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import geopandas as gpd
import numpy as np
import shapely
from geopandas import GeoDataFrame, GeoSeries
from libpysal.graph import Graph
from numpy.typing import NDArray
from packaging.version import Version
from pandas import Series
from scipy import sparse
__all__ = [
"orientation",
"shared_walls",
"alignment",
"neighbor_distance",
"mean_interbuilding_distance",
"building_adjacency",
"neighbors",
"street_alignment",
"cell_alignment",
]
GPD_GE_013 = Version(gpd.__version__) >= Version("0.13.0")
def orientation(geometry: GeoDataFrame | GeoSeries) -> Series:
"""Calculate the orientation of objects.
The 'orientation' is defined as the deviation of orientation of the bounding
rectangle from cardinal directions. As such it is within a range 0 - 45. The
orientation of LineStrings is represented by the orientation of the line connecting
the first and the last point of the segment.
Adapted from :cite:`schirmer2015`.
Parameters
----------
geometry : GeoDataFrame | GeoSeries
A GeoDataFrame or GeoSeries containing polygons to analyse.
Returns
-------
Series
Examples
--------
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> momepy.orientation(buildings)
0 41.051468
1 20.829200
2 20.969610
3 20.811525
4 20.412895
...
139 21.107057
140 13.669062
141 13.671217
142 21.463914
143 13.754569
Name: orientation, Length: 144, dtype: float64
"""
geom_types = geometry.geom_type
poly_mask = geom_types.str.contains("Polygon")
line_mask = geom_types.str.contains("Line")
result = np.full(len(geometry), np.nan, dtype=float)
if poly_mask.any():
bboxes = shapely.minimum_rotated_rectangle(geometry.geometry.loc[poly_mask])
coords = shapely.get_coordinates(bboxes)
pt0 = coords[::5]
pt1 = coords[1::5]
angle = np.arctan2(pt1[:, 0] - pt0[:, 0], pt1[:, 1] - pt0[:, 1])
result[poly_mask] = np.degrees(angle)
if line_mask.any():
first = shapely.get_point(geometry.geometry, 0)
last = shapely.get_point(geometry.geometry, -1)
pt0 = shapely.get_coordinates(first)
pt1 = shapely.get_coordinates(last)
angle = np.arctan2(pt1[:, 0] - pt0[:, 0], pt1[:, 1] - pt0[:, 1])
result[line_mask] = np.degrees(angle)
return Series(
np.abs((result + 45) % 90 - 45),
index=geometry.index,
dtype=float,
name="orientation",
)
def shared_walls(
geometry: GeoDataFrame | GeoSeries, strict: bool = True, tolerance: float = 0.01
) -> Series:
"""Calculate the length of shared walls of adjacent elements (typically buildings).
Note that data needs to be topologically correct. Overlapping polygons will lead to
incorrect results.
Adapted from :cite:`hamaina2012a`.
Parameters
----------
geometry : GeoDataFrame | GeoSeries
A GeoDataFrame or GeoSeries containing polygons to analyse.
strict : bool
Perform calculations based on strict contiguity. If set to `False`,
consider overlapping or nearly overlapping polygons as touching.
tolerance: float
Tolerance for non-strict calculations, if strict is True, tolerance
has no effect on the results.
Returns
-------
Series
Examples
--------
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> momepy.shared_walls(buildings)
0 0.000000
1 33.805154
2 39.766297
3 40.604643
4 40.455735
...
139 9.886397
140 0.000000
141 0.000000
142 19.332735
143 10.876113
Name: shared_walls, Length: 144, dtype: float64
"""
predicate = "touches"
if not strict:
orig_lengths = geometry.length
geometry = geometry.buffer(tolerance)
predicate = "intersects"
if GPD_GE_013:
inp, res = geometry.sindex.query(geometry.geometry, predicate=predicate)
else:
inp, res = geometry.sindex.query_bulk(geometry.geometry, predicate=predicate)
mask = inp != res
inp, res = inp[mask], res[mask]
left = geometry.geometry.take(inp).reset_index(drop=True)
right = geometry.geometry.take(res).reset_index(drop=True)
intersections = left.intersection(right).length
walls = intersections.groupby(inp).sum()
walls.index = geometry.index.take(walls.index)
results = Series(0.0, index=geometry.index, name="shared_walls")
results.loc[walls.index] = walls
if not strict:
results = (results / 2) - (2 * tolerance)
results = results.clip(0, orig_lengths)
return results
def alignment(orientation: Series, graph: Graph) -> Series:
"""Calculate the mean deviation of orientation adjacent elements
.. math::
\\frac{1}{n}\\sum_{i=1}^n dev_i=\\frac{dev_1+dev_2+\\cdots+dev_n}{n}
Takes orientation of adjacent elements defined in ``graph`` and calculates the
mean deviation.
Notes
-----
The index of ``orientation`` must match the index along which the ``graph`` is
built.
Parameters
----------
orientation : Series
A series containing orientation (e.g. measured by the :func:`orientation`
function) indexed using the same index that has been used to build the graph.
graph : libpysal.graph.Graph
Graph representing spatial relationships between elements.
Returns
-------
Series
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> orientation = momepy.orientation(buildings)
Define a spatial graph that includes observations within its own neighborhood:
>>> delaunay = graph.Graph.build_triangulation(
... buildings.centroid
... ).assign_self_weight()
>>> delaunay
<Graph of 144 nodes and 970 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Alignment of orienation within triangulated neighbors:
>>> momepy.alignment(orientation, delaunay)
0 14.639585
1 0.217417
2 0.205626
3 0.151730
4 0.352692
...
139 1.970642
140 0.127322
141 0.161906
142 4.350890
143 0.084884
Name: alignment, Length: 144, dtype: float64
"""
orientation_expanded = orientation.loc[graph._adjacency.index.get_level_values(1)]
orientation_expanded.index = graph._adjacency.index.get_level_values(0)
r = (orientation_expanded - orientation).abs().groupby(level=0).mean()
r.name = "alignment"
return r
def neighbor_distance(geometry: GeoDataFrame | GeoSeries, graph: Graph) -> Series:
"""Calculate the mean distance to adjacent elements.
Takes geometry of adjacent elements defined in ``graph`` and calculates the
mean distance.
Notes
-----
The index of ``geometry`` must match the index along which the ``graph`` is
built.
Parameters
----------
geometry : GeoDataFrame | GeoSeries
A GeoDataFrame or GeoSeries containing geometries to analyse.
graph : libpysal.graph.Graph
Graph representing spatial relationships between elements.
Returns
-------
Series
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
Define a spatial graph:
>>> delaunay = graph.Graph.build_triangulation(buildings.centroid)
>>> delaunay
<Graph of 144 nodes and 826 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Mean distance to adjacent buildings within triangulated neighbors:
>>> momepy.neighbor_distance(buildings, delaunay)
0 29.185890
1 30.244905
2 47.052305
3 22.831824
4 16.183615
...
139 39.698734
140 20.634252
141 38.208668
142 6.304569
143 14.551355
Length: 144, dtype: float64
"""
geoms = geometry.geometry.loc[graph._adjacency.index.get_level_values(1)]
geoms.index = graph._adjacency.index.get_level_values(0)
mean_distance = (
(geoms.distance(geometry.geometry, align=True)).groupby(level=0).mean()
)
mean_distance.loc[graph.isolates] = np.nan
return mean_distance
def mean_interbuilding_distance(
geometry: GeoDataFrame | GeoSeries,
adjacency_graph: Graph,
neighborhood_graph: Graph,
) -> Series:
"""Calculate the mean distance between adjacent geometries within a set neighborhood
For each building, this function takes a neighborhood based on the neighbors within
a ``neighborhood_graph`` and calculates the mean distance between adjacent buildings
within this neighborhood where adjacency is captured by ``adjacency_graph``.
Notes
-----
The index of ``geometry`` must match the index along which both of the graphs are
built.
Parameters
----------
geometry : GeoDataFrame | GeoSeries
A GeoDataFrame or GeoSeries containing geometries to analyse.
adjacency_graph : libpysal.graph.Graph
Graph representing the adjacency of geometries. Typically, this is a contiguity
graph derived from tessellation cells linked to buildings.
neighborhood_graph : libpysal.graph.Graph
Graph representing the extent around each geometry within which to calculate
the mean interbuilding distance. This can be a distance based graph, KNN graph,
higher order contiguity, etc.
Returns
-------
Series
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
Define a spatial graph denoting building adjacency:
>>> delaunay = graph.Graph.build_triangulation(buildings.centroid)
>>> delaunay
<Graph of 144 nodes and 826 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Define a spatial graph denoting the neighborhood:
>>> knn15 = graph.Graph.build_knn(buildings.centroid, k=15)
>>> knn15
<Graph of 144 nodes and 2160 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Measure mean interbuilding distance:
>>> momepy.mean_interbuilding_distance(buildings, delaunay, knn15)
0 29.516506
1 18.673132
2 23.277728
3 25.409034
4 18.454463
...
139 21.642580
140 16.427126
141 17.792155
142 10.844367
143 14.896066
Name: mean_interbuilding_distance, Length: 144, dtype: float64
"""
distance = Series(
shapely.distance(
geometry.geometry.loc[
adjacency_graph._adjacency.index.get_level_values(0)
].values,
geometry.geometry.loc[
adjacency_graph._adjacency.index.get_level_values(1)
].values,
),
index=adjacency_graph._adjacency.index,
name="distance",
)
distance_matrix = (
distance.astype("Sparse[float]").sparse.to_coo(sort_labels=True)[0].tocsr()
)
neighborhood_matrix = sparse.coo_matrix(neighborhood_graph.sparse).tocsr()
mean_distances = np.zeros(distance_matrix.shape[0], dtype=float)
for i in range(distance_matrix.shape[0]):
neighborhood_indices = np.append(neighborhood_matrix[i].indices, i)
sub_matrix = distance_matrix[neighborhood_indices][:, neighborhood_indices]
mean_distances[i] = sub_matrix.sum() / sub_matrix.nnz
return Series(
mean_distances, index=geometry.index, name="mean_interbuilding_distance"
)
def building_adjacency(
contiguity_graph: Graph,
neighborhood_graph: Graph,
) -> Series:
"""Calculate the level of building adjacency.
Building adjacency reflects how much buildings tend to join together into larger
structures. It is calculated as a ratio of joined built-up structures captured by
``contiguity_graph`` and buildings within the neighborhood defined in
``neighborhood_graph``.
Adapted from :cite:`vanderhaegen2017`.
Notes
-----
Both graphs must be built on the same index.
Parameters
----------
contiguity_graph : libpysal.graph.Graph
Graph representing contiguity between geometries, typically a rook contiguity
graph derived from buildings.
neighborhood_graph : libpysal.graph.Graph
Graph representing the extent around each geometry within which to calculate
the level of building adjacency. This can be a distance based graph, KNN graph,
higher order contiguity, etc.
Returns
-------
Series
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
Define a spatial graph denoting building contiguity:
>>> contig = graph.Graph.build_contiguity(buildings)
>>> contig
<Graph of 144 nodes and 248 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Define a spatial graph denoting the neighborhood:
>>> knn15 = graph.Graph.build_knn(buildings.centroid, k=15)
>>> knn15
<Graph of 144 nodes and 2160 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Measure mean interbuilding distance:
>>> momepy.building_adjacency(contig, knn15)
0 0.6875
1 0.1875
2 0.1875
3 0.2500
4 0.1875
...
139 0.4375
140 0.1875
141 0.1875
142 0.1875
143 0.2500
Name: building_adjacency, Length: 144, dtype: float64
"""
components = contiguity_graph.component_labels
# check if self-weights are present, otherwise assign them to treat self as part of
# the neighborhood
has_self_weights = (
neighborhood_graph._adjacency.index.get_level_values("focal")
== neighborhood_graph._adjacency.index.get_level_values("neighbor")
).sum() == neighborhood_graph.n
if not has_self_weights:
neighborhood_graph = neighborhood_graph.assign_self_weight()
grouper = components.loc[
neighborhood_graph._adjacency.index.get_level_values(1)
].groupby(neighborhood_graph._adjacency.index.get_level_values(0))
result = grouper.agg("nunique") / grouper.agg("count")
result.name = "building_adjacency"
result.index.name = None
return result
def neighbors(
geometry: GeoDataFrame | GeoSeries, graph: Graph, weighted=False
) -> Series:
"""Calculate the number of neighbours captured by ``graph``.
If ``weighted=True``, the number of neighbours will be divided by the perimeter of
the object to return a relative value (neighbors per meter).
Adapted from :cite:`hermosilla2012`.
Notes
-----
The index of ``geometry`` must match the index along which the ``graph`` is
built.
Parameters
----------
gdf : GeoDataFrame | GeoSeries
GeoDataFrame containing geometries to analyse.
graph : libpysal.graph.Graph
Graph representing spatial relationships between elements.
weighted : bool
If True, the number of neighbours will be divided by the perimeter of the object
to return a relative value (neighbors per meter).
Returns
-------
Series
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> tessellation = momepy.morphological_tessellation(buildings)
Define a spatial graph denoting adjacency:
>>> contig = graph.Graph.build_contiguity(tessellation)
>>> contig
<Graph of 144 nodes and 768 nonzero edges indexed by
[0, 1, 2, 3, 4, ...]>
Number of neighbors of each tessellation cell:
>>> momepy.neighbors(tessellation, contig)
focal
0 4
1 9
2 3
3 3
4 7
..
139 3
140 6
141 12
142 2
143 5
Name: neighbors, Length: 144, dtype: int64
Weighted by the tessellation area:
>>> momepy.neighbors(tessellation, contig, weighted=True)
focal
0 0.012732
1 0.010116
2 0.013350
3 0.010172
4 0.038916
...
139 0.020037
140 0.036766
141 0.045287
142 0.044147
143 0.051799
Name: neighbors, Length: 144, dtype: float64
"""
if weighted:
r = graph.cardinalities / geometry.length
else:
r = graph.cardinalities
r.name = "neighbors"
return r
def street_alignment(
building_orientation: Series,
street_orientation: Series,
street_index: Series,
) -> Series:
"""Calulate the deviation of the building orientation from the street orientation.
Parameters
----------
building_orientation : Series
Series with the orientation of buildings. Can be measured using
:func:`orientation`.
street_orientation : Series
Series with the orientation of streets. Can be measured using
:func:`orientation`.
street_index : Series
Series with the index of the street to which the building belongs. Can be
retrieved using :func:`momepy.get_nearest_street`.
Returns
-------
Series
Examples
--------
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> streets = geopandas.read_file(path, layer="streets")
Get street index.
>>> buildings["street_index"] = momepy.get_nearest_street(buildings, streets)
>>> buildings.head()
uID geometry street_index
0 1 POLYGON ((1603599.221 6464369.816, 1603602.984... 0.0
1 2 POLYGON ((1603042.88 6464261.498, 1603038.961 ... 33.0
2 3 POLYGON ((1603044.65 6464178.035, 1603049.192 ... 10.0
3 4 POLYGON ((1603036.557 6464141.467, 1603036.969... 8.0
4 5 POLYGON ((1603082.387 6464142.022, 1603081.574... 8.0
Compute orientations.
>>> blg_orient = momepy.orientation(buildings)
>>> str_orient = momepy.orientation(streets)
Compute street alignment.
>>> momepy.street_alignment(blg_orient, str_orient, buildings["street_index"])
0 0.290739
1 4.542071
2 0.105745
3 0.424903
4 0.823533
...
139 1.779876
140 0.109254
141 0.466453
142 1.223387
143 0.455081
Name: street_alignment, Length: 144, dtype: float64
"""
r = (building_orientation - street_orientation.loc[street_index].values).abs()
r.name = "street_alignment"
return r
def cell_alignment(
left_orientation: NDArray[np.float64] | Series,
right_orientation: NDArray[np.float64] | Series,
) -> Series:
"""
Calculate the difference between cell orientation and the orientation of object.
.. math::
\\left|{\\textit{building orientation} - \\textit{cell orientation}}\\right|
Notes
-----
``left_orientation`` and ``right_orientation`` must be aligned or have an index.
Parameters
----------
left_orientation : np.array, pd.Series
The ``np.array``, or `pd.Series`` with orientation of cells.
This can be calculated using :func:`orientation`.
right_orientation : np.array, pd.Series
The ``np.array`` or ``pd.Series`` with orientation of objects.
This can be calculated using :func:`orientation`.
Returns
-------
Series
Examples
--------
>>> from libpysal import graph
>>> path = momepy.datasets.get_path("bubenec")
>>> buildings = geopandas.read_file(path, layer="buildings")
>>> tessellation = momepy.morphological_tessellation(buildings)
Measure orientations:
>>> blg_orient = momepy.orientation(buildings)
>>> tess_orient = momepy.orientation(tessellation)
Compute alignment:
>>> momepy.cell_alignment(blg_orient, tess_orient)
0 0.854788
1 20.829200
2 5.552120
3 4.052674
4 0.159289
...
139 0.189750
140 17.920139
141 0.393708
142 0.024618
143 0.252122
Name: orientation, Length: 144, dtype: float64
"""
if not isinstance(left_orientation, Series):
left_orientation = Series(left_orientation)
if not isinstance(right_orientation, Series):
right_orientation = Series(right_orientation)
return (left_orientation - right_orientation).abs()
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