Predicates
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.
See also
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
>>> from shapely import LineString, Point, Polygon >>> line = LineString([(0, 0), (1, 1)]) >>> contains(line, Point(0, 0)) False >>> contains(line, Point(0.5, 0.5)) True >>> area = Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]) >>> contains(area, Point(0, 0)) False >>> contains(area, line) True >>> contains(area, LineString([(0, 0), (2, 2)])) False >>> polygon_with_hole = Polygon( ... [(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)], ... holes=[[(2, 2), (2, 4), (4, 4), (4, 2), (2, 2)]] ... ) >>> contains(polygon_with_hole, Point(1, 1)) True >>> contains(polygon_with_hole, Point(2, 2)) False >>> contains(polygon_with_hole, 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.
See also
contains
contains which allows common boundary points
prepare
improve performance by preparing
a
(the first argument)
Examples
>>> from shapely import Polygon >>> area1 = Polygon([(0, 0), (3, 0), (3, 3), (0, 3), (0, 0)]) >>> area2 = Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]) >>> area3 = Polygon([(1, 1), (2, 1), (2, 2), (1, 2), (1, 1)])
area1
andarea2
have a common border:>>> contains(area1, area2) True >>> contains_properly(area1, area2) False
area3
is completely insidearea1
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.
See also
covers
covered_by(A, B) == covers(B, A)
prepare
improve performance by preparing
a
(the first argument)
Examples
>>> from shapely import LineString, Point, Polygon >>> line = LineString([(0, 0), (1, 1)]) >>> covered_by(Point(0, 0), line) True >>> covered_by(Point(0.5, 0.5), line) True >>> area = Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]) >>> covered_by(Point(0, 0), area) True >>> covered_by(line, area) True >>> covered_by(LineString([(0, 0), (2, 2)]), area) False >>> polygon_with_hole = Polygon( ... [(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)], ... holes=[[(2, 2), (2, 4), (4, 4), (4, 2), (2, 2)]] ... ) >>> covered_by(Point(1, 1), polygon_with_hole) True >>> covered_by(Point(2, 2), polygon_with_hole) True >>> covered_by(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.
See also
covered_by
covers(A, B) == covered_by(B, A)
prepare
improve performance by preparing
a
(the first argument)
Examples
>>> from shapely import LineString, Point, Polygon >>> line = LineString([(0, 0), (1, 1)]) >>> covers(line, Point(0, 0)) True >>> covers(line, Point(0.5, 0.5)) True >>> area = Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]) >>> covers(area, Point(0, 0)) True >>> covers(area, line) True >>> covers(area, LineString([(0, 0), (2, 2)])) False >>> polygon_with_hole = Polygon( ... [(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)], ... holes=[[(2, 2), (2, 4), (4, 4), (4, 2), (2, 2)]] ... ) >>> covers(polygon_with_hole, Point(1, 1)) True >>> covers(polygon_with_hole, Point(2, 2)) True >>> covers(polygon_with_hole, 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.
See also
prepare
improve performance by preparing
a
(the first argument)
Examples
>>> from shapely import LineString, MultiPoint, Point, Polygon >>> line = LineString([(0, 0), (1, 1)]) >>> # A contains B: >>> crosses(line, Point(0.5, 0.5)) False >>> # A and B intersect at a point but do not share all points: >>> crosses(line, MultiPoint([(0, 1), (0.5, 0.5)])) True >>> crosses(line, LineString([(0, 1), (1, 0)])) True >>> # A is contained by B; their intersection is a line (same dimension): >>> crosses(line, LineString([(0, 0), (2, 2)])) False >>> area = 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, LineString([(0, 0), (2, 2)])) True >>> # A contains B: >>> crosses(area, Point(0.5, 0.5)) False >>> # A contains some but not all points of B; they intersect at a point: >>> crosses(area, 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.
See also
intersects
disjoint(A, B) == ~intersects(A, B)
prepare
improve performance by preparing
a
(the first argument)
Examples
>>> from shapely import GeometryCollection, LineString, Point >>> line = LineString([(0, 0), (1, 1)]) >>> disjoint(line, Point(0, 0)) False >>> disjoint(line, Point(0, 1)) True >>> disjoint(line, LineString([(0, 2), (2, 0)])) False >>> empty = GeometryCollection() >>> 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.
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.
See also
distance
compute the actual distance between A and B
prepare
improve performance by preparing
a
(the first argument)
Examples
>>> from shapely import Point >>> point = Point(0.5, 0.5) >>> dwithin(point, Point(2, 0.5), 2) True >>> dwithin(point, Point(2, 0.5), [2, 1.5, 1]).tolist() [True, True, False] >>> dwithin(point, 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.
See also
equals_exact
Check if A and B are structurally equal given a specified tolerance.
Examples
>>> from shapely import GeometryCollection, LineString, Polygon >>> line = LineString([(0, 0), (5, 5), (10, 10)]) >>> equals(line, LineString([(0, 0), (10, 10)])) True >>> equals(Polygon(), GeometryCollection()) 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.
See also
equals
Check if A and B are spatially equal.
Examples
>>> from shapely import Point, Polygon >>> point1 = Point(50, 50) >>> point2 = 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 = Polygon([(0, 0), (1, 1), (0, 1), (0, 0)]) >>> polygon2 = 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.
See also
get_coordinate_dimension
Examples
>>> from shapely import Point >>> has_z(Point(0, 0)) False >>> has_z(Point(0, 0, 0)) True >>> has_z(Point(0, 0, float("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.
See also
disjoint
intersects(A, B) == ~disjoint(A, B)
prepare
improve performance by preparing
a
(the first argument)
Examples
>>> from shapely import LineString, Point >>> line = LineString([(0, 0), (1, 1)]) >>> intersects(line, Point(0, 0)) True >>> intersects(line, Point(0, 1)) False >>> intersects(line, LineString([(0, 2), (2, 0)])) True >>> intersects(None, None) False
- is_ccw(geometry, **kwargs)#
Returns True if a linestring or linearring is counterclockwise.
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 linearringsis_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.
See also
Examples
>>> from shapely import LinearRing, LineString, Point >>> is_ccw(LinearRing([(0, 0), (0, 1), (1, 1), (0, 0)])) False >>> is_ccw(LinearRing([(0, 0), (1, 1), (0, 1), (0, 0)])) True >>> is_ccw(LineString([(0, 0), (1, 1), (0, 1)])) False >>> is_ccw(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.
See also
is_ring
Checks additionally if the geometry is simple.
Examples
>>> from shapely import LineString, Point >>> is_closed(LineString([(0, 0), (1, 1)])) False >>> is_closed(LineString([(0, 0), (0, 1), (1, 1), (0, 0)])) True >>> is_closed(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.
See also
is_missing
checks if the object is a geometry
Examples
>>> from shapely import Point >>> is_empty(Point()) True >>> is_empty(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.
See also
is_missing
check if an object is missing (None)
is_valid_input
check if an object is a geometry or None
Examples
>>> from shapely import GeometryCollection, Point >>> is_geometry(Point(0, 0)) True >>> is_geometry(GeometryCollection()) 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.
See also
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
>>> from shapely import GeometryCollection, Point >>> is_missing(Point(0, 0)) False >>> is_missing(GeometryCollection()) 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.
See also
is_valid_input
check if an object is a geometry or None
prepare
prepare a geometry
Examples
>>> from shapely import Point, prepare >>> geometry = Point(0, 0) >>> is_prepared(Point(0, 0)) False >>> 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.
See also
Examples
>>> from shapely import LineString, Point >>> is_ring(Point(0, 0)) False >>> geom = LineString([(0, 0), (1, 1)]) >>> is_closed(geom), is_simple(geom), is_ring(geom) (False, True, False) >>> geom = LineString([(0, 0), (0, 1), (1, 1), (0, 0)]) >>> is_closed(geom), is_simple(geom), is_ring(geom) (True, True, True) >>> geom = 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.
See also
Examples
>>> from shapely import LineString, Polygon >>> is_simple(Polygon([(1, 1), (2, 1), (2, 2), (1, 1)])) True >>> is_simple(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.
See also
is_valid_reason
Returns the reason in case of invalid.
Examples
>>> from shapely import GeometryCollection, LineString, Polygon >>> is_valid(LineString([(0, 0), (1, 1)])) True >>> is_valid(Polygon([(0, 0), (1, 1), (1, 2), (1, 1), (0, 0)])) False >>> is_valid(GeometryCollection()) 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.
See also
is_geometry
checks if an object is a geometry
is_missing
checks if an object is None
Examples
>>> from shapely import GeometryCollection, Point >>> is_valid_input(Point(0, 0)) True >>> is_valid_input(GeometryCollection()) 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.
See also
is_valid
returns True or False
Examples
>>> from shapely import LineString, Polygon >>> is_valid_reason(LineString([(0, 0), (1, 1)])) 'Valid Geometry' >>> is_valid_reason(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.
See also
prepare
improve performance by preparing
a
(the first argument)
Examples
>>> from shapely import LineString, Point, Polygon >>> poly = 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, Polygon([(0, 0), (0, 2), (2, 2), (2, 0), (0, 0)])) False >>> # A partially overlaps with B: >>> overlaps(poly, Polygon([(2, 2), (2, 6), (6, 6), (6, 2), (2, 2)])) True >>> line = LineString([(2, 2), (6, 6)]) >>> # A and B are different dimensions; they cannot overlap: >>> overlaps(poly, line) False >>> overlaps(poly, Point(2, 2)) False >>> # A and B share some but not all points: >>> overlaps(line, LineString([(0, 0), (4, 4)])) True >>> # A and B intersect only at a point (lower dimension); they do not overlap >>> overlaps(line, 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
>>> from shapely import LineString, Point >>> point = Point(0, 0) >>> line = 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, otherwiseFalse
. The pattern specified can be an exact match (0
,1
or2
), a boolean match (uppercaseT
orF
), or a wildcard (*
). For example, the pattern for thewithin
predicate is'T*F**F***'
.- Parameters
- a, bGeometry or array_like
- patternstring
- **kwargs
For other keyword-only arguments, see the NumPy ufunc docs.
Examples
>>> from shapely import Point, Polygon >>> point = Point(0.5, 0.5) >>> square = 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.
See also
prepare
improve performance by preparing
a
(the first argument)
Examples
>>> from shapely import LineString, Point, Polygon >>> line = LineString([(0, 2), (2, 0)]) >>> touches(line, Point(0, 2)) True >>> touches(line, Point(1, 1)) False >>> touches(line, LineString([(0, 0), (1, 1)])) True >>> touches(line, LineString([(0, 0), (2, 2)])) False >>> area = Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]) >>> touches(area, Point(0.5, 0)) True >>> touches(area, Point(0.5, 0.5)) False >>> touches(area, line) True >>> touches(area, 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.
See also
contains
within(A, B) == contains(B, A)
prepare
improve performance by preparing
a
(the first argument)
Examples
>>> from shapely import LineString, Point, Polygon >>> line = LineString([(0, 0), (1, 1)]) >>> within(Point(0, 0), line) False >>> within(Point(0.5, 0.5), line) True >>> area = Polygon([(0, 0), (1, 0), (1, 1), (0, 1), (0, 0)]) >>> within(Point(0, 0), area) False >>> within(line, area) True >>> within(LineString([(0, 0), (2, 2)]), area) False >>> polygon_with_hole = Polygon( ... [(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)], ... holes=[[(2, 2), (2, 4), (4, 4), (4, 2), (2, 2)]] ... ) >>> within(Point(1, 1), polygon_with_hole) True >>> within(Point(2, 2), polygon_with_hole) False >>> within(LineString([(1, 1), (5, 5)]), polygon_with_hole) False >>> within(area, area) True >>> within(None, area) False