Fortune's algorithm for Voronoi diagrams.
Foronoi is a Python implementation of the Fortune’s algorithm based on the description of “Computational Geometry: Algorithms and Applications” by de Berg et al.
This algorithm is a sweep line algorithm that scans top down over the cell points and traces out the lines via breakpoints in between parabola’s (arcs). When lines converge, a circle event happens which inserts a new vertex.
Documentation can be found here.
pip install foronoiFirst, clone the repository and then install the package.
git clone https://github.com/Yatoom/foronoi.git
cd foronoi
python setup.py installNote: you need to use sudo python3 setup.py install on most Linux distributions.
Example that uses a polygon as a bounding box.
from foronoi import Voronoi, Polygon, Visualizer, VoronoiObserver
# Define some points (a.k.a sites or cell points)
points = [
(2.5, 2.5),
(4, 7.5),
(7.5, 2.5),
(6, 7.5),
(4, 4),
(3, 3),
(6, 3),
]
# Define a bounding box / polygon
polygon = Polygon([
(2.5, 10),
(5, 10),
(10, 5),
(10, 2.5),
(5, 0),
(2.5, 0),
(0, 2.5),
(0, 5),
])
# Initialize the algorithm
v = Voronoi(polygon)
# Attach a Voronoi Observer that monitors and visualizes the construction of
# the Voronoi Diagram step-by-step. See for more information
# examples/quickstart.py or examples/observers.py.
v.attach_observer(VoronoiObserver())
# Create the diagram
v.create_diagram(points=points)
# Get properties. See more examples in examples/quickstart.py
edges = v.edges
vertices = v.vertices
arcs = v.arcs
points = v.points
# Plotting
# Note: plot_border_to_site() indicates with dashed line to which site a border
# belongs. The site's first edge is colored green.
Visualizer(v, canvas_offset=1)\
.plot_sites(show_labels=True)\
.plot_edges(show_labels=False)\
.plot_vertices()\
.plot_border_to_site()\
.show()
for point in v.sites:
print(f"{point.xy} \t {point.area()}")Output:
(2.5, 2.5) 11.529761904761905
(4, 7.5) 15.064062500000006
(7.5, 2.5) 11.75
(6, 7.5) 10.520833333333329
(4, 4) 7.640625
(3, 3) 5.946354166666666
(6, 3) 9.423363095238095
More examples can be found in the examples/ folder.
vertices = v.sites[0].get_vertices()
coords = [(vertex.x, vertex.y) for vertex in vertices]
print(coords)Output:
[(0.167, 5.333), (4.5, 1.0), (4.643, 0.0), (2.5, 0), (0, 2.5), (0, 5)]To run unit tests, run the following comand.
python3 -m "nose" foronoi/tests/unit.py
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