# Predicates¶

contains(a, b, **kwargs)

Returns True if geometry B is completely inside geometry A.

A contains B if no points of B lie in the exterior of A and at least one point of the interior of B lies in the interior of A.

Note: following this definition, a geometry does not contain its boundary, but it does contain itself. See `contains_properly` for a version where a geometry does not contain itself.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`within`

`contains(A, B) == within(B, A)`

`contains_properly`

contains with no common boundary points

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> line = Geometry("LINESTRING(0 0, 1 1)")
>>> contains(line, Geometry("POINT (0 0)"))
False
>>> contains(line, Geometry("POINT (0.5 0.5)"))
True
>>> area = Geometry("POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))")
>>> contains(area, Geometry("POINT (0 0)"))
False
>>> contains(area, line)
True
>>> contains(area, Geometry("LINESTRING(0 0, 2 2)"))
False
>>> polygon_with_hole = Geometry("POLYGON((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 4 2, 4 4, 2 4, 2 2))")
>>> contains(polygon_with_hole, Geometry("POINT(1 1)"))
True
>>> contains(polygon_with_hole, Geometry("POINT(2 2)"))
False
>>> contains(polygon_with_hole, Geometry("LINESTRING(1 1, 5 5)"))
False
>>> contains(area, area)
True
>>> contains(area, None)
False
```
contains_properly(a, b, **kwargs)

Returns True if geometry B is completely inside geometry A, with no common boundary points.

A contains B properly if B intersects the interior of A but not the boundary (or exterior). This means that a geometry A does not “contain properly” itself, which contrasts with the `contains` function, where common points on the boundary are allowed.

Note: this function will prepare the geometries under the hood if needed. You can prepare the geometries in advance to avoid repeated preparation when calling this function multiple times.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`contains`

contains which allows common boundary points

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> area1 = Geometry("POLYGON((0 0, 3 0, 3 3, 0 3, 0 0))")
>>> area2 = Geometry("POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))")
>>> area3 = Geometry("POLYGON((1 1, 2 1, 2 2, 1 2, 1 1))")
```

`area1` and `area2` have a common border:

```>>> contains(area1, area2)
True
>>> contains_properly(area1, area2)
False
```

`area3` is completely inside `area1` with no common border:

```>>> contains(area1, area3)
True
>>> contains_properly(area1, area3)
True
```
covered_by(a, b, **kwargs)

Returns True if no point in geometry A is outside geometry B.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`covers`

`covered_by(A, B) == covers(B, A)`

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> line = Geometry("LINESTRING(0 0, 1 1)")
>>> covered_by(Geometry("POINT (0 0)"), line)
True
>>> covered_by(Geometry("POINT (0.5 0.5)"), line)
True
>>> area = Geometry("POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))")
>>> covered_by(Geometry("POINT (0 0)"), area)
True
>>> covered_by(line, area)
True
>>> covered_by(Geometry("LINESTRING(0 0, 2 2)"), area)
False
>>> polygon_with_hole = Geometry("POLYGON((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 4 2, 4 4, 2 4, 2 2))")  # NOQA
>>> covered_by(Geometry("POINT(1 1)"), polygon_with_hole)
True
>>> covered_by(Geometry("POINT(2 2)"), polygon_with_hole)
True
>>> covered_by(Geometry("LINESTRING(1 1, 5 5)"), polygon_with_hole)
False
>>> covered_by(area, area)
True
>>> covered_by(None, area)
False
```
covers(a, b, **kwargs)

Returns True if no point in geometry B is outside geometry A.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`covered_by`

`covers(A, B) == covered_by(B, A)`

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> line = Geometry("LINESTRING(0 0, 1 1)")
>>> covers(line, Geometry("POINT (0 0)"))
True
>>> covers(line, Geometry("POINT (0.5 0.5)"))
True
>>> area = Geometry("POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))")
>>> covers(area, Geometry("POINT (0 0)"))
True
>>> covers(area, line)
True
>>> covers(area, Geometry("LINESTRING(0 0, 2 2)"))
False
>>> polygon_with_hole = Geometry("POLYGON((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 4 2, 4 4, 2 4, 2 2))")  # NOQA
>>> covers(polygon_with_hole, Geometry("POINT(1 1)"))
True
>>> covers(polygon_with_hole, Geometry("POINT(2 2)"))
True
>>> covers(polygon_with_hole, Geometry("LINESTRING(1 1, 5 5)"))
False
>>> covers(area, area)
True
>>> covers(area, None)
False
```
crosses(a, b, **kwargs)

Returns True if A and B spatially cross.

A crosses B if they have some but not all interior points in common, the intersection is one dimension less than the maximum dimension of A or B, and the intersection is not equal to either A or B.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> line = Geometry("LINESTRING(0 0, 1 1)")
>>> # A contains B:
>>> crosses(line, Geometry("POINT (0.5 0.5)"))
False
>>> # A and B intersect at a point but do not share all points:
>>> crosses(line, Geometry("MULTIPOINT ((0 1), (0.5 0.5))"))
True
>>> crosses(line, Geometry("LINESTRING(0 1, 1 0)"))
True
>>> # A is contained by B; their intersection is a line (same dimension):
>>> crosses(line, Geometry("LINESTRING(0 0, 2 2)"))
False
>>> area = Geometry("POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))")
>>> # A contains B:
>>> crosses(area, line)
False
>>> # A and B intersect with a line (lower dimension) but do not share all points:
>>> crosses(area, Geometry("LINESTRING(0 0, 2 2)"))
True
>>> # A contains B:
>>> crosses(area, Geometry("POINT (0.5 0.5)"))
False
>>> # A contains some but not all points of B; they intersect at a point:
>>> crosses(area, Geometry("MULTIPOINT ((2 2), (0.5 0.5))"))
True
```
disjoint(a, b, **kwargs)

Returns True if A and B do not share any point in space.

Disjoint implies that overlaps, touches, within, and intersects are False. Note missing (None) values are never disjoint.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`intersects`

`disjoint(A, B) == ~intersects(A, B)`

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> line = Geometry("LINESTRING(0 0, 1 1)")
>>> disjoint(line, Geometry("POINT (0 0)"))
False
>>> disjoint(line, Geometry("POINT (0 1)"))
True
>>> disjoint(line, Geometry("LINESTRING(0 2, 2 0)"))
False
>>> empty = Geometry("GEOMETRYCOLLECTION EMPTY")
>>> disjoint(line, empty)
True
>>> disjoint(empty, empty)
True
>>> disjoint(empty, None)
False
>>> disjoint(None, None)
False
```
dwithin(a, b, distance, **kwargs)

Returns True if the geometries are within a given distance.

Note

‘dwithin’ requires at least GEOS 3.10.0.

Using this function is more efficient than computing the distance and comparing the result.

Parameters
a, bGeometry or array_like
distancefloat

Negative distances always return False.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`distance`

compute the actual distance between A and B

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> point = Geometry("POINT (0.5 0.5)")
>>> dwithin(point, Geometry("POINT (2 0.5)"), 2)
True
>>> dwithin(point, Geometry("POINT (2 0.5)"), [2, 1.5, 1]).tolist()
[True, True, False]
>>> dwithin(point, Geometry("POINT (0.5 0.5)"), 0)
True
>>> dwithin(point, None, 100)
False
```
equals(a, b, **kwargs)

Returns True if A and B are spatially equal.

If A is within B and B is within A, A and B are considered equal. The ordering of points can be different.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`equals_exact`

Check if A and B are structurally equal given a specified tolerance.

Examples

```>>> line = Geometry("LINESTRING(0 0, 5 5, 10 10)")
>>> equals(line, Geometry("LINESTRING(0 0, 10 10)"))
True
>>> equals(Geometry("POLYGON EMPTY"), Geometry("GEOMETRYCOLLECTION EMPTY"))
True
>>> equals(None, None)
False
```
equals_exact(a, b, tolerance=0.0, **kwargs)

Returns True if A and B are structurally equal.

This method uses exact coordinate equality, which requires coordinates to be equal (within specified tolerance) and and in the same order for all components of a geometry. This is in contrast with the `equals` function which uses spatial (topological) equality.

Parameters
a, bGeometry or array_like
tolerancefloat or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`equals`

Check if A and B are spatially equal.

Examples

```>>> point1 = Geometry("POINT(50 50)")
>>> point2 = Geometry("POINT(50.1 50.1)")
>>> equals_exact(point1, point2)
False
>>> equals_exact(point1, point2, tolerance=0.2)
True
>>> equals_exact(point1, None, tolerance=0.2)
False
```

Difference between structucal and spatial equality:

```>>> polygon1 = Geometry("POLYGON((0 0, 1 1, 0 1, 0 0))")
>>> polygon2 = Geometry("POLYGON((0 0, 0 1, 1 1, 0 0))")
>>> equals_exact(polygon1, polygon2)
False
>>> equals(polygon1, polygon2)
True
```
has_z(geometry, **kwargs)

Returns True if a geometry has a Z coordinate.

Note that this function returns False if the (first) Z coordinate equals NaN or if the geometry is empty.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`get_coordinate_dimension`

Examples

```>>> has_z(Geometry("POINT (0 0)"))
False
>>> has_z(Geometry("POINT Z (0 0 0)"))
True
>>> has_z(Geometry("POINT Z(0 0 nan)"))
False
```
intersects(a, b, **kwargs)

Returns True if A and B share any portion of space.

Intersects implies that overlaps, touches and within are True.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`disjoint`

`intersects(A, B) == ~disjoint(A, B)`

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> line = Geometry("LINESTRING(0 0, 1 1)")
>>> intersects(line, Geometry("POINT (0 0)"))
True
>>> intersects(line, Geometry("POINT (0 1)"))
False
>>> intersects(line, Geometry("LINESTRING(0 2, 2 0)"))
True
>>> intersects(None, None)
False
```
is_ccw(geometry, **kwargs)

Returns True if a linestring or linearring is counterclockwise.

Note

‘is_ccw’ requires at least GEOS 3.7.0.

Note that there are no checks on whether lines are actually closed and not self-intersecting, while this is a requirement for is_ccw. The recommended usage of this function for linestrings is `is_ccw(g) & is_simple(g)` and for linearrings `is_ccw(g) & is_valid(g)`.

Parameters
geometryGeometry or array_like

This function will return False for non-linear goemetries and for lines with fewer than 4 points (including the closing point).

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_simple`

Checks if a linestring is closed and simple.

`is_valid`

Checks additionally if the geometry is simple.

Examples

```>>> is_ccw(Geometry("LINEARRING (0 0, 0 1, 1 1, 0 0)"))
False
>>> is_ccw(Geometry("LINEARRING (0 0, 1 1, 0 1, 0 0)"))
True
>>> is_ccw(Geometry("LINESTRING (0 0, 1 1, 0 1)"))
False
>>> is_ccw(Geometry("POINT (0 0)"))
False
```
is_closed(geometry, **kwargs)

Returns True if a linestring’s first and last points are equal.

Parameters
geometryGeometry or array_like

This function will return False for non-linestrings.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_ring`

Checks additionally if the geometry is simple.

Examples

```>>> is_closed(Geometry("LINESTRING (0 0, 1 1)"))
False
>>> is_closed(Geometry("LINESTRING(0 0, 0 1, 1 1, 0 0)"))
True
>>> is_closed(Geometry("POINT (0 0)"))
False
```
is_empty(geometry, **kwargs)

Returns True if a geometry is an empty point, polygon, etc.

Parameters
geometryGeometry or array_like

Any geometry type is accepted.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_missing`

checks if the object is a geometry

Examples

```>>> is_empty(Geometry("POINT EMPTY"))
True
>>> is_empty(Geometry("POINT (0 0)"))
False
>>> is_empty(None)
False
```
is_geometry(geometry, **kwargs)

Returns True if the object is a geometry

Parameters
geometryany object or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_missing`

check if an object is missing (None)

`is_valid_input`

check if an object is a geometry or None

Examples

```>>> is_geometry(Geometry("POINT (0 0)"))
True
>>> is_geometry(Geometry("GEOMETRYCOLLECTION EMPTY"))
True
>>> is_geometry(None)
False
>>> is_geometry("text")
False
```
is_missing(geometry, **kwargs)

Returns True if the object is not a geometry (None)

Parameters
geometryany object or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_geometry`

check if an object is a geometry

`is_valid_input`

check if an object is a geometry or None

`is_empty`

checks if the object is an empty geometry

Examples

```>>> is_missing(Geometry("POINT (0 0)"))
False
>>> is_missing(Geometry("GEOMETRYCOLLECTION EMPTY"))
False
>>> is_missing(None)
True
>>> is_missing("text")
False
```
is_prepared(geometry, **kwargs)

Returns True if a Geometry is prepared.

Note that it is not necessary to check if a geometry is already prepared before preparing it. It is more efficient to call `prepare` directly because it will skip geometries that are already prepared.

This function will return False for missing geometries (None).

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_valid_input`

check if an object is a geometry or None

`prepare`

prepare a geometry

Examples

```>>> geometry = Geometry("POINT (0 0)")
>>> is_prepared(Geometry("POINT (0 0)"))
False
>>> from pygeos import prepare; prepare(geometry);
>>> is_prepared(geometry)
True
>>> is_prepared(None)
False
```
is_ring(geometry, **kwargs)

Returns True if a linestring is closed and simple.

Parameters
geometryGeometry or array_like

This function will return False for non-linestrings.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_closed`

Checks only if the geometry is closed.

`is_simple`

Checks only if the geometry is simple.

Examples

```>>> is_ring(Geometry("POINT (0 0)"))
False
>>> geom = Geometry("LINESTRING(0 0, 1 1)")
>>> is_closed(geom), is_simple(geom), is_ring(geom)
(False, True, False)
>>> geom = Geometry("LINESTRING(0 0, 0 1, 1 1, 0 0)")
>>> is_closed(geom), is_simple(geom), is_ring(geom)
(True, True, True)
>>> geom = Geometry("LINESTRING(0 0, 1 1, 0 1, 1 0, 0 0)")
>>> is_closed(geom), is_simple(geom), is_ring(geom)
(True, False, False)
```
is_simple(geometry, **kwargs)

Returns True if a Geometry has no anomalous geometric points, such as self-intersections or self tangency.

Note that polygons and linearrings are assumed to be simple. Use is_valid to check these kind of geometries for self-intersections.

Parameters
geometryGeometry or array_like

This function will return False for geometrycollections.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_ring`

Checks additionally if the geometry is closed.

`is_valid`

Checks whether a geometry is well formed.

Examples

```>>> is_simple(Geometry("POLYGON((1 1, 2 1, 2 2, 1 1))"))
True
>>> is_simple(Geometry("LINESTRING(0 0, 1 1, 0 1, 1 0, 0 0)"))
False
>>> is_simple(None)
False
```
is_valid(geometry, **kwargs)

Returns True if a geometry is well formed.

Parameters
geometryGeometry or array_like

Any geometry type is accepted. Returns False for missing values.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_valid_reason`

Returns the reason in case of invalid.

Examples

```>>> is_valid(Geometry("LINESTRING(0 0, 1 1)"))
True
>>> is_valid(Geometry("POLYGON((0 0, 1 1, 1 2, 1 1, 0 0))"))
False
>>> is_valid(Geometry("GEOMETRYCOLLECTION EMPTY"))
True
>>> is_valid(None)
False
```
is_valid_input(geometry, **kwargs)

Returns True if the object is a geometry or None

Parameters
geometryany object or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_geometry`

checks if an object is a geometry

`is_missing`

checks if an object is None

Examples

```>>> is_valid_input(Geometry("POINT (0 0)"))
True
>>> is_valid_input(Geometry("GEOMETRYCOLLECTION EMPTY"))
True
>>> is_valid_input(None)
True
>>> is_valid_input(1.0)
False
>>> is_valid_input("text")
False
```
is_valid_reason(geometry, **kwargs)

Returns a string stating if a geometry is valid and if not, why.

Parameters
geometryGeometry or array_like

Any geometry type is accepted. Returns None for missing values.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`is_valid`

returns True or False

Examples

```>>> is_valid_reason(Geometry("LINESTRING(0 0, 1 1)"))
'Valid Geometry'
>>> is_valid_reason(Geometry("POLYGON((0 0, 1 1, 1 2, 1 1, 0 0))"))
'Ring Self-intersection[1 1]'
>>> is_valid_reason(None) is None
True
```
overlaps(a, b, **kwargs)

Returns True if A and B spatially overlap.

A and B overlap if they have some but not all points in common, have the same dimension, and the intersection of the interiors of the two geometries has the same dimension as the geometries themselves. That is, only polyons can overlap other polygons and only lines can overlap other lines.

If either A or B are None, the output is always False.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> poly = Geometry("POLYGON ((0 0, 0 4, 4 4, 4 0, 0 0))")
>>> # A and B share all points (are spatially equal):
>>> overlaps(poly, poly)
False
>>> # A contains B; all points of B are within A:
>>> overlaps(poly, Geometry("POLYGON ((0 0, 0 2, 2 2, 2 0, 0 0))"))
False
>>> # A partially overlaps with B:
>>> overlaps(poly, Geometry("POLYGON ((2 2, 2 6, 6 6, 6 2, 2 2))"))
True
>>> line = Geometry("LINESTRING (2 2, 6 6)")
>>> # A and B are different dimensions; they cannot overlap:
>>> overlaps(poly, line)
False
>>> overlaps(poly, Geometry("POINT (2 2)"))
False
>>> # A and B share some but not all points:
>>> overlaps(line, Geometry("LINESTRING (0 0, 4 4)"))
True
>>> # A and B intersect only at a point (lower dimension); they do not overlap
>>> overlaps(line, Geometry("LINESTRING (6 0, 0 6)"))
False
>>> overlaps(poly, None)
False
>>> overlaps(None, None)
False
```
relate(a, b, **kwargs)

Returns a string representation of the DE-9IM intersection matrix.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> point = Geometry("POINT (0 0)")
>>> line = Geometry("LINESTRING(0 0, 1 1)")
>>> relate(point, line)
'F0FFFF102'
```
relate_pattern(a, b, pattern, **kwargs)

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

This function compares the DE-9IM code string for two geometries against a specified pattern. If the string matches the pattern then `True` is returned, otherwise `False`. The pattern specified can be an exact match (`0`, `1` or `2`), a boolean match (uppercase `T` or `F`), or a wildcard (`*`). For example, the pattern for the `within` predicate is `'T*F**F***'`.

Parameters
a, bGeometry or array_like
patternstring
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> point = Geometry("POINT (0.5 0.5)")
>>> square = Geometry("POLYGON((0 0, 0 1, 1 1, 1 0, 0 0))")
>>> relate(point, square)
'0FFFFF212'
>>> relate_pattern(point, square, "T*F**F***")
True
```
touches(a, b, **kwargs)

Returns True if the only points shared between A and B are on the boundary of A and B.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> line = Geometry("LINESTRING(0 2, 2 0)")
>>> touches(line, Geometry("POINT(0 2)"))
True
>>> touches(line, Geometry("POINT(1 1)"))
False
>>> touches(line, Geometry("LINESTRING(0 0, 1 1)"))
True
>>> touches(line, Geometry("LINESTRING(0 0, 2 2)"))
False
>>> area = Geometry("POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))")
>>> touches(area, Geometry("POINT(0.5 0)"))
True
>>> touches(area, Geometry("POINT(0.5 0.5)"))
False
>>> touches(area, line)
True
>>> touches(area, Geometry("POLYGON((0 1, 1 1, 1 2, 0 2, 0 1))"))
True
```
within(a, b, **kwargs)

Returns True if geometry A is completely inside geometry B.

A is within B if no points of A lie in the exterior of B and at least one point of the interior of A lies in the interior of B.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`contains`

`within(A, B) == contains(B, A)`

`prepare`

improve performance by preparing `a` (the first argument)

Examples

```>>> line = Geometry("LINESTRING(0 0, 1 1)")
>>> within(Geometry("POINT (0 0)"), line)
False
>>> within(Geometry("POINT (0.5 0.5)"), line)
True
>>> area = Geometry("POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))")
>>> within(Geometry("POINT (0 0)"), area)
False
>>> within(line, area)
True
>>> within(Geometry("LINESTRING(0 0, 2 2)"), area)
False
>>> polygon_with_hole = Geometry("POLYGON((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 4 2, 4 4, 2 4, 2 2))")  # NOQA
>>> within(Geometry("POINT(1 1)"), polygon_with_hole)
True
>>> within(Geometry("POINT(2 2)"), polygon_with_hole)
False
>>> within(Geometry("LINESTRING(1 1, 5 5)"), polygon_with_hole)
False
>>> within(area, area)
True
>>> within(None, area)
False
```