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polylabel.py
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polylabel.py
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"""Provides functions for finding the pole of inaccessibility for a given polygon."""
from heapq import heappop, heappush
from shapely.errors import TopologicalError
from shapely.geometry import Point
class Cell:
"""A `Cell`'s centroid is a potential solution to find the pole of inaccessibility.
Rich comparison operators are used for sorting `Cell` objects in a priority
queue based on the potential maximum distance of any theoretical point
within a cell to a given polygon's exterior boundary.
"""
def __init__(self, x, y, h, polygon):
"""Initialize a Cell object.
Parameters
----------
x, y : float
The x- and y-coordinates of the cell centroid.
h : float
Half of the cell size.
polygon : shapely.geometry.Polygon
The polygon associated with the cell.
"""
self.x = x
self.y = y
self.h = h # half of cell size
self.centroid = Point(x, y) # cell centroid, potential solution
# distance from cell centroid to polygon exterior
self.distance = self._dist(polygon)
# max distance to polygon exterior within a cell
self.max_distance = self.distance + h * 1.4142135623730951 # sqrt(2)
# rich comparison operators for sorting in minimum priority queue
def __lt__(self, other):
"""Compare Cell objects based on their maximum distance."""
return self.max_distance > other.max_distance
def __le__(self, other):
"""Compare Cell objects based on their maximum distance."""
return self.max_distance >= other.max_distance
def __eq__(self, other):
"""Compare Cell objects based on their maximum distance."""
return self.max_distance == other.max_distance
def __ne__(self, other):
"""Compare Cell objects based on their maximum distance."""
return self.max_distance != other.max_distance
def __gt__(self, other):
"""Compare Cell objects based on their maximum distance."""
return self.max_distance < other.max_distance
def __ge__(self, other):
"""Compare Cell objects based on their maximum distance."""
return self.max_distance <= other.max_distance
def _dist(self, polygon):
"""Signed distance from Cell centroid to polygon outline.
The returned value is negative if the point is outside of the polygon
exterior boundary.
"""
inside = polygon.contains(self.centroid)
distance = self.centroid.distance(polygon.exterior)
for interior in polygon.interiors:
distance = min(distance, self.centroid.distance(interior))
if inside:
return distance
return -distance
def polylabel(polygon, tolerance=1.0):
"""Find pole of inaccessibility for a given polygon.
Based on Vladimir Agafonkin's https://github.com/mapbox/polylabel
Parameters
----------
polygon : shapely.geometry.Polygon
Polygon for which to find the pole of inaccessibility.
tolerance : int or float, optional
`tolerance` represents the highest resolution in units of the
input geometry that will be considered for a solution. (default
value is 1.0).
Returns
-------
shapely.geometry.Point
A point representing the pole of inaccessibility for the given input
polygon.
Raises
------
shapely.errors.TopologicalError
If the input polygon is not a valid geometry.
Example
-------
>>> from shapely import LineString
>>> polygon = LineString([(0, 0), (50, 200), (100, 100), (20, 50),
... (-100, -20), (-150, -200)]).buffer(100)
>>> polylabel(polygon, tolerance=10).wkt
'POINT (59.35615556364569 121.83919629746435)'
"""
if not polygon.is_valid:
raise TopologicalError("Invalid polygon")
minx, miny, maxx, maxy = polygon.bounds
width = maxx - minx
height = maxy - miny
cell_size = min(width, height)
h = cell_size / 2.0
cell_queue = []
# First best cell approximation is one constructed from the centroid
# of the polygon
x, y = polygon.centroid.coords[0]
best_cell = Cell(x, y, 0, polygon)
# Special case for rectangular polygons avoiding floating point error
bbox_cell = Cell(minx + width / 2.0, miny + height / 2, 0, polygon)
if bbox_cell.distance > best_cell.distance:
best_cell = bbox_cell
# build a regular square grid covering the polygon
x = minx
while x < maxx:
y = miny
while y < maxy:
heappush(cell_queue, Cell(x + h, y + h, h, polygon))
y += cell_size
x += cell_size
# minimum priority queue
while cell_queue:
cell = heappop(cell_queue)
# update the best cell if we find a better one
if cell.distance > best_cell.distance:
best_cell = cell
# continue to the next iteration if we can't find a better solution
# based on tolerance
if cell.max_distance - best_cell.distance <= tolerance:
continue
# split the cell into quadrants
h = cell.h / 2.0
heappush(cell_queue, Cell(cell.x - h, cell.y - h, h, polygon))
heappush(cell_queue, Cell(cell.x + h, cell.y - h, h, polygon))
heappush(cell_queue, Cell(cell.x - h, cell.y + h, h, polygon))
heappush(cell_queue, Cell(cell.x + h, cell.y + h, h, polygon))
return best_cell.centroid