extend far beyond the original geometry. To prevent unreasonable geometry, the mitre limit allows controlling the maximum length of the join corner. Corners with a ratio which exceed the limit will be beveled.

point_on_surface()#

Returns a point guaranteed to be within the object, cheaply.

Alias of representative_point.

project(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of line_locate_point.

relate(other)#

Returns the DE-9IM intersection matrix for the two geometries (string)

relate_pattern(other, pattern)#

Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False

representative_point()#

Returns a point guaranteed to be within the object, cheaply.

Alias of point_on_surface.

reverse()#

Returns a copy of this geometry with the order of coordinates reversed.

If the geometry is a polygon with interior rings, the interior rings are also reversed.

Points are unchanged.

`is_ccw`

Checks if a geometry is clockwise.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (1, 2)]).reverse()
<LINESTRING (1 2, 0 0)>
>>> Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]).reverse()
<POLYGON ((0 0, 0 1, 1 1, 1 0, 0 0))>
```
segmentize(tolerance)#

Adds vertices to line segments based on tolerance.

Additional vertices will be added to every line segment in an input geometry so that segments are no greater than tolerance. New vertices will evenly subdivide each segment.

Only linear components of input geometries are densified; other geometries are returned unmodified.

Parameters
tolerancefloat or array_like

Additional vertices will be added so that all line segments are no greater than this value. Must be greater than 0.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (0, 10)]).segmentize(tolerance=5)
<LINESTRING (0 0, 0 5, 0 10)>
>>> Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]).segmentize(tolerance=5)
<POLYGON ((0 0, 5 0, 10 0, 10 5, 10 10, 5 10, 0 10, 0 5, 0 0))>
```
simplify(tolerance, preserve_topology=True)#

Returns a simplified geometry produced by the Douglas-Peucker algorithm

Coordinates of the simplified geometry will be no more than the tolerance distance from the original. Unless the topology preserving option is used, the algorithm may produce self-intersecting or otherwise invalid geometries.

svg(scale_factor=1.0, stroke_color=None, opacity=None)#

Returns SVG polyline element for the LineString geometry.

Parameters
scale_factorfloat

Multiplication factor for the SVG stroke-width. Default is 1.

stroke_colorstr, optional

Hex string for stroke color. Default is to use “#66cc99” if geometry is valid, and “#ff3333” if invalid.

opacityfloat

Float number between 0 and 1 for color opacity. Default value is 0.8

symmetric_difference(other)#

Returns the symmetric difference of the geometries (Shapely geometry)

touches(other)#

Returns True if geometries touch, else False

union(other)#

Returns the union of the geometries (Shapely geometry)

within(other)#

Returns True if geometry is within the other, else False

property wkb#

WKB representation of the geometry

property wkb_hex#

WKB hex representation of the geometry

property wkt#

WKT representation of the geometry

property xy#

Separate arrays of X and Y coordinate values

Example:

```>>> x, y = LineString([(0, 0), (1, 1)]).xy
>>> list(x)
[0.0, 1.0]
>>> list(y)
[0.0, 1.0]
```
class MultiLineString(lines=None)#

Bases: `shapely.geometry.base.BaseMultipartGeometry`

A collection of one or more LineStrings.

A MultiLineString has non-zero length and zero area.

Parameters
linessequence

A sequence LineStrings, or a sequence of line-like coordinate sequences or array-likes (see accepted input for LineString).

Examples

Construct a MultiLineString containing two LineStrings.

```>>> lines = MultiLineString([[[0, 0], [1, 2]], [[4, 4], [5, 6]]])
```
Attributes
geomssequence

A sequence of LineStrings

Methods

 `almost_equals`(other[, decimal]) True if geometries are equal at all coordinates to a specified decimal place. `buffer`(distance[, resolution, quadsegs, ...]) Get a geometry that represents all points within a distance of this geometry. `contains`(other) Returns True if the geometry contains the other, else False `covered_by`(other) Returns True if the geometry is covered by the other, else False `covers`(other) Returns True if the geometry covers the other, else False `crosses`(other) Returns True if the geometries cross, else False `difference`(other) Returns the difference of the geometries `disjoint`(other) Returns True if geometries are disjoint, else False `distance`(other) Unitless distance to other geometry (float) `equals`(other) Returns True if geometries are equal, else False. `equals_exact`(other, tolerance) True if geometries are equal to within a specified tolerance. `hausdorff_distance`(other) Unitless hausdorff distance to other geometry (float) `interpolate`(distance[, normalized]) Return a point at the specified distance along a linear geometry `intersection`(other) Returns the intersection of the geometries `intersects`(other) Returns True if geometries intersect, else False `line_interpolate_point`(distance[, normalized]) Return a point at the specified distance along a linear geometry `line_locate_point`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point Converts geometry to normal form (or canonical form). `overlaps`(other) Returns True if geometries overlap, else False Returns a point guaranteed to be within the object, cheaply. `project`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point `relate`(other) Returns the DE-9IM intersection matrix for the two geometries (string) `relate_pattern`(other, pattern) Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False Returns a point guaranteed to be within the object, cheaply. Returns a copy of this geometry with the order of coordinates reversed. `segmentize`(tolerance) Adds vertices to line segments based on tolerance. `simplify`(tolerance[, preserve_topology]) Returns a simplified geometry produced by the Douglas-Peucker algorithm `svg`([scale_factor, stroke_color, opacity]) Returns a group of SVG polyline elements for the LineString geometry. Returns the symmetric difference of the geometries (Shapely geometry) `touches`(other) Returns True if geometries touch, else False `union`(other) Returns the union of the geometries (Shapely geometry) `within`(other) Returns True if geometry is within the other, else False
 geometryType
__eq__(value, /)#

Return self==value.

__ge__(value, /)#

Return self>=value.

property __geo_interface__#

Dictionary representation of the geometry

__gt__(value, /)#

Return self>value.

__hash__(/)#

Return hash(self).

__le__(value, /)#

Return self<=value.

__lt__(value, /)#

Return self<value.

__ne__(value, /)#

Return self!=value.

static __new__(self, lines=None)#
__or__(other)#

Return self|value.

__reduce__()#

Helper for pickle.

__repr__()#

Return repr(self).

__str__()#

Return str(self).

almost_equals(other, decimal=6)#

True if geometries are equal at all coordinates to a specified decimal place.

Deprecated since version 1.8.0: The ‘almost_equals()’ method is deprecated and will be removed in Shapely 2.0 because the name is confusing. The ‘equals_exact()’ method should be used instead.

Refers to approximate coordinate equality, which requires coordinates to be approximately equal and in the same order for all components of a geometry.

Because of this it is possible for “equals()” to be True for two geometries and “almost_equals()” to be False.

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property area#

Unitless area of the geometry (float)

property boundary#

Returns a lower dimension geometry that bounds the object

The boundary of a polygon is a line, the boundary of a line is a collection of points. The boundary of a point is an empty (null) collection.

property bounds#

Returns minimum bounding region (minx, miny, maxx, maxy)

buffer(distance, resolution=16, quadsegs=None, cap_style=1, join_style=1, mitre_limit=5.0, single_sided=False)#

Get a geometry that represents all points within a distance of this geometry.

A positive distance produces a dilation, a negative distance an erosion. A very small or zero distance may sometimes be used to “tidy” a polygon.

Parameters
distancefloat

The distance to buffer around the object.

resolutionint, optional

The resolution of the buffer around each vertex of the object.

Sets the number of line segments used to approximate an angle fillet. Note: the use of a quadsegs parameter is deprecated and will be gone from the next major release.

cap_styleint, optional

The styles of caps are: CAP_STYLE.round (1), CAP_STYLE.flat (2), and CAP_STYLE.square (3).

join_styleint, optional

The styles of joins between offset segments are: JOIN_STYLE.round (1), JOIN_STYLE.mitre (2), and JOIN_STYLE.bevel (3).

mitre_limitfloat, optional

The mitre limit ratio is used for very sharp corners. The mitre ratio is the ratio of the distance from the corner to the end of the mitred offset corner. When two line segments meet at a sharp angle, a miter join will extend the original geometry. To prevent unreasonable geometry, the mitre limit allows controlling the maximum length of the join corner. Corners with a ratio which exceed the limit will be beveled.

single_sidebool, optional

The side used is determined by the sign of the buffer distance:

a positive distance indicates the left-hand side a negative distance indicates the right-hand side

The single-sided buffer of point geometries is the same as the regular buffer. The End Cap Style for single-sided buffers is always ignored, and forced to the equivalent of CAP_FLAT.

Returns
Geometry

Notes

The return value is a strictly two-dimensional geometry. All Z coordinates of the original geometry will be ignored.

Examples

```>>> from shapely.wkt import loads
>>> g = loads('POINT (0.0 0.0)')
```

16-gon approx of a unit radius circle:

```>>> g.buffer(1.0).area
3.1365484905459...
```

128-gon approximation:

```>>> g.buffer(1.0, 128).area
3.141513801144...
```

triangle approximation:

```>>> g.buffer(1.0, 3).area
3.0
>>> list(g.buffer(1.0, cap_style=CAP_STYLE.square).exterior.coords)
[(1.0, 1.0), (1.0, -1.0), (-1.0, -1.0), (-1.0, 1.0), (1.0, 1.0)]
>>> g.buffer(1.0, cap_style=CAP_STYLE.square).area
4.0
```
property centroid#

Returns the geometric center of the object

contains(other)#

Returns True if the geometry contains the other, else False

property convex_hull#

Imagine an elastic band stretched around the geometry: that’s a convex hull, more or less

The convex hull of a three member multipoint, for example, is a triangular polygon.

property coords#

covered_by(other)#

Returns True if the geometry is covered by the other, else False

covers(other)#

Returns True if the geometry covers the other, else False

crosses(other)#

Returns True if the geometries cross, else False

difference(other)#

Returns the difference of the geometries

disjoint(other)#

Returns True if geometries are disjoint, else False

distance(other)#

Unitless distance to other geometry (float)

property envelope#

A figure that envelopes the geometry

equals(other)#

Returns True if geometries are equal, else False.

This method considers point-set equality (or topological equality), and is equivalent to (self.within(other) & self.contains(other)).

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals(
...     LineString([(0, 0), (1, 1), (2, 2)])
... )
True
```
equals_exact(other, tolerance)#

True if geometries are equal to within a specified tolerance.

Parameters
otherBaseGeometry

The other geometry object in this comparison.

tolerancefloat

Absolute tolerance in the same units as coordinates.

This method considers coordinate equality, which requires
coordinates to be equal and in the same order for all components
of a geometry.
Because of this it is possible for “equals()” to be True for two
geometries and “equals_exact()” to be False.
Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property geom_type#

Name of the geometry’s type, such as ‘Point’

property has_z#

True if the geometry’s coordinate sequence(s) have z values (are 3-dimensional)

hausdorff_distance(other)#

Unitless hausdorff distance to other geometry (float)

interpolate(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of line_interpolate_point.

intersection(other)#

Returns the intersection of the geometries

intersects(other)#

Returns True if geometries intersect, else False

property is_closed#

True if the geometry is closed, else False

Applicable only to 1-D geometries.

property is_empty#

True if the set of points in this geometry is empty, else False

property is_ring#

True if the geometry is a closed ring, else False

property is_simple#

True if the geometry is simple, meaning that any self-intersections are only at boundary points, else False

property is_valid#

True if the geometry is valid (definition depends on sub-class), else False

property length#

Unitless length of the geometry (float)

line_interpolate_point(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of interpolate.

line_locate_point(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of project.

property minimum_clearance#

Unitless distance by which a node could be moved to produce an invalid geometry (float)

property minimum_rotated_rectangle#

Returns the general minimum bounding rectangle of the geometry. Can possibly be rotated. If the convex hull of the object is a degenerate (line or point) this same degenerate is returned.

normalize()#

Converts geometry to normal form (or canonical form).

This method orders the coordinates, rings of a polygon and parts of multi geometries consistently. Typically useful for testing purposes (for example in combination with equals_exact).

Examples

```>>> from shapely import MultiLineString
>>> line = MultiLineString([[(0, 0), (1, 1)], [(3, 3), (2, 2)]])
>>> line.normalize()
<MULTILINESTRING ((2 2, 3 3), (0 0, 1 1))>
```
overlaps(other)#

Returns True if geometries overlap, else False

point_on_surface()#

Returns a point guaranteed to be within the object, cheaply.

Alias of representative_point.

project(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of line_locate_point.

relate(other)#

Returns the DE-9IM intersection matrix for the two geometries (string)

relate_pattern(other, pattern)#

Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False

representative_point()#

Returns a point guaranteed to be within the object, cheaply.

Alias of point_on_surface.

reverse()#

Returns a copy of this geometry with the order of coordinates reversed.

If the geometry is a polygon with interior rings, the interior rings are also reversed.

Points are unchanged.

`is_ccw`

Checks if a geometry is clockwise.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (1, 2)]).reverse()
<LINESTRING (1 2, 0 0)>
>>> Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]).reverse()
<POLYGON ((0 0, 0 1, 1 1, 1 0, 0 0))>
```
segmentize(tolerance)#

Adds vertices to line segments based on tolerance.

Additional vertices will be added to every line segment in an input geometry so that segments are no greater than tolerance. New vertices will evenly subdivide each segment.

Only linear components of input geometries are densified; other geometries are returned unmodified.

Parameters
tolerancefloat or array_like

Additional vertices will be added so that all line segments are no greater than this value. Must be greater than 0.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (0, 10)]).segmentize(tolerance=5)
<LINESTRING (0 0, 0 5, 0 10)>
>>> Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]).segmentize(tolerance=5)
<POLYGON ((0 0, 5 0, 10 0, 10 5, 10 10, 5 10, 0 10, 0 5, 0 0))>
```
simplify(tolerance, preserve_topology=True)#

Returns a simplified geometry produced by the Douglas-Peucker algorithm

Coordinates of the simplified geometry will be no more than the tolerance distance from the original. Unless the topology preserving option is used, the algorithm may produce self-intersecting or otherwise invalid geometries.

svg(scale_factor=1.0, stroke_color=None, opacity=None)#

Returns a group of SVG polyline elements for the LineString geometry.

Parameters
scale_factorfloat

Multiplication factor for the SVG stroke-width. Default is 1.

stroke_colorstr, optional

Hex string for stroke color. Default is to use “#66cc99” if geometry is valid, and “#ff3333” if invalid.

opacityfloat

Float number between 0 and 1 for color opacity. Default value is 0.8

symmetric_difference(other)#

Returns the symmetric difference of the geometries (Shapely geometry)

touches(other)#

Returns True if geometries touch, else False

union(other)#

Returns the union of the geometries (Shapely geometry)

within(other)#

Returns True if geometry is within the other, else False

property wkb#

WKB representation of the geometry

property wkb_hex#

WKB hex representation of the geometry

property wkt#

WKT representation of the geometry

property xy#

Separate arrays of X and Y coordinate values

class MultiPoint(points=None)#

Bases: `shapely.geometry.base.BaseMultipartGeometry`

A collection of one or more Points.

A MultiPoint has zero area and zero length.

Parameters
pointssequence

A sequence of Points, or a sequence of (x, y [,z]) numeric coordinate pairs or triples, or an array-like of shape (N, 2) or (N, 3).

Examples

Construct a MultiPoint containing two Points

```>>> from shapely import Point
>>> ob = MultiPoint([[0.0, 0.0], [1.0, 2.0]])
>>> len(ob.geoms)
2
>>> type(ob.geoms[0]) == Point
True
```
Attributes
geomssequence

A sequence of Points

Methods

 `almost_equals`(other[, decimal]) True if geometries are equal at all coordinates to a specified decimal place. `buffer`(distance[, resolution, quadsegs, ...]) Get a geometry that represents all points within a distance of this geometry. `contains`(other) Returns True if the geometry contains the other, else False `covered_by`(other) Returns True if the geometry is covered by the other, else False `covers`(other) Returns True if the geometry covers the other, else False `crosses`(other) Returns True if the geometries cross, else False `difference`(other) Returns the difference of the geometries `disjoint`(other) Returns True if geometries are disjoint, else False `distance`(other) Unitless distance to other geometry (float) `equals`(other) Returns True if geometries are equal, else False. `equals_exact`(other, tolerance) True if geometries are equal to within a specified tolerance. `hausdorff_distance`(other) Unitless hausdorff distance to other geometry (float) `interpolate`(distance[, normalized]) Return a point at the specified distance along a linear geometry `intersection`(other) Returns the intersection of the geometries `intersects`(other) Returns True if geometries intersect, else False `line_interpolate_point`(distance[, normalized]) Return a point at the specified distance along a linear geometry `line_locate_point`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point Converts geometry to normal form (or canonical form). `overlaps`(other) Returns True if geometries overlap, else False Returns a point guaranteed to be within the object, cheaply. `project`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point `relate`(other) Returns the DE-9IM intersection matrix for the two geometries (string) `relate_pattern`(other, pattern) Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False Returns a point guaranteed to be within the object, cheaply. Returns a copy of this geometry with the order of coordinates reversed. `segmentize`(tolerance) Adds vertices to line segments based on tolerance. `simplify`(tolerance[, preserve_topology]) Returns a simplified geometry produced by the Douglas-Peucker algorithm `svg`([scale_factor, fill_color, opacity]) Returns a group of SVG circle elements for the MultiPoint geometry. Returns the symmetric difference of the geometries (Shapely geometry) `touches`(other) Returns True if geometries touch, else False `union`(other) Returns the union of the geometries (Shapely geometry) `within`(other) Returns True if geometry is within the other, else False
 geometryType
__eq__(value, /)#

Return self==value.

__ge__(value, /)#

Return self>=value.

property __geo_interface__#

Dictionary representation of the geometry

__gt__(value, /)#

Return self>value.

__hash__(/)#

Return hash(self).

__le__(value, /)#

Return self<=value.

__lt__(value, /)#

Return self<value.

__ne__(value, /)#

Return self!=value.

static __new__(self, points=None)#
__or__(other)#

Return self|value.

__reduce__()#

Helper for pickle.

__repr__()#

Return repr(self).

__str__()#

Return str(self).

almost_equals(other, decimal=6)#

True if geometries are equal at all coordinates to a specified decimal place.

Deprecated since version 1.8.0: The ‘almost_equals()’ method is deprecated and will be removed in Shapely 2.0 because the name is confusing. The ‘equals_exact()’ method should be used instead.

Refers to approximate coordinate equality, which requires coordinates to be approximately equal and in the same order for all components of a geometry.

Because of this it is possible for “equals()” to be True for two geometries and “almost_equals()” to be False.

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property area#

Unitless area of the geometry (float)

property boundary#

Returns a lower dimension geometry that bounds the object

The boundary of a polygon is a line, the boundary of a line is a collection of points. The boundary of a point is an empty (null) collection.

property bounds#

Returns minimum bounding region (minx, miny, maxx, maxy)

buffer(distance, resolution=16, quadsegs=None, cap_style=1, join_style=1, mitre_limit=5.0, single_sided=False)#

Get a geometry that represents all points within a distance of this geometry.

A positive distance produces a dilation, a negative distance an erosion. A very small or zero distance may sometimes be used to “tidy” a polygon.

Parameters
distancefloat

The distance to buffer around the object.

resolutionint, optional

The resolution of the buffer around each vertex of the object.

Sets the number of line segments used to approximate an angle fillet. Note: the use of a quadsegs parameter is deprecated and will be gone from the next major release.

cap_styleint, optional

The styles of caps are: CAP_STYLE.round (1), CAP_STYLE.flat (2), and CAP_STYLE.square (3).

join_styleint, optional

The styles of joins between offset segments are: JOIN_STYLE.round (1), JOIN_STYLE.mitre (2), and JOIN_STYLE.bevel (3).

mitre_limitfloat, optional

The mitre limit ratio is used for very sharp corners. The mitre ratio is the ratio of the distance from the corner to the end of the mitred offset corner. When two line segments meet at a sharp angle, a miter join will extend the original geometry. To prevent unreasonable geometry, the mitre limit allows controlling the maximum length of the join corner. Corners with a ratio which exceed the limit will be beveled.

single_sidebool, optional

The side used is determined by the sign of the buffer distance:

a positive distance indicates the left-hand side a negative distance indicates the right-hand side

The single-sided buffer of point geometries is the same as the regular buffer. The End Cap Style for single-sided buffers is always ignored, and forced to the equivalent of CAP_FLAT.

Returns
Geometry

Notes

The return value is a strictly two-dimensional geometry. All Z coordinates of the original geometry will be ignored.

Examples

```>>> from shapely.wkt import loads
>>> g = loads('POINT (0.0 0.0)')
```

16-gon approx of a unit radius circle:

```>>> g.buffer(1.0).area
3.1365484905459...
```

128-gon approximation:

```>>> g.buffer(1.0, 128).area
3.141513801144...
```

triangle approximation:

```>>> g.buffer(1.0, 3).area
3.0
>>> list(g.buffer(1.0, cap_style=CAP_STYLE.square).exterior.coords)
[(1.0, 1.0), (1.0, -1.0), (-1.0, -1.0), (-1.0, 1.0), (1.0, 1.0)]
>>> g.buffer(1.0, cap_style=CAP_STYLE.square).area
4.0
```
property centroid#

Returns the geometric center of the object

contains(other)#

Returns True if the geometry contains the other, else False

property convex_hull#

Imagine an elastic band stretched around the geometry: that’s a convex hull, more or less

The convex hull of a three member multipoint, for example, is a triangular polygon.

property coords#

covered_by(other)#

Returns True if the geometry is covered by the other, else False

covers(other)#

Returns True if the geometry covers the other, else False

crosses(other)#

Returns True if the geometries cross, else False

difference(other)#

Returns the difference of the geometries

disjoint(other)#

Returns True if geometries are disjoint, else False

distance(other)#

Unitless distance to other geometry (float)

property envelope#

A figure that envelopes the geometry

equals(other)#

Returns True if geometries are equal, else False.

This method considers point-set equality (or topological equality), and is equivalent to (self.within(other) & self.contains(other)).

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals(
...     LineString([(0, 0), (1, 1), (2, 2)])
... )
True
```
equals_exact(other, tolerance)#

True if geometries are equal to within a specified tolerance.

Parameters
otherBaseGeometry

The other geometry object in this comparison.

tolerancefloat

Absolute tolerance in the same units as coordinates.

This method considers coordinate equality, which requires
coordinates to be equal and in the same order for all components
of a geometry.
Because of this it is possible for “equals()” to be True for two
geometries and “equals_exact()” to be False.
Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property geom_type#

Name of the geometry’s type, such as ‘Point’

property has_z#

True if the geometry’s coordinate sequence(s) have z values (are 3-dimensional)

hausdorff_distance(other)#

Unitless hausdorff distance to other geometry (float)

interpolate(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of line_interpolate_point.

intersection(other)#

Returns the intersection of the geometries

intersects(other)#

Returns True if geometries intersect, else False

property is_closed#

True if the geometry is closed, else False

Applicable only to 1-D geometries.

property is_empty#

True if the set of points in this geometry is empty, else False

property is_ring#

True if the geometry is a closed ring, else False

property is_simple#

True if the geometry is simple, meaning that any self-intersections are only at boundary points, else False

property is_valid#

True if the geometry is valid (definition depends on sub-class), else False

property length#

Unitless length of the geometry (float)

line_interpolate_point(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of interpolate.

line_locate_point(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of project.

property minimum_clearance#

Unitless distance by which a node could be moved to produce an invalid geometry (float)

property minimum_rotated_rectangle#

Returns the general minimum bounding rectangle of the geometry. Can possibly be rotated. If the convex hull of the object is a degenerate (line or point) this same degenerate is returned.

normalize()#

Converts geometry to normal form (or canonical form).

This method orders the coordinates, rings of a polygon and parts of multi geometries consistently. Typically useful for testing purposes (for example in combination with equals_exact).

Examples

```>>> from shapely import MultiLineString
>>> line = MultiLineString([[(0, 0), (1, 1)], [(3, 3), (2, 2)]])
>>> line.normalize()
<MULTILINESTRING ((2 2, 3 3), (0 0, 1 1))>
```
overlaps(other)#

Returns True if geometries overlap, else False

point_on_surface()#

Returns a point guaranteed to be within the object, cheaply.

Alias of representative_point.

project(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of line_locate_point.

relate(other)#

Returns the DE-9IM intersection matrix for the two geometries (string)

relate_pattern(other, pattern)#

Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False

representative_point()#

Returns a point guaranteed to be within the object, cheaply.

Alias of point_on_surface.

reverse()#

Returns a copy of this geometry with the order of coordinates reversed.

If the geometry is a polygon with interior rings, the interior rings are also reversed.

Points are unchanged.

`is_ccw`

Checks if a geometry is clockwise.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (1, 2)]).reverse()
<LINESTRING (1 2, 0 0)>
>>> Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]).reverse()
<POLYGON ((0 0, 0 1, 1 1, 1 0, 0 0))>
```
segmentize(tolerance)#

Adds vertices to line segments based on tolerance.

Additional vertices will be added to every line segment in an input geometry so that segments are no greater than tolerance. New vertices will evenly subdivide each segment.

Only linear components of input geometries are densified; other geometries are returned unmodified.

Parameters
tolerancefloat or array_like

Additional vertices will be added so that all line segments are no greater than this value. Must be greater than 0.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (0, 10)]).segmentize(tolerance=5)
<LINESTRING (0 0, 0 5, 0 10)>
>>> Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]).segmentize(tolerance=5)
<POLYGON ((0 0, 5 0, 10 0, 10 5, 10 10, 5 10, 0 10, 0 5, 0 0))>
```
simplify(tolerance, preserve_topology=True)#

Returns a simplified geometry produced by the Douglas-Peucker algorithm

Coordinates of the simplified geometry will be no more than the tolerance distance from the original. Unless the topology preserving option is used, the algorithm may produce self-intersecting or otherwise invalid geometries.

svg(scale_factor=1.0, fill_color=None, opacity=None)#

Returns a group of SVG circle elements for the MultiPoint geometry.

Parameters
scale_factorfloat

Multiplication factor for the SVG circle diameters. Default is 1.

fill_colorstr, optional

Hex string for fill color. Default is to use “#66cc99” if geometry is valid, and “#ff3333” if invalid.

opacityfloat

Float number between 0 and 1 for color opacity. Default value is 0.6

symmetric_difference(other)#

Returns the symmetric difference of the geometries (Shapely geometry)

touches(other)#

Returns True if geometries touch, else False

union(other)#

Returns the union of the geometries (Shapely geometry)

within(other)#

Returns True if geometry is within the other, else False

property wkb#

WKB representation of the geometry

property wkb_hex#

WKB hex representation of the geometry

property wkt#

WKT representation of the geometry

property xy#

Separate arrays of X and Y coordinate values

class MultiPolygon(polygons=None)#

Bases: `shapely.geometry.base.BaseMultipartGeometry`

A collection of one or more Polygons.

If component polygons overlap the collection is invalid and some operations on it may fail.

Parameters
polygonssequence

A sequence of Polygons, or a sequence of (shell, holes) tuples where shell is the sequence representation of a linear ring (see LinearRing) and holes is a sequence of such linear rings.

Examples

Construct a MultiPolygon from a sequence of coordinate tuples

```>>> from shapely import Polygon
>>> ob = MultiPolygon([
...     (
...     ((0.0, 0.0), (0.0, 1.0), (1.0, 1.0), (1.0, 0.0)),
...     [((0.1,0.1), (0.1,0.2), (0.2,0.2), (0.2,0.1))]
...     )
... ])
>>> len(ob.geoms)
1
>>> type(ob.geoms[0]) == Polygon
True
```
Attributes
geomssequence

A sequence of Polygon instances

Methods

 `almost_equals`(other[, decimal]) True if geometries are equal at all coordinates to a specified decimal place. `buffer`(distance[, resolution, quadsegs, ...]) Get a geometry that represents all points within a distance of this geometry. `contains`(other) Returns True if the geometry contains the other, else False `covered_by`(other) Returns True if the geometry is covered by the other, else False `covers`(other) Returns True if the geometry covers the other, else False `crosses`(other) Returns True if the geometries cross, else False `difference`(other) Returns the difference of the geometries `disjoint`(other) Returns True if geometries are disjoint, else False `distance`(other) Unitless distance to other geometry (float) `equals`(other) Returns True if geometries are equal, else False. `equals_exact`(other, tolerance) True if geometries are equal to within a specified tolerance. `hausdorff_distance`(other) Unitless hausdorff distance to other geometry (float) `interpolate`(distance[, normalized]) Return a point at the specified distance along a linear geometry `intersection`(other) Returns the intersection of the geometries `intersects`(other) Returns True if geometries intersect, else False `line_interpolate_point`(distance[, normalized]) Return a point at the specified distance along a linear geometry `line_locate_point`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point Converts geometry to normal form (or canonical form). `overlaps`(other) Returns True if geometries overlap, else False Returns a point guaranteed to be within the object, cheaply. `project`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point `relate`(other) Returns the DE-9IM intersection matrix for the two geometries (string) `relate_pattern`(other, pattern) Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False Returns a point guaranteed to be within the object, cheaply. Returns a copy of this geometry with the order of coordinates reversed. `segmentize`(tolerance) Adds vertices to line segments based on tolerance. `simplify`(tolerance[, preserve_topology]) Returns a simplified geometry produced by the Douglas-Peucker algorithm `svg`([scale_factor, fill_color, opacity]) Returns group of SVG path elements for the MultiPolygon geometry. Returns the symmetric difference of the geometries (Shapely geometry) `touches`(other) Returns True if geometries touch, else False `union`(other) Returns the union of the geometries (Shapely geometry) `within`(other) Returns True if geometry is within the other, else False
 geometryType
__eq__(value, /)#

Return self==value.

__ge__(value, /)#

Return self>=value.

property __geo_interface__#

Dictionary representation of the geometry

__gt__(value, /)#

Return self>value.

__hash__(/)#

Return hash(self).

__le__(value, /)#

Return self<=value.

__lt__(value, /)#

Return self<value.

__ne__(value, /)#

Return self!=value.

static __new__(self, polygons=None)#
__or__(other)#

Return self|value.

__reduce__()#

Helper for pickle.

__repr__()#

Return repr(self).

__str__()#

Return str(self).

almost_equals(other, decimal=6)#

True if geometries are equal at all coordinates to a specified decimal place.

Deprecated since version 1.8.0: The ‘almost_equals()’ method is deprecated and will be removed in Shapely 2.0 because the name is confusing. The ‘equals_exact()’ method should be used instead.

Refers to approximate coordinate equality, which requires coordinates to be approximately equal and in the same order for all components of a geometry.

Because of this it is possible for “equals()” to be True for two geometries and “almost_equals()” to be False.

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property area#

Unitless area of the geometry (float)

property boundary#

Returns a lower dimension geometry that bounds the object

The boundary of a polygon is a line, the boundary of a line is a collection of points. The boundary of a point is an empty (null) collection.

property bounds#

Returns minimum bounding region (minx, miny, maxx, maxy)

buffer(distance, resolution=16, quadsegs=None, cap_style=1, join_style=1, mitre_limit=5.0, single_sided=False)#

Get a geometry that represents all points within a distance of this geometry.

A positive distance produces a dilation, a negative distance an erosion. A very small or zero distance may sometimes be used to “tidy” a polygon.

Parameters
distancefloat

The distance to buffer around the object.

resolutionint, optional

The resolution of the buffer around each vertex of the object.

Sets the number of line segments used to approximate an angle fillet. Note: the use of a quadsegs parameter is deprecated and will be gone from the next major release.

cap_styleint, optional

The styles of caps are: CAP_STYLE.round (1), CAP_STYLE.flat (2), and CAP_STYLE.square (3).

join_styleint, optional

The styles of joins between offset segments are: JOIN_STYLE.round (1), JOIN_STYLE.mitre (2), and JOIN_STYLE.bevel (3).

mitre_limitfloat, optional

The mitre limit ratio is used for very sharp corners. The mitre ratio is the ratio of the distance from the corner to the end of the mitred offset corner. When two line segments meet at a sharp angle, a miter join will extend the original geometry. To prevent unreasonable geometry, the mitre limit allows controlling the maximum length of the join corner. Corners with a ratio which exceed the limit will be beveled.

single_sidebool, optional

The side used is determined by the sign of the buffer distance:

a positive distance indicates the left-hand side a negative distance indicates the right-hand side

The single-sided buffer of point geometries is the same as the regular buffer. The End Cap Style for single-sided buffers is always ignored, and forced to the equivalent of CAP_FLAT.

Returns
Geometry

Notes

The return value is a strictly two-dimensional geometry. All Z coordinates of the original geometry will be ignored.

Examples

```>>> from shapely.wkt import loads
>>> g = loads('POINT (0.0 0.0)')
```

16-gon approx of a unit radius circle:

```>>> g.buffer(1.0).area
3.1365484905459...
```

128-gon approximation:

```>>> g.buffer(1.0, 128).area
3.141513801144...
```

triangle approximation:

```>>> g.buffer(1.0, 3).area
3.0
>>> list(g.buffer(1.0, cap_style=CAP_STYLE.square).exterior.coords)
[(1.0, 1.0), (1.0, -1.0), (-1.0, -1.0), (-1.0, 1.0), (1.0, 1.0)]
>>> g.buffer(1.0, cap_style=CAP_STYLE.square).area
4.0
```
property centroid#

Returns the geometric center of the object

contains(other)#

Returns True if the geometry contains the other, else False

property convex_hull#

Imagine an elastic band stretched around the geometry: that’s a convex hull, more or less

The convex hull of a three member multipoint, for example, is a triangular polygon.

property coords#

covered_by(other)#

Returns True if the geometry is covered by the other, else False

covers(other)#

Returns True if the geometry covers the other, else False

crosses(other)#

Returns True if the geometries cross, else False

difference(other)#

Returns the difference of the geometries

disjoint(other)#

Returns True if geometries are disjoint, else False

distance(other)#

Unitless distance to other geometry (float)

property envelope#

A figure that envelopes the geometry

equals(other)#

Returns True if geometries are equal, else False.

This method considers point-set equality (or topological equality), and is equivalent to (self.within(other) & self.contains(other)).

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals(
...     LineString([(0, 0), (1, 1), (2, 2)])
... )
True
```
equals_exact(other, tolerance)#

True if geometries are equal to within a specified tolerance.

Parameters
otherBaseGeometry

The other geometry object in this comparison.

tolerancefloat

Absolute tolerance in the same units as coordinates.

This method considers coordinate equality, which requires
coordinates to be equal and in the same order for all components
of a geometry.
Because of this it is possible for “equals()” to be True for two
geometries and “equals_exact()” to be False.
Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property geom_type#

Name of the geometry’s type, such as ‘Point’

property has_z#

True if the geometry’s coordinate sequence(s) have z values (are 3-dimensional)

hausdorff_distance(other)#

Unitless hausdorff distance to other geometry (float)

interpolate(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of line_interpolate_point.

intersection(other)#

Returns the intersection of the geometries

intersects(other)#

Returns True if geometries intersect, else False

property is_closed#

True if the geometry is closed, else False

Applicable only to 1-D geometries.

property is_empty#

True if the set of points in this geometry is empty, else False

property is_ring#

True if the geometry is a closed ring, else False

property is_simple#

True if the geometry is simple, meaning that any self-intersections are only at boundary points, else False

property is_valid#

True if the geometry is valid (definition depends on sub-class), else False

property length#

Unitless length of the geometry (float)

line_interpolate_point(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of interpolate.

line_locate_point(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of project.

property minimum_clearance#

Unitless distance by which a node could be moved to produce an invalid geometry (float)

property minimum_rotated_rectangle#

Returns the general minimum bounding rectangle of the geometry. Can possibly be rotated. If the convex hull of the object is a degenerate (line or point) this same degenerate is returned.

normalize()#

Converts geometry to normal form (or canonical form).

This method orders the coordinates, rings of a polygon and parts of multi geometries consistently. Typically useful for testing purposes (for example in combination with equals_exact).

Examples

```>>> from shapely import MultiLineString
>>> line = MultiLineString([[(0, 0), (1, 1)], [(3, 3), (2, 2)]])
>>> line.normalize()
<MULTILINESTRING ((2 2, 3 3), (0 0, 1 1))>
```
overlaps(other)#

Returns True if geometries overlap, else False

point_on_surface()#

Returns a point guaranteed to be within the object, cheaply.

Alias of representative_point.

project(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of line_locate_point.

relate(other)#

Returns the DE-9IM intersection matrix for the two geometries (string)

relate_pattern(other, pattern)#

Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False

representative_point()#

Returns a point guaranteed to be within the object, cheaply.

Alias of point_on_surface.

reverse()#

Returns a copy of this geometry with the order of coordinates reversed.

If the geometry is a polygon with interior rings, the interior rings are also reversed.

Points are unchanged.

`is_ccw`

Checks if a geometry is clockwise.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (1, 2)]).reverse()
<LINESTRING (1 2, 0 0)>
>>> Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]).reverse()
<POLYGON ((0 0, 0 1, 1 1, 1 0, 0 0))>
```
segmentize(tolerance)#

Adds vertices to line segments based on tolerance.

Additional vertices will be added to every line segment in an input geometry so that segments are no greater than tolerance. New vertices will evenly subdivide each segment.

Only linear components of input geometries are densified; other geometries are returned unmodified.

Parameters
tolerancefloat or array_like

Additional vertices will be added so that all line segments are no greater than this value. Must be greater than 0.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (0, 10)]).segmentize(tolerance=5)
<LINESTRING (0 0, 0 5, 0 10)>
>>> Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]).segmentize(tolerance=5)
<POLYGON ((0 0, 5 0, 10 0, 10 5, 10 10, 5 10, 0 10, 0 5, 0 0))>
```
simplify(tolerance, preserve_topology=True)#

Returns a simplified geometry produced by the Douglas-Peucker algorithm

Coordinates of the simplified geometry will be no more than the tolerance distance from the original. Unless the topology preserving option is used, the algorithm may produce self-intersecting or otherwise invalid geometries.

svg(scale_factor=1.0, fill_color=None, opacity=None)#

Returns group of SVG path elements for the MultiPolygon geometry.

Parameters
scale_factorfloat

Multiplication factor for the SVG stroke-width. Default is 1.

fill_colorstr, optional

Hex string for fill color. Default is to use “#66cc99” if geometry is valid, and “#ff3333” if invalid.

opacityfloat

Float number between 0 and 1 for color opacity. Default value is 0.6

symmetric_difference(other)#

Returns the symmetric difference of the geometries (Shapely geometry)

touches(other)#

Returns True if geometries touch, else False

union(other)#

Returns the union of the geometries (Shapely geometry)

within(other)#

Returns True if geometry is within the other, else False

property wkb#

WKB representation of the geometry

property wkb_hex#

WKB hex representation of the geometry

property wkt#

WKT representation of the geometry

property xy#

Separate arrays of X and Y coordinate values

class Point(*args)#

Bases: `shapely.geometry.base.BaseGeometry`

A geometry type that represents a single coordinate with x,y and possibly z values.

A point is a zero-dimensional feature and has zero length and zero area.

Parameters
argsfloat, or sequence of floats

The coordinates can either be passed as a single parameter, or as individual float values using multiple parameters:

1. 1 parameter: a sequence or array-like of with 2 or 3 values.

2. 2 or 3 parameters (float): x, y, and possibly z.

Examples

Constructing the Point using separate parameters for x and y:

```>>> p = Point(1.0, -1.0)
```

Constructing the Point using a list of x, y coordinates:

```>>> p = Point([1.0, -1.0])
>>> print(p)
POINT (1 -1)
>>> p.y
-1.0
>>> p.x
1.0
```
Attributes
x, y, zfloat

Coordinate values

Methods

 `almost_equals`(other[, decimal]) True if geometries are equal at all coordinates to a specified decimal place. `buffer`(distance[, resolution, quadsegs, ...]) Get a geometry that represents all points within a distance of this geometry. `contains`(other) Returns True if the geometry contains the other, else False `covered_by`(other) Returns True if the geometry is covered by the other, else False `covers`(other) Returns True if the geometry covers the other, else False `crosses`(other) Returns True if the geometries cross, else False `difference`(other) Returns the difference of the geometries `disjoint`(other) Returns True if geometries are disjoint, else False `distance`(other) Unitless distance to other geometry (float) `equals`(other) Returns True if geometries are equal, else False. `equals_exact`(other, tolerance) True if geometries are equal to within a specified tolerance. `hausdorff_distance`(other) Unitless hausdorff distance to other geometry (float) `interpolate`(distance[, normalized]) Return a point at the specified distance along a linear geometry `intersection`(other) Returns the intersection of the geometries `intersects`(other) Returns True if geometries intersect, else False `line_interpolate_point`(distance[, normalized]) Return a point at the specified distance along a linear geometry `line_locate_point`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point Converts geometry to normal form (or canonical form). `overlaps`(other) Returns True if geometries overlap, else False Returns a point guaranteed to be within the object, cheaply. `project`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point `relate`(other) Returns the DE-9IM intersection matrix for the two geometries (string) `relate_pattern`(other, pattern) Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False Returns a point guaranteed to be within the object, cheaply. Returns a copy of this geometry with the order of coordinates reversed. `segmentize`(tolerance) Adds vertices to line segments based on tolerance. `simplify`(tolerance[, preserve_topology]) Returns a simplified geometry produced by the Douglas-Peucker algorithm `svg`([scale_factor, fill_color, opacity]) Returns SVG circle element for the Point geometry. Returns the symmetric difference of the geometries (Shapely geometry) `touches`(other) Returns True if geometries touch, else False `union`(other) Returns the union of the geometries (Shapely geometry) `within`(other) Returns True if geometry is within the other, else False
 geometryType
__eq__(value, /)#

Return self==value.

__ge__(value, /)#

Return self>=value.

property __geo_interface__#

Dictionary representation of the geometry

__gt__(value, /)#

Return self>value.

__hash__(/)#

Return hash(self).

__le__(value, /)#

Return self<=value.

__lt__(value, /)#

Return self<value.

__ne__(value, /)#

Return self!=value.

static __new__(self, *args)#
__or__(other)#

Return self|value.

__reduce__()#

Helper for pickle.

__repr__()#

Return repr(self).

__str__()#

Return str(self).

almost_equals(other, decimal=6)#

True if geometries are equal at all coordinates to a specified decimal place.

Deprecated since version 1.8.0: The ‘almost_equals()’ method is deprecated and will be removed in Shapely 2.0 because the name is confusing. The ‘equals_exact()’ method should be used instead.

Refers to approximate coordinate equality, which requires coordinates to be approximately equal and in the same order for all components of a geometry.

Because of this it is possible for “equals()” to be True for two geometries and “almost_equals()” to be False.

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property area#

Unitless area of the geometry (float)

property boundary#

Returns a lower dimension geometry that bounds the object

The boundary of a polygon is a line, the boundary of a line is a collection of points. The boundary of a point is an empty (null) collection.

property bounds#

Returns minimum bounding region (minx, miny, maxx, maxy)

buffer(distance, resolution=16, quadsegs=None, cap_style=1, join_style=1, mitre_limit=5.0, single_sided=False)#

Get a geometry that represents all points within a distance of this geometry.

A positive distance produces a dilation, a negative distance an erosion. A very small or zero distance may sometimes be used to “tidy” a polygon.

Parameters
distancefloat

The distance to buffer around the object.

resolutionint, optional

The resolution of the buffer around each vertex of the object.

Sets the number of line segments used to approximate an angle fillet. Note: the use of a quadsegs parameter is deprecated and will be gone from the next major release.

cap_styleint, optional

The styles of caps are: CAP_STYLE.round (1), CAP_STYLE.flat (2), and CAP_STYLE.square (3).

join_styleint, optional

The styles of joins between offset segments are: JOIN_STYLE.round (1), JOIN_STYLE.mitre (2), and JOIN_STYLE.bevel (3).

mitre_limitfloat, optional

The mitre limit ratio is used for very sharp corners. The mitre ratio is the ratio of the distance from the corner to the end of the mitred offset corner. When two line segments meet at a sharp angle, a miter join will extend the original geometry. To prevent unreasonable geometry, the mitre limit allows controlling the maximum length of the join corner. Corners with a ratio which exceed the limit will be beveled.

single_sidebool, optional

The side used is determined by the sign of the buffer distance:

a positive distance indicates the left-hand side a negative distance indicates the right-hand side

The single-sided buffer of point geometries is the same as the regular buffer. The End Cap Style for single-sided buffers is always ignored, and forced to the equivalent of CAP_FLAT.

Returns
Geometry

Notes

The return value is a strictly two-dimensional geometry. All Z coordinates of the original geometry will be ignored.

Examples

```>>> from shapely.wkt import loads
>>> g = loads('POINT (0.0 0.0)')
```

16-gon approx of a unit radius circle:

```>>> g.buffer(1.0).area
3.1365484905459...
```

128-gon approximation:

```>>> g.buffer(1.0, 128).area
3.141513801144...
```

triangle approximation:

```>>> g.buffer(1.0, 3).area
3.0
>>> list(g.buffer(1.0, cap_style=CAP_STYLE.square).exterior.coords)
[(1.0, 1.0), (1.0, -1.0), (-1.0, -1.0), (-1.0, 1.0), (1.0, 1.0)]
>>> g.buffer(1.0, cap_style=CAP_STYLE.square).area
4.0
```
property centroid#

Returns the geometric center of the object

contains(other)#

Returns True if the geometry contains the other, else False

property convex_hull#

Imagine an elastic band stretched around the geometry: that’s a convex hull, more or less

The convex hull of a three member multipoint, for example, is a triangular polygon.

property coords#

covered_by(other)#

Returns True if the geometry is covered by the other, else False

covers(other)#

Returns True if the geometry covers the other, else False

crosses(other)#

Returns True if the geometries cross, else False

difference(other)#

Returns the difference of the geometries

disjoint(other)#

Returns True if geometries are disjoint, else False

distance(other)#

Unitless distance to other geometry (float)

property envelope#

A figure that envelopes the geometry

equals(other)#

Returns True if geometries are equal, else False.

This method considers point-set equality (or topological equality), and is equivalent to (self.within(other) & self.contains(other)).

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals(
...     LineString([(0, 0), (1, 1), (2, 2)])
... )
True
```
equals_exact(other, tolerance)#

True if geometries are equal to within a specified tolerance.

Parameters
otherBaseGeometry

The other geometry object in this comparison.

tolerancefloat

Absolute tolerance in the same units as coordinates.

This method considers coordinate equality, which requires
coordinates to be equal and in the same order for all components
of a geometry.
Because of this it is possible for “equals()” to be True for two
geometries and “equals_exact()” to be False.
Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property geom_type#

Name of the geometry’s type, such as ‘Point’

property has_z#

True if the geometry’s coordinate sequence(s) have z values (are 3-dimensional)

hausdorff_distance(other)#

Unitless hausdorff distance to other geometry (float)

interpolate(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of line_interpolate_point.

intersection(other)#

Returns the intersection of the geometries

intersects(other)#

Returns True if geometries intersect, else False

property is_closed#

True if the geometry is closed, else False

Applicable only to 1-D geometries.

property is_empty#

True if the set of points in this geometry is empty, else False

property is_ring#

True if the geometry is a closed ring, else False

property is_simple#

True if the geometry is simple, meaning that any self-intersections are only at boundary points, else False

property is_valid#

True if the geometry is valid (definition depends on sub-class), else False

property length#

Unitless length of the geometry (float)

line_interpolate_point(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of interpolate.

line_locate_point(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of project.

property minimum_clearance#

Unitless distance by which a node could be moved to produce an invalid geometry (float)

property minimum_rotated_rectangle#

Returns the general minimum bounding rectangle of the geometry. Can possibly be rotated. If the convex hull of the object is a degenerate (line or point) this same degenerate is returned.

normalize()#

Converts geometry to normal form (or canonical form).

This method orders the coordinates, rings of a polygon and parts of multi geometries consistently. Typically useful for testing purposes (for example in combination with equals_exact).

Examples

```>>> from shapely import MultiLineString
>>> line = MultiLineString([[(0, 0), (1, 1)], [(3, 3), (2, 2)]])
>>> line.normalize()
<MULTILINESTRING ((2 2, 3 3), (0 0, 1 1))>
```
overlaps(other)#

Returns True if geometries overlap, else False

point_on_surface()#

Returns a point guaranteed to be within the object, cheaply.

Alias of representative_point.

project(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of line_locate_point.

relate(other)#

Returns the DE-9IM intersection matrix for the two geometries (string)

relate_pattern(other, pattern)#

Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False

representative_point()#

Returns a point guaranteed to be within the object, cheaply.

Alias of point_on_surface.

reverse()#

Returns a copy of this geometry with the order of coordinates reversed.

If the geometry is a polygon with interior rings, the interior rings are also reversed.

Points are unchanged.

`is_ccw`

Checks if a geometry is clockwise.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (1, 2)]).reverse()
<LINESTRING (1 2, 0 0)>
>>> Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]).reverse()
<POLYGON ((0 0, 0 1, 1 1, 1 0, 0 0))>
```
segmentize(tolerance)#

Adds vertices to line segments based on tolerance.

Additional vertices will be added to every line segment in an input geometry so that segments are no greater than tolerance. New vertices will evenly subdivide each segment.

Only linear components of input geometries are densified; other geometries are returned unmodified.

Parameters
tolerancefloat or array_like

Additional vertices will be added so that all line segments are no greater than this value. Must be greater than 0.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (0, 10)]).segmentize(tolerance=5)
<LINESTRING (0 0, 0 5, 0 10)>
>>> Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]).segmentize(tolerance=5)
<POLYGON ((0 0, 5 0, 10 0, 10 5, 10 10, 5 10, 0 10, 0 5, 0 0))>
```
simplify(tolerance, preserve_topology=True)#

Returns a simplified geometry produced by the Douglas-Peucker algorithm

Coordinates of the simplified geometry will be no more than the tolerance distance from the original. Unless the topology preserving option is used, the algorithm may produce self-intersecting or otherwise invalid geometries.

svg(scale_factor=1.0, fill_color=None, opacity=None)#

Returns SVG circle element for the Point geometry.

Parameters
scale_factorfloat

Multiplication factor for the SVG circle diameter. Default is 1.

fill_colorstr, optional

Hex string for fill color. Default is to use “#66cc99” if geometry is valid, and “#ff3333” if invalid.

opacityfloat

Float number between 0 and 1 for color opacity. Default value is 0.6

symmetric_difference(other)#

Returns the symmetric difference of the geometries (Shapely geometry)

touches(other)#

Returns True if geometries touch, else False

union(other)#

Returns the union of the geometries (Shapely geometry)

within(other)#

Returns True if geometry is within the other, else False

property wkb#

WKB representation of the geometry

property wkb_hex#

WKB hex representation of the geometry

property wkt#

WKT representation of the geometry

property x#

Return x coordinate.

property xy#

Separate arrays of X and Y coordinate values

Example:
```>>> x, y = Point(0, 0).xy
>>> list(x)
[0.0]
>>> list(y)
[0.0]
```
property y#

Return y coordinate.

property z#

Return z coordinate.

class Polygon(shell=None, holes=None)#

Bases: `shapely.geometry.base.BaseGeometry`

A geometry type representing an area that is enclosed by a linear ring.

A polygon is a two-dimensional feature and has a non-zero area. It may have one or more negative-space “holes” which are also bounded by linear rings. If any rings cross each other, the feature is invalid and operations on it may fail.

Parameters
shellsequence

A sequence of (x, y [,z]) numeric coordinate pairs or triples, or an array-like with shape (N, 2) or (N, 3). Also can be a sequence of Point objects.

holessequence

A sequence of objects which satisfy the same requirements as the shell parameters above

Examples

Create a square polygon with no holes

```>>> coords = ((0., 0.), (0., 1.), (1., 1.), (1., 0.), (0., 0.))
>>> polygon = Polygon(coords)
>>> polygon.area
1.0
```
Attributes
exteriorLinearRing

The ring which bounds the positive space of the polygon.

A sequence of rings which bound all existing holes.

Methods

 `almost_equals`(other[, decimal]) True if geometries are equal at all coordinates to a specified decimal place. `buffer`(distance[, resolution, quadsegs, ...]) Get a geometry that represents all points within a distance of this geometry. `contains`(other) Returns True if the geometry contains the other, else False `covered_by`(other) Returns True if the geometry is covered by the other, else False `covers`(other) Returns True if the geometry covers the other, else False `crosses`(other) Returns True if the geometries cross, else False `difference`(other) Returns the difference of the geometries `disjoint`(other) Returns True if geometries are disjoint, else False `distance`(other) Unitless distance to other geometry (float) `equals`(other) Returns True if geometries are equal, else False. `equals_exact`(other, tolerance) True if geometries are equal to within a specified tolerance. `from_bounds`(xmin, ymin, xmax, ymax) Construct a Polygon() from spatial bounds. `hausdorff_distance`(other) Unitless hausdorff distance to other geometry (float) `interpolate`(distance[, normalized]) Return a point at the specified distance along a linear geometry `intersection`(other) Returns the intersection of the geometries `intersects`(other) Returns True if geometries intersect, else False `line_interpolate_point`(distance[, normalized]) Return a point at the specified distance along a linear geometry `line_locate_point`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point Converts geometry to normal form (or canonical form). `overlaps`(other) Returns True if geometries overlap, else False Returns a point guaranteed to be within the object, cheaply. `project`(other[, normalized]) Returns the distance along this geometry to a point nearest the specified point `relate`(other) Returns the DE-9IM intersection matrix for the two geometries (string) `relate_pattern`(other, pattern) Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False Returns a point guaranteed to be within the object, cheaply. Returns a copy of this geometry with the order of coordinates reversed. `segmentize`(tolerance) Adds vertices to line segments based on tolerance. `simplify`(tolerance[, preserve_topology]) Returns a simplified geometry produced by the Douglas-Peucker algorithm `svg`([scale_factor, fill_color, opacity]) Returns SVG path element for the Polygon geometry. Returns the symmetric difference of the geometries (Shapely geometry) `touches`(other) Returns True if geometries touch, else False `union`(other) Returns the union of the geometries (Shapely geometry) `within`(other) Returns True if geometry is within the other, else False
 geometryType
__eq__(value, /)#

Return self==value.

__ge__(value, /)#

Return self>=value.

property __geo_interface__#

Dictionary representation of the geometry

__gt__(value, /)#

Return self>value.

__hash__(/)#

Return hash(self).

__le__(value, /)#

Return self<=value.

__lt__(value, /)#

Return self<value.

__ne__(value, /)#

Return self!=value.

static __new__(self, shell=None, holes=None)#
__or__(other)#

Return self|value.

__reduce__()#

Helper for pickle.

__repr__()#

Return repr(self).

__str__()#

Return str(self).

almost_equals(other, decimal=6)#

True if geometries are equal at all coordinates to a specified decimal place.

Deprecated since version 1.8.0: The ‘almost_equals()’ method is deprecated and will be removed in Shapely 2.0 because the name is confusing. The ‘equals_exact()’ method should be used instead.

Refers to approximate coordinate equality, which requires coordinates to be approximately equal and in the same order for all components of a geometry.

Because of this it is possible for “equals()” to be True for two geometries and “almost_equals()” to be False.

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
property area#

Unitless area of the geometry (float)

property boundary#

Returns a lower dimension geometry that bounds the object

The boundary of a polygon is a line, the boundary of a line is a collection of points. The boundary of a point is an empty (null) collection.

property bounds#

Returns minimum bounding region (minx, miny, maxx, maxy)

buffer(distance, resolution=16, quadsegs=None, cap_style=1, join_style=1, mitre_limit=5.0, single_sided=False)#

Get a geometry that represents all points within a distance of this geometry.

A positive distance produces a dilation, a negative distance an erosion. A very small or zero distance may sometimes be used to “tidy” a polygon.

Parameters
distancefloat

The distance to buffer around the object.

resolutionint, optional

The resolution of the buffer around each vertex of the object.

Sets the number of line segments used to approximate an angle fillet. Note: the use of a quadsegs parameter is deprecated and will be gone from the next major release.

cap_styleint, optional

The styles of caps are: CAP_STYLE.round (1), CAP_STYLE.flat (2), and CAP_STYLE.square (3).

join_styleint, optional

The styles of joins between offset segments are: JOIN_STYLE.round (1), JOIN_STYLE.mitre (2), and JOIN_STYLE.bevel (3).

mitre_limitfloat, optional

The mitre limit ratio is used for very sharp corners. The mitre ratio is the ratio of the distance from the corner to the end of the mitred offset corner. When two line segments meet at a sharp angle, a miter join will extend the original geometry. To prevent unreasonable geometry, the mitre limit allows controlling the maximum length of the join corner. Corners with a ratio which exceed the limit will be beveled.

single_sidebool, optional

The side used is determined by the sign of the buffer distance:

a positive distance indicates the left-hand side a negative distance indicates the right-hand side

The single-sided buffer of point geometries is the same as the regular buffer. The End Cap Style for single-sided buffers is always ignored, and forced to the equivalent of CAP_FLAT.

Returns
Geometry

Notes

The return value is a strictly two-dimensional geometry. All Z coordinates of the original geometry will be ignored.

Examples

```>>> from shapely.wkt import loads
>>> g = loads('POINT (0.0 0.0)')
```

16-gon approx of a unit radius circle:

```>>> g.buffer(1.0).area
3.1365484905459...
```

128-gon approximation:

```>>> g.buffer(1.0, 128).area
3.141513801144...
```

triangle approximation:

```>>> g.buffer(1.0, 3).area
3.0
>>> list(g.buffer(1.0, cap_style=CAP_STYLE.square).exterior.coords)
[(1.0, 1.0), (1.0, -1.0), (-1.0, -1.0), (-1.0, 1.0), (1.0, 1.0)]
>>> g.buffer(1.0, cap_style=CAP_STYLE.square).area
4.0
```
property centroid#

Returns the geometric center of the object

contains(other)#

Returns True if the geometry contains the other, else False

property convex_hull#

Imagine an elastic band stretched around the geometry: that’s a convex hull, more or less

The convex hull of a three member multipoint, for example, is a triangular polygon.

property coords#

covered_by(other)#

Returns True if the geometry is covered by the other, else False

covers(other)#

Returns True if the geometry covers the other, else False

crosses(other)#

Returns True if the geometries cross, else False

difference(other)#

Returns the difference of the geometries

disjoint(other)#

Returns True if geometries are disjoint, else False

distance(other)#

Unitless distance to other geometry (float)

property envelope#

A figure that envelopes the geometry

equals(other)#

Returns True if geometries are equal, else False.

This method considers point-set equality (or topological equality), and is equivalent to (self.within(other) & self.contains(other)).

Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals(
...     LineString([(0, 0), (1, 1), (2, 2)])
... )
True
```
equals_exact(other, tolerance)#

True if geometries are equal to within a specified tolerance.

Parameters
otherBaseGeometry

The other geometry object in this comparison.

tolerancefloat

Absolute tolerance in the same units as coordinates.

This method considers coordinate equality, which requires
coordinates to be equal and in the same order for all components
of a geometry.
Because of this it is possible for “equals()” to be True for two
geometries and “equals_exact()” to be False.
Returns
bool

Examples

```>>> LineString(
...     [(0, 0), (2, 2)]
... ).equals_exact(
...     LineString([(0, 0), (1, 1), (2, 2)]),
...     1e-6
... )
False
```
classmethod from_bounds(xmin, ymin, xmax, ymax)#

Construct a Polygon() from spatial bounds.

property geom_type#

Name of the geometry’s type, such as ‘Point’

property has_z#

True if the geometry’s coordinate sequence(s) have z values (are 3-dimensional)

hausdorff_distance(other)#

Unitless hausdorff distance to other geometry (float)

interpolate(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of line_interpolate_point.

intersection(other)#

Returns the intersection of the geometries

intersects(other)#

Returns True if geometries intersect, else False

property is_closed#

True if the geometry is closed, else False

Applicable only to 1-D geometries.

property is_empty#

True if the set of points in this geometry is empty, else False

property is_ring#

True if the geometry is a closed ring, else False

property is_simple#

True if the geometry is simple, meaning that any self-intersections are only at boundary points, else False

property is_valid#

True if the geometry is valid (definition depends on sub-class), else False

property length#

Unitless length of the geometry (float)

line_interpolate_point(distance, normalized=False)#

Return a point at the specified distance along a linear geometry

Negative length values are taken as measured in the reverse direction from the end of the geometry. Out-of-range index values are handled by clamping them to the valid range of values. If the normalized arg is True, the distance will be interpreted as a fraction of the geometry’s length.

Alias of interpolate.

line_locate_point(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of project.

property minimum_clearance#

Unitless distance by which a node could be moved to produce an invalid geometry (float)

property minimum_rotated_rectangle#

Returns the general minimum bounding rectangle of the geometry. Can possibly be rotated. If the convex hull of the object is a degenerate (line or point) this same degenerate is returned.

normalize()#

Converts geometry to normal form (or canonical form).

This method orders the coordinates, rings of a polygon and parts of multi geometries consistently. Typically useful for testing purposes (for example in combination with equals_exact).

Examples

```>>> from shapely import MultiLineString
>>> line = MultiLineString([[(0, 0), (1, 1)], [(3, 3), (2, 2)]])
>>> line.normalize()
<MULTILINESTRING ((2 2, 3 3), (0 0, 1 1))>
```
overlaps(other)#

Returns True if geometries overlap, else False

point_on_surface()#

Returns a point guaranteed to be within the object, cheaply.

Alias of representative_point.

project(other, normalized=False)#

Returns the distance along this geometry to a point nearest the specified point

If the normalized arg is True, return the distance normalized to the length of the linear geometry.

Alias of line_locate_point.

relate(other)#

Returns the DE-9IM intersection matrix for the two geometries (string)

relate_pattern(other, pattern)#

Returns True if the DE-9IM string code for the relationship between the geometries satisfies the pattern, else False

representative_point()#

Returns a point guaranteed to be within the object, cheaply.

Alias of point_on_surface.

reverse()#

Returns a copy of this geometry with the order of coordinates reversed.

If the geometry is a polygon with interior rings, the interior rings are also reversed.

Points are unchanged.

`is_ccw`

Checks if a geometry is clockwise.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (1, 2)]).reverse()
<LINESTRING (1 2, 0 0)>
>>> Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]).reverse()
<POLYGON ((0 0, 0 1, 1 1, 1 0, 0 0))>
```
segmentize(tolerance)#

Adds vertices to line segments based on tolerance.

Additional vertices will be added to every line segment in an input geometry so that segments are no greater than tolerance. New vertices will evenly subdivide each segment.

Only linear components of input geometries are densified; other geometries are returned unmodified.

Parameters
tolerancefloat or array_like

Additional vertices will be added so that all line segments are no greater than this value. Must be greater than 0.

Examples

```>>> from shapely import LineString, Polygon
>>> LineString([(0, 0), (0, 10)]).segmentize(tolerance=5)
<LINESTRING (0 0, 0 5, 0 10)>
>>> Polygon([(0, 0), (10, 0), (10, 10), (0, 10), (0, 0)]).segmentize(tolerance=5)
<POLYGON ((0 0, 5 0, 10 0, 10 5, 10 10, 5 10, 0 10, 0 5, 0 0))>
```
simplify(tolerance, preserve_topology=True)#

Returns a simplified geometry produced by the Douglas-Peucker algorithm

Coordinates of the simplified geometry will be no more than the tolerance distance from the original. Unless the topology preserving option is used, the algorithm may produce self-intersecting or otherwise invalid geometries.

svg(scale_factor=1.0, fill_color=None, opacity=None)#

Returns SVG path element for the Polygon geometry.

Parameters
scale_factorfloat

Multiplication factor for the SVG stroke-width. Default is 1.

fill_colorstr, optional

Hex string for fill color. Default is to use “#66cc99” if geometry is valid, and “#ff3333” if invalid.

opacityfloat

Float number between 0 and 1 for color opacity. Default value is 0.6

symmetric_difference(other)#

Returns the symmetric difference of the geometries (Shapely geometry)

touches(other)#

Returns True if geometries touch, else False

union(other)#

Returns the union of the geometries (Shapely geometry)

within(other)#

Returns True if geometry is within the other, else False

property wkb#

WKB representation of the geometry

property wkb_hex#

WKB hex representation of the geometry

property wkt#

WKT representation of the geometry

property xy#

Separate arrays of X and Y coordinate values

box(minx, miny, maxx, maxy, ccw=True)#

Returns a rectangular polygon with configurable normal vector

mapping(ob)#

Returns a GeoJSON-like mapping from a Geometry or any object which implements __geo_interface__

Parameters
ob :

An object which implements __geo_interface__.

Returns
dict

Examples

```>>> pt = Point(0, 0)
>>> mapping(pt)
{'type': 'Point', 'coordinates': (0.0, 0.0)}
```
shape(context)#

Returns a new, independent geometry with coordinates copied from the context. Changes to the original context will not be reflected in the geometry object.

Parameters
context :

a GeoJSON-like dict, which provides a “type” member describing the type of the geometry and “coordinates” member providing a list of coordinates, or an object which implements __geo_interface__.

Returns
Geometry object

Examples

Create a Point from GeoJSON, and then create a copy using __geo_interface__.

```>>> context = {'type': 'Point', 'coordinates': [0, 1]}
>>> geom = shape(context)
>>> geom.type == 'Point'
True
>>> geom.wkt
'POINT (0 1)'
>>> geom2 = shape(geom)
>>> geom == geom2
True
```