"""
Voronoi tesslation of 2-d point sets.
Adapted from https://gist.github.com/pv/8036995
"""
import numpy as np
from scipy.spatial import Voronoi
__author__ = "Serge Rey <sjsrey@gmail.com>"
__all__ = ["voronoi_frames"]
def voronoi(points, radius=None):
"""Determine finite Voronoi diagram for a 2-d point set.
See also ``voronoi_regions()``.
Parameters
----------
points : array_like
An nx2 array of points.
radius : float (optional)
The distance to 'points at infinity'. Default is ``None.``
Returns
-------
vor : tuple
A two-element tuple consisting of a list and an array. Each element of
the list contains the sequence of the indices of Voronoi vertices
composing a Voronoi polygon (region), whereas the array contains
the Voronoi vertex coordinates.
Examples
--------
>>> points = [(10.2, 5.1), (4.7, 2.2), (5.3, 5.7), (2.7, 5.3)]
>>> regions, coordinates = voronoi(points)
>>> regions
[[1, 3, 2], [4, 5, 1, 0], [0, 1, 7, 6], [9, 0, 8]]
>>> coordinates
array([[ 4.21783296, 4.08408578],
[ 7.51956025, 3.51807539],
[ 9.4642193 , 19.3994576 ],
[ 14.98210684, -10.63503022],
[ -9.22691341, -4.58994414],
[ 14.98210684, -10.63503022],
[ 1.78491801, 19.89803294],
[ 9.4642193 , 19.3994576 ],
[ 1.78491801, 19.89803294],
[ -9.22691341, -4.58994414]])
"""
vor = voronoi_regions(Voronoi(points), radius=radius)
return vor
def voronoi_regions(vor, radius=None):
"""Finite voronoi regions for a 2-d point set. See also ``voronoi()``.
Parameters
----------
vor : scipy.spatial.Voronoi
A planar Voronoi diagram.
radius : float (optional)
Distance to 'points at infinity'. Default is ``None.``
Returns
-------
regions_vertices : tuple
A two-element tuple consisting of a list of finite voronoi regions
and an array Voronoi vertex coordinates.
"""
new_regions = []
new_vertices = vor.vertices.tolist()
center = vor.points.mean(axis=0)
if radius is None:
radius = vor.points.ptp().max() * 2
all_ridges = {}
for (p1, p2), (v1, v2) in zip(vor.ridge_points, vor.ridge_vertices):
all_ridges.setdefault(p1, []).append((p2, v1, v2))
all_ridges.setdefault(p2, []).append((p1, v1, v2))
for p1, region in enumerate(vor.point_region):
vertices = vor.regions[region]
if all(v >= 0 for v in vertices):
new_regions.append(vertices)
continue
ridges = all_ridges[p1]
new_region = [v for v in vertices if v >= 0]
for p2, v1, v2 in ridges:
if v2 < 0:
v1, v2 = v2, v1
if v1 >= 0:
continue
t = vor.points[p2] - vor.points[p1]
t /= np.linalg.norm(t)
n = np.array([-t[1], t[0]])
midpoint = vor.points[[p1, p2]].mean(axis=0)
direction = np.sign(np.dot(midpoint - center, n)) * n
far_point = vor.vertices[v2] + direction * radius
new_region.append(len(new_vertices))
new_vertices.append(far_point.tolist())
vs = np.asarray([new_vertices[v] for v in new_region])
c = vs.mean(axis=0)
angles = np.arctan2(vs[:, 1] - c[1], vs[:, 0] - c[0])
new_region = np.array(new_region)[np.argsort(angles)]
new_regions.append(new_region.tolist())
regions_vertices = new_regions, np.asarray(new_vertices)
return regions_vertices
def as_dataframes(regions, vertices, points):
"""Helper function to store finite Voronoi regions and
originator points as ``geopandas`` (or ``pandas``) dataframes.
Parameters
----------
regions : list
Each element of the list contains sequence of the indexes of
voronoi vertices composing a vornoi polygon (region).
vertices : array_like
The coordinates of the vornoi vertices.
points : array_like
The originator points.
Returns
-------
region_df : geopandas.GeoDataFrame
Finite Voronoi polygons as geometries.
points_df : geopandas.GeoDataFrame
Originator points as geometries.
Raises
------
ImportError
Raised when ``geopandas`` is not available.
ImportError
Raised when ``shapely`` is not available.
"""
try:
import geopandas as gpd
except ImportError:
gpd = None
try:
from shapely.geometry import Polygon, Point
except ImportError:
from .shapes import Polygon, Point
if gpd is not None:
region_df = gpd.GeoDataFrame()
region_df["geometry"] = [Polygon(vertices[region]) for region in regions]
point_df = gpd.GeoDataFrame()
point_df["geometry"] = gpd.GeoSeries(Point(pnt) for pnt in points)
else:
import pandas as pd
region_df = pd.DataFrame()
region_df["geometry"] = [
Polygon(vertices[region].tolist()) for region in regions
]
point_df = pd.DataFrame()
point_df["geometry"] = [Point(pnt) for pnt in points]
return region_df, point_df
[docs]def voronoi_frames(points, radius=None, clip="extent"):
"""Composite helper to return Voronoi regions and
generator points as individual dataframes.
Parameters
----------
points : array_like
The originator points.
radius : float
The distance to 'points at infinity' used in building voronoi cells.
Default is ``None``.
clip : {str, shapely.geometry.Polygon}
An overloaded option about how to clip the voronoi cells.
Default is ``'extent'``. Options are as follows.
* ``'none'``/``None`` -- No clip is applied. Voronoi cells may be arbitrarily larger that the source map. Note that this may lead to cells that are many orders of magnitude larger in extent than the original map. Not recommended.
* ``'bbox'``/``'extent'``/``'bounding box'`` -- Clip the voronoi cells to the bounding box of the input points.
* ``'chull``/``'convex hull'`` -- Clip the voronoi cells to the convex hull of the input points.
* ``'ashape'``/``'ahull'`` -- Clip the voronoi cells to the tightest hull that contains all points (e.g. the smallest alphashape, using ``libpysal.cg.alpha_shape_auto``).
* Polygon -- Clip to an arbitrary Polygon.
Returns
-------
reg_vtx : tuple
Two ``geopandas.GeoDataFrame`` (or ``pandas.DataFrame`` if ``geopandas``
is unavailable) objects--``(region_df, points_df)``--of finite
Voronoi polygons and the originator points as geometries.
Notes
-----
If ``geopandas`` is not available the return types will be
``pandas.DataFrame`` objects, each with a geometry column populated
with PySAL shapes. If ``geopandas`` is available, return types are
``pandas.GeoDataFrame`` objects with a geometry column populated
with shapely geometry types.
Examples
--------
>>> points = [(10.2, 5.1), (4.7, 2.2), (5.3, 5.7), (2.7, 5.3)]
>>> regions_df, points_df = voronoi_frames(points)
>>> regions_df.shape
(4, 1)
>>> regions_df.shape == points_df.shape
True
"""
regions, vertices = voronoi(points, radius=radius)
regions, vertices = as_dataframes(regions, vertices, points)
if clip:
regions = clip_voronoi_frames_to_extent(regions, vertices, clip=clip)
reg_vtx = regions, vertices
return reg_vtx
def clip_voronoi_frames_to_extent(regions, vertices, clip="extent"):
"""Generate a geopandas.GeoDataFrame of Voronoi cells clipped to
a specified extent.
Parameters
----------
regions : geopandas.GeoDataFrame
A (geo)dataframe containing voronoi cells to clip.
vertices : geopandas.GeoDataFrame
A (geo)dataframe containing vertices used to build voronoi cells.
clip : str, shapely.geometry.Polygon
An overloaded option about how to clip the voronoi cells.
The options are:
- 'none'/None: No clip is applied. Voronoi cells may be arbitrarily
larger that the source map. Note that this may lead to cells that
are many orders of magnitude larger in extent than
the original map. Not recommended.
- 'bbox'/'extent'/'bounding box': Clip the voronoi cells to the
bounding box of the input points.
- 'chull'/'convex hull': Clip the voronoi cells to the
convex hull of the input points.
- 'ashape'/'ahull': Clip the voronoi cells to the tightest hull that
contains all points (e.g. the smallest alphashape,
using ``libpysal.cg.alpha_shape_auto``).
- Polygon: Clip to an arbitrary Polygon.
Returns
-------
clipped_regions : geopandas.GeoDataFrame
A ``geopandas.GeoDataFrame`` of clipped voronoi regions.
Raises
------
ImportError
Raised when ``shapely`` is not available.
ImportError
Raised when ``geopandas`` is not available.
ValueError
Raised when in invalid value for ``clip`` is passed in.
"""
try:
from shapely.geometry import Polygon
except ImportError:
raise ImportError("Shapely is required to clip voronoi regions.")
try:
import geopandas
except ImportError:
raise ImportError("Geopandas is required to clip voronoi regions.")
if isinstance(clip, Polygon):
clipper = geopandas.GeoDataFrame(geometry=[clip])
elif clip is None:
return regions
elif clip.lower() == "none":
return regions
elif clip.lower() in ("bounds", "bounding box", "bbox", "extent"):
min_x, min_y, max_x, max_y = vertices.total_bounds
bounding_poly = Polygon(
[
(min_x, min_y),
(min_x, max_y),
(max_x, max_y),
(max_x, min_y),
(min_x, min_y),
]
)
clipper = geopandas.GeoDataFrame(geometry=[bounding_poly])
elif clip.lower() in ("chull", "convex hull", "convex_hull"):
clipper = geopandas.GeoDataFrame(
geometry=[vertices.geometry.unary_union.convex_hull]
)
elif clip.lower() in (
"ahull",
"alpha hull",
"alpha_hull",
"ashape",
"alpha shape",
"alpha_shape",
):
from .alpha_shapes import alpha_shape_auto
from ..weights.distance import get_points_array
coordinates = get_points_array(vertices.geometry)
clipper = geopandas.GeoDataFrame(geometry=[alpha_shape_auto(coordinates)])
else:
raise ValueError(
"Clip type '{}' not understood. Try one "
" of the supported options: [None, 'extent', "
"'chull', 'ahull'].".format(clip)
)
clipped_regions = geopandas.overlay(regions, clipper, how="intersection")
return clipped_regions