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Davidson Gomes
2025-04-25 15:30:54 -03:00
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"""Support for various GEOS geometry operations."""
import shapely
from shapely.algorithms.polylabel import polylabel # noqa
from shapely.errors import GeometryTypeError
from shapely.geometry import (
GeometryCollection,
LineString,
MultiLineString,
MultiPoint,
Point,
Polygon,
shape,
)
from shapely.geometry.base import BaseGeometry
from shapely.prepared import prep
__all__ = [
"clip_by_rect",
"linemerge",
"nearest_points",
"operator",
"orient",
"polygonize",
"polygonize_full",
"shared_paths",
"snap",
"split",
"substring",
"transform",
"triangulate",
"unary_union",
"validate",
"voronoi_diagram",
]
class CollectionOperator:
def shapeup(self, ob):
if isinstance(ob, BaseGeometry):
return ob
else:
try:
return shape(ob)
except (ValueError, AttributeError):
return LineString(ob)
def polygonize(self, lines):
"""Create polygons from a source of lines.
The source may be a MultiLineString, a sequence of LineString objects,
or a sequence of objects than can be adapted to LineStrings.
"""
source = getattr(lines, "geoms", None) or lines
try:
source = iter(source)
except TypeError:
source = [source]
finally:
obs = [self.shapeup(line) for line in source]
collection = shapely.polygonize(obs)
return collection.geoms
def polygonize_full(self, lines):
"""Create polygons from a source of lines.
The polygons and leftover geometries are returned as well.
The source may be a MultiLineString, a sequence of LineString objects,
or a sequence of objects than can be adapted to LineStrings.
Returns a tuple of objects: (polygons, cut edges, dangles, invalid ring
lines). Each are a geometry collection.
Dangles are edges which have one or both ends which are not incident on
another edge endpoint. Cut edges are connected at both ends but do not
form part of polygon. Invalid ring lines form rings which are invalid
(bowties, etc).
"""
source = getattr(lines, "geoms", None) or lines
try:
source = iter(source)
except TypeError:
source = [source]
finally:
obs = [self.shapeup(line) for line in source]
return shapely.polygonize_full(obs)
def linemerge(self, lines, directed=False):
"""Merge all connected lines from a source.
The source may be a MultiLineString, a sequence of LineString objects,
or a sequence of objects than can be adapted to LineStrings. Returns a
LineString or MultiLineString when lines are not contiguous.
"""
source = None
if getattr(lines, "geom_type", None) == "MultiLineString":
source = lines
elif hasattr(lines, "geoms"):
# other Multi geometries
source = MultiLineString([ls.coords for ls in lines.geoms])
elif hasattr(lines, "__iter__"):
try:
source = MultiLineString([ls.coords for ls in lines])
except AttributeError:
source = MultiLineString(lines)
if source is None:
raise ValueError(f"Cannot linemerge {lines}")
return shapely.line_merge(source, directed=directed)
def unary_union(self, geoms):
"""Return the union of a sequence of geometries.
Usually used to convert a collection into the smallest set of polygons
that cover the same area.
"""
return shapely.union_all(geoms, axis=None)
operator = CollectionOperator()
polygonize = operator.polygonize
polygonize_full = operator.polygonize_full
linemerge = operator.linemerge
unary_union = operator.unary_union
def triangulate(geom, tolerance=0.0, edges=False):
"""Create the Delaunay triangulation and return a list of geometries.
The source may be any geometry type. All vertices of the geometry will be
used as the points of the triangulation.
From the GEOS documentation:
tolerance is the snapping tolerance used to improve the robustness of
the triangulation computation. A tolerance of 0.0 specifies that no
snapping will take place.
If edges is False, a list of Polygons (triangles) will be returned.
Otherwise the list of LineString edges is returned.
"""
collection = shapely.delaunay_triangles(geom, tolerance=tolerance, only_edges=edges)
return list(collection.geoms)
def voronoi_diagram(geom, envelope=None, tolerance=0.0, edges=False):
"""Construct a Voronoi Diagram [1] from the given geometry.
Returns a list of geometries.
Parameters
----------
geom: geometry
the input geometry whose vertices will be used to calculate
the final diagram.
envelope: geometry, None
clipping envelope for the returned diagram, automatically
determined if None. The diagram will be clipped to the larger
of this envelope or an envelope surrounding the sites.
tolerance: float, 0.0
sets the snapping tolerance used to improve the robustness
of the computation. A tolerance of 0.0 specifies that no
snapping will take place.
edges: bool, False
If False, return regions as polygons. Else, return only
edges e.g. LineStrings.
GEOS documentation can be found at [2]
Returns
-------
GeometryCollection
geometries representing the Voronoi regions.
Notes
-----
The tolerance `argument` can be finicky and is known to cause the
algorithm to fail in several cases. If you're using `tolerance`
and getting a failure, try removing it. The test cases in
tests/test_voronoi_diagram.py show more details.
References
----------
[1] https://en.wikipedia.org/wiki/Voronoi_diagram
[2] https://geos.osgeo.org/doxygen/geos__c_8h_source.html (line 730)
"""
try:
result = shapely.voronoi_polygons(
geom, tolerance=tolerance, extend_to=envelope, only_edges=edges
)
except shapely.GEOSException as err:
errstr = "Could not create Voronoi Diagram with the specified inputs "
errstr += f"({err!s})."
if tolerance:
errstr += " Try running again with default tolerance value."
raise ValueError(errstr) from err
if result.geom_type != "GeometryCollection":
return GeometryCollection([result])
return result
def validate(geom):
"""Return True if the geometry is valid."""
return shapely.is_valid_reason(geom)
def transform(func, geom):
"""Apply `func` to all coordinates of `geom`.
Returns a new geometry of the same type from the transformed coordinates.
`func` maps x, y, and optionally z to output xp, yp, zp. The input
parameters may iterable types like lists or arrays or single values.
The output shall be of the same type. Scalars in, scalars out.
Lists in, lists out.
For example, here is an identity function applicable to both types
of input.
def id_func(x, y, z=None):
return tuple(filter(None, [x, y, z]))
g2 = transform(id_func, g1)
Using pyproj >= 2.1, this example will accurately project Shapely geometries:
import pyproj
wgs84 = pyproj.CRS('EPSG:4326')
utm = pyproj.CRS('EPSG:32618')
project = pyproj.Transformer.from_crs(wgs84, utm, always_xy=True).transform
g2 = transform(project, g1)
Note that the always_xy kwarg is required here as Shapely geometries only support
X,Y coordinate ordering.
Lambda expressions such as the one in
g2 = transform(lambda x, y, z=None: (x+1.0, y+1.0), g1)
also satisfy the requirements for `func`.
"""
if geom.is_empty:
return geom
if geom.geom_type in ("Point", "LineString", "LinearRing", "Polygon"):
# First we try to apply func to x, y, z sequences. When func is
# optimized for sequences, this is the fastest, though zipping
# the results up to go back into the geometry constructors adds
# extra cost.
try:
if geom.geom_type in ("Point", "LineString", "LinearRing"):
return type(geom)(zip(*func(*zip(*geom.coords))))
elif geom.geom_type == "Polygon":
shell = type(geom.exterior)(zip(*func(*zip(*geom.exterior.coords))))
holes = [
type(ring)(zip(*func(*zip(*ring.coords))))
for ring in geom.interiors
]
return type(geom)(shell, holes)
# A func that assumes x, y, z are single values will likely raise a
# TypeError, in which case we'll try again.
except TypeError:
if geom.geom_type in ("Point", "LineString", "LinearRing"):
return type(geom)([func(*c) for c in geom.coords])
elif geom.geom_type == "Polygon":
shell = type(geom.exterior)([func(*c) for c in geom.exterior.coords])
holes = [
type(ring)([func(*c) for c in ring.coords])
for ring in geom.interiors
]
return type(geom)(shell, holes)
elif geom.geom_type.startswith("Multi") or geom.geom_type == "GeometryCollection":
return type(geom)([transform(func, part) for part in geom.geoms])
else:
raise GeometryTypeError(f"Type {geom.geom_type!r} not recognized")
def nearest_points(g1, g2):
"""Return the calculated nearest points in the input geometries.
The points are returned in the same order as the input geometries.
"""
seq = shapely.shortest_line(g1, g2)
if seq is None:
if g1.is_empty:
raise ValueError("The first input geometry is empty")
else:
raise ValueError("The second input geometry is empty")
p1 = shapely.get_point(seq, 0)
p2 = shapely.get_point(seq, 1)
return (p1, p2)
def snap(g1, g2, tolerance):
"""Snaps an input geometry (g1) to reference (g2) geometry's vertices.
Parameters
----------
g1 : geometry
The first geometry
g2 : geometry
The second geometry
tolerance : float
The snapping tolerance
Refer to :func:`shapely.snap` for full documentation.
"""
return shapely.snap(g1, g2, tolerance)
def shared_paths(g1, g2):
"""Find paths shared between the two given lineal geometries.
Returns a GeometryCollection with two elements:
- First element is a MultiLineString containing shared paths with the
same direction for both inputs.
- Second element is a MultiLineString containing shared paths with the
opposite direction for the two inputs.
Parameters
----------
g1 : geometry
The first geometry
g2 : geometry
The second geometry
"""
if not isinstance(g1, LineString):
raise GeometryTypeError("First geometry must be a LineString")
if not isinstance(g2, LineString):
raise GeometryTypeError("Second geometry must be a LineString")
return shapely.shared_paths(g1, g2)
class SplitOp:
@staticmethod
def _split_polygon_with_line(poly, splitter):
"""Split a Polygon with a LineString."""
if not isinstance(poly, Polygon):
raise GeometryTypeError("First argument must be a Polygon")
if not isinstance(splitter, (LineString, MultiLineString)):
raise GeometryTypeError("Second argument must be a (Multi)LineString")
union = poly.boundary.union(splitter)
# greatly improves split performance for big geometries with many
# holes (the following contains checks) with minimal overhead
# for common cases
poly = prep(poly)
# some polygonized geometries may be holes, we do not want them
# that's why we test if the original polygon (poly) contains
# an inner point of polygonized geometry (pg)
return [
pg for pg in polygonize(union) if poly.contains(pg.representative_point())
]
@staticmethod
def _split_line_with_line(line, splitter):
"""Split a LineString with another (Multi)LineString or (Multi)Polygon."""
# if splitter is a polygon, pick it's boundary
if splitter.geom_type in ("Polygon", "MultiPolygon"):
splitter = splitter.boundary
if not isinstance(line, LineString):
raise GeometryTypeError("First argument must be a LineString")
if not isinstance(splitter, LineString) and not isinstance(
splitter, MultiLineString
):
raise GeometryTypeError(
"Second argument must be either a LineString or a MultiLineString"
)
# | s\l | Interior | Boundary | Exterior |
# |----------|----------|----------|----------|
# | Interior | 0 or F | * | * | At least one of these two must be 0 # noqa: E501
# | Boundary | 0 or F | * | * | So either '0********' or '[0F]**0*****' # noqa: E501
# | Exterior | * | * | * | No overlapping interiors ('1********') # noqa: E501
relation = splitter.relate(line)
if relation[0] == "1":
# The lines overlap at some segment (linear intersection of interiors)
raise ValueError("Input geometry segment overlaps with the splitter.")
elif relation[0] == "0" or relation[3] == "0":
# The splitter crosses or touches the line's interior
# --> return multilinestring from the split
return line.difference(splitter)
else:
# The splitter does not cross or touch the line's interior
# --> return collection with identity line
return [line]
@staticmethod
def _split_line_with_point(line, splitter):
"""Split a LineString with a Point."""
if not isinstance(line, LineString):
raise GeometryTypeError("First argument must be a LineString")
if not isinstance(splitter, Point):
raise GeometryTypeError("Second argument must be a Point")
# check if point is in the interior of the line
if not line.relate_pattern(splitter, "0********"):
# point not on line interior --> return collection with single identity line
# (REASONING: Returning a list with the input line reference and creating a
# GeometryCollection at the general split function prevents unnecessary
# copying of linestrings in multipoint splitting function)
return [line]
elif line.coords[0] == splitter.coords[0]:
# if line is a closed ring the previous test doesn't behave as desired
return [line]
# point is on line, get the distance from the first point on line
distance_on_line = line.project(splitter)
coords = list(line.coords)
# split the line at the point and create two new lines
current_position = 0.0
for i in range(len(coords) - 1):
point1 = coords[i]
point2 = coords[i + 1]
dx = point1[0] - point2[0]
dy = point1[1] - point2[1]
segment_length = (dx**2 + dy**2) ** 0.5
current_position += segment_length
if distance_on_line == current_position:
# splitter is exactly on a vertex
return [LineString(coords[: i + 2]), LineString(coords[i + 1 :])]
elif distance_on_line < current_position:
# splitter is between two vertices
return [
LineString(coords[: i + 1] + [splitter.coords[0]]),
LineString([splitter.coords[0]] + coords[i + 1 :]),
]
return [line]
@staticmethod
def _split_line_with_multipoint(line, splitter):
"""Split a LineString with a MultiPoint."""
if not isinstance(line, LineString):
raise GeometryTypeError("First argument must be a LineString")
if not isinstance(splitter, MultiPoint):
raise GeometryTypeError("Second argument must be a MultiPoint")
chunks = [line]
for pt in splitter.geoms:
new_chunks = []
for chunk in filter(lambda x: not x.is_empty, chunks):
# add the newly split 2 lines or the same line if not split
new_chunks.extend(SplitOp._split_line_with_point(chunk, pt))
chunks = new_chunks
return chunks
@staticmethod
def split(geom, splitter):
"""Split a geometry by another geometry and return a collection of geometries.
This function is the theoretical opposite of the union of
the split geometry parts. If the splitter does not split the geometry, a
collection with a single geometry equal to the input geometry is
returned.
The function supports:
- Splitting a (Multi)LineString by a (Multi)Point or (Multi)LineString
or (Multi)Polygon
- Splitting a (Multi)Polygon by a LineString
It may be convenient to snap the splitter with low tolerance to the
geometry. For example in the case of splitting a line by a point, the
point must be exactly on the line, for the line to be correctly split.
When splitting a line by a polygon, the boundary of the polygon is used
for the operation. When splitting a line by another line, a ValueError
is raised if the two overlap at some segment.
Parameters
----------
geom : geometry
The geometry to be split
splitter : geometry
The geometry that will split the input geom
Examples
--------
>>> import shapely.ops
>>> from shapely import Point, LineString
>>> pt = Point((1, 1))
>>> line = LineString([(0,0), (2,2)])
>>> result = shapely.ops.split(line, pt)
>>> result.wkt
'GEOMETRYCOLLECTION (LINESTRING (0 0, 1 1), LINESTRING (1 1, 2 2))'
"""
if geom.geom_type in ("MultiLineString", "MultiPolygon"):
return GeometryCollection(
[i for part in geom.geoms for i in SplitOp.split(part, splitter).geoms]
)
elif geom.geom_type == "LineString":
if splitter.geom_type in (
"LineString",
"MultiLineString",
"Polygon",
"MultiPolygon",
):
split_func = SplitOp._split_line_with_line
elif splitter.geom_type == "Point":
split_func = SplitOp._split_line_with_point
elif splitter.geom_type == "MultiPoint":
split_func = SplitOp._split_line_with_multipoint
else:
raise GeometryTypeError(
f"Splitting a LineString with a {splitter.geom_type} is "
"not supported"
)
elif geom.geom_type == "Polygon":
if splitter.geom_type in ("LineString", "MultiLineString"):
split_func = SplitOp._split_polygon_with_line
else:
raise GeometryTypeError(
f"Splitting a Polygon with a {splitter.geom_type} is not supported"
)
else:
raise GeometryTypeError(
f"Splitting {geom.geom_type} geometry is not supported"
)
return GeometryCollection(split_func(geom, splitter))
split = SplitOp.split
def substring(geom, start_dist, end_dist, normalized=False):
"""Return a line segment between specified distances along a LineString.
Negative distance 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 start distance equals the end distance, a Point is returned.
If the start distance is actually beyond the end distance, then the
reversed substring is returned such that the start distance is
at the first coordinate.
Parameters
----------
geom : LineString
The geometry to get a substring of.
start_dist : float
The distance along `geom` of the start of the substring.
end_dist : float
The distance along `geom` of the end of the substring.
normalized : bool, False
Whether the distance parameters are interpreted as a
fraction of the geometry's length.
Returns
-------
Union[Point, LineString]
The substring between `start_dist` and `end_dist` or a Point
if they are at the same location.
Raises
------
TypeError
If `geom` is not a LineString.
Examples
--------
>>> from shapely.geometry import LineString
>>> from shapely.ops import substring
>>> ls = LineString((i, 0) for i in range(6))
>>> ls.wkt
'LINESTRING (0 0, 1 0, 2 0, 3 0, 4 0, 5 0)'
>>> substring(ls, start_dist=1, end_dist=3).wkt
'LINESTRING (1 0, 2 0, 3 0)'
>>> substring(ls, start_dist=3, end_dist=1).wkt
'LINESTRING (3 0, 2 0, 1 0)'
>>> substring(ls, start_dist=1, end_dist=-3).wkt
'LINESTRING (1 0, 2 0)'
>>> substring(ls, start_dist=0.2, end_dist=-0.6, normalized=True).wkt
'LINESTRING (1 0, 2 0)'
Returning a `Point` when `start_dist` and `end_dist` are at the
same location.
>>> substring(ls, 2.5, -2.5).wkt
'POINT (2.5 0)'
"""
if not isinstance(geom, LineString):
raise GeometryTypeError(
"Can only calculate a substring of LineString geometries. "
f"A {geom.geom_type} was provided."
)
# Filter out cases in which to return a point
if start_dist == end_dist:
return geom.interpolate(start_dist, normalized=normalized)
elif not normalized and start_dist >= geom.length and end_dist >= geom.length:
return geom.interpolate(geom.length, normalized=normalized)
elif not normalized and -start_dist >= geom.length and -end_dist >= geom.length:
return geom.interpolate(0, normalized=normalized)
elif normalized and start_dist >= 1 and end_dist >= 1:
return geom.interpolate(1, normalized=normalized)
elif normalized and -start_dist >= 1 and -end_dist >= 1:
return geom.interpolate(0, normalized=normalized)
if normalized:
start_dist *= geom.length
end_dist *= geom.length
# Filter out cases where distances meet at a middle point from opposite ends.
if start_dist < 0 < end_dist and abs(start_dist) + end_dist == geom.length:
return geom.interpolate(end_dist)
elif end_dist < 0 < start_dist and abs(end_dist) + start_dist == geom.length:
return geom.interpolate(start_dist)
start_point = geom.interpolate(start_dist)
end_point = geom.interpolate(end_dist)
if start_dist < 0:
start_dist = geom.length + start_dist # Values may still be negative,
if end_dist < 0: # but only in the out-of-range
end_dist = geom.length + end_dist # sense, not the wrap-around sense.
reverse = start_dist > end_dist
if reverse:
start_dist, end_dist = end_dist, start_dist
start_dist = max(start_dist, 0) # to avoid duplicating the first vertex
if reverse:
vertex_list = [tuple(*end_point.coords)]
else:
vertex_list = [tuple(*start_point.coords)]
coords = list(geom.coords)
current_distance = 0
for p1, p2 in zip(coords, coords[1:]): # noqa
if start_dist < current_distance < end_dist:
vertex_list.append(p1)
elif current_distance >= end_dist:
break
current_distance += ((p2[0] - p1[0]) ** 2 + (p2[1] - p1[1]) ** 2) ** 0.5
if reverse:
vertex_list.append(tuple(*start_point.coords))
# reverse direction result
vertex_list = reversed(vertex_list)
else:
vertex_list.append(tuple(*end_point.coords))
return LineString(vertex_list)
def clip_by_rect(geom, xmin, ymin, xmax, ymax):
"""Return the portion of a geometry within a rectangle.
The geometry is clipped in a fast but possibly dirty way. The output is
not guaranteed to be valid. No exceptions will be raised for topological
errors.
Parameters
----------
geom : geometry
The geometry to be clipped
xmin : float
Minimum x value of the rectangle
ymin : float
Minimum y value of the rectangle
xmax : float
Maximum x value of the rectangle
ymax : float
Maximum y value of the rectangle
Notes
-----
New in 1.7.
"""
if geom.is_empty:
return geom
return shapely.clip_by_rect(geom, xmin, ymin, xmax, ymax)
def orient(geom, sign=1.0):
"""Return a properly oriented copy of the given geometry.
The signed area of the result will have the given sign. A sign of
1.0 means that the coordinates of the product's exterior rings will
be oriented counter-clockwise.
It is recommended to use :func:`shapely.orient_polygons` instead.
Parameters
----------
geom : Geometry
The original geometry. May be a Polygon, MultiPolygon, or
GeometryCollection.
sign : float, optional.
The sign of the result's signed area.
Returns
-------
Geometry
"""
return shapely.orient_polygons(geom, exterior_cw=sign < 0)