pyvoronoi

A wrapper for Boost's Voronoi diagram library. The full documentation of the Boost Voronoi API is available here.

Install

The installation have been tested on Windows and Linux Ubuntu. If you notice any issue on Mac, reach out to us, we are interested in making sure it works for you.

Windows users will need Microsoft Visual C++ installed on their machine. You can find information about the version needed on this link. Python version from 3.5 to 3.12 rely on Visual C++ 14.x.

Dependencies

Cython dependency is optional. Cpp sources generated with Cython are available in releases.

Note on using the setup.py:

setup.py operates in 2 modes that are based on the presence of the dev file in the root of the project.

• When dev is present, Cython will be used to compile the .pyx sources. This is the development mode (as you get it in the git repository).

• When dev is absent, C/C++ compiler will be used to compile the .cpp sources (that were prepared in in the development mode). This is the distribution mode (as you get it on PyPI).

This way the package can be used without or with an incompatible version of Cython.

The idea comes from Matt Shannon's bandmat library.

From PyPI

Cython not required.

pip install pyvoronoi

From source

Cython required.

Clone the repository:

git clone https://github.com/fabanc/pyvoronoi.git

Install:

python setup.py install

After every modification of .pyx files compile with Cython:

python setup.py build_ext --inplace

Note in order to build the wheels, you will need to also install wheel

pip install wheel

Using

Create a new instance, passing the scaling factor into the constructor:

import pyvoronoi
pv = pyvoronoi.Pyvoronoi(10)

Since the voronoi library uses integer representation for points, the scaling factor chosen must be high enough to avoid roundoff error when converting from point coordinates to integers.

Add points and segments:

pv.AddPoint([0, 0])
pv.AddSegment([[1,5],[2,2]])

Call Construct() and get the edges and vertices:

pv.Construct()
edges = pv.GetEdges()
vertices = pv.GetVertices()
cells = pv.GetCells()

Note that vertices, edges, and cells, can be accessed individually. The methods above are just convenience wrappers around the following functions:

• GetVertex

• GetEdge

• Get Cell

def GetVertices(self):
    count = self.CountVertices()
    output = []
    for index in  range(count):
        output.append(self.GetVertex(index))
    return output

def GetEdges(self):
    count = self.CountEdges()
    output = []
    for index in range(count):
        output.append(self.GetEdge(index))
    return output

def GetCells(self):
    count = self.CountCells()
    output = []
    for index in range(count):
        output.append(self.GetCell(index))
    return output

If you are running python 2.x, you might want to write your own wrappers using xrange. This will be more efficient.

Edges have the following properties:

• start, end contain the indices of the start and end vertices or -1 if the edge is infinite at that end.
• is_primary is true if the edge is not coincident with any of the source inputs.
• is_linear is true if the edge is linear (not curved).
• cell is the identifier of the cell this segment is part of.
• twin is the identifier of the twin segment as defined in the boost voronoi API.

Cells have the following properties:

• cell_identifier is the index of the cell.
• site is the index of the site which generated this cell (same as site1, site2 on the edges).
• contains_point is true if the site was generated by a point.
• contains_segment is true if the site was generated by a segment.
• is_open is true if any of the cell's edges is infinite.
• is_degenerate is true if the cell doesn't have an incident edge. Can happen if a few input segments share a common endpoint.
• vertices contains indices into the vertex array.
• edges contains indices into the edge array.

pv = pyvoronoi.Pyvoronoi(100)
pv.AddSegment([[0.1,0.8],[0.3,0.6]])
pv.AddSegment([[0.3,0.6],[0.4,0.6]])
pv.AddSegment([[0.4,0.6],[0.4,0.5]])
pv.AddSegment([[0.4,0.6],[0.4,0.7]])
pv.AddSegment([[0.4,0.7],[0.5,0.8]])
pv.AddSegment([[0.4,0.7],[0.5,0.6]])
pv.AddSegment([[0.5,0.6],[0.7,0.7]])

pv.Construct()
edges = pv.GetEdges()
vertices = pv.GetVertices()
cells = pv.GetCells()
print("Cell Count: {0}".format(len(cells)))
for c in cells:
    print("Cell contains point: {0}. Contains segment: {1}. Is open: {2}, Site Index: {3}".format(c.contains_point, c.contains_segment, c.is_open, c.site))
    print(",".join(map(str,c.vertices)))
    for sIndex in c.edges:
        print("Start Index: {0}, End Index = {1}".format(edges[sIndex].start, edges[sIndex].end))

Some output edges returned by the boost voronoi API are suposed to be curved. In the C++ API, it is up to you to code it. Luckily, you can do it in python using the following the function DiscretizeCurvedEdge. The sample below shows you how to do that:

for cIndex in range(len(cells)):
    cell = cells[cIndex]
    if cell.is_open == False:
        for i in range(len(cell.edges)):
            e = edges[cell.edges[i]]
            startVertex = vertices[e.start]
            endVertex = vertices[e.end]

            max_distance  = distance([startVertex.X, startVertex.Y], [endVertex.X, endVertex.Y]) / 10
            if startVertex != -1 and endVertex != -1:
                if(e.is_linear == True):
                    array = [[startVertex.X, startVertex.Y],[endVertex.X, endVertex.Y]]
                else:
                    points = pv.DiscretizeCurvedEdge(i, max_distance)
                    for p in points:
                        print "{0},{1}".format(p[0], p[1])

The curve interpolation code can return 2 exceptions.

• FocusOnDirectixException: this happens when the input point is on the segment side. In that cases, it makes no sense to interpolate a parabola between those two geometries since a parabola equation is supposed to find an equidistant point between the two geometries.

• UnsolvableParabolaEquation: there are cases where the point returned by boost does not fit with the parabola equation (for a same position on the x-axis, we get 2 different points, both equidistant). Understanding this issue is still under investigation. It is possible to mitigate this issue by setting an optional 3rd parameter of the function DiscretizeCurvedEdge). A higher value means more tolerance to this exception. The recommended value would be 1 / Scaling Factor.

License

• Pyvoronoi is available under MIT license <http://opensource.org/licenses/MIT>__.
• The core Voronoi library is available under Boost Software License <http://www.boost.org/LICENSE_1_0.txt>__. Freeware for both open source and commercial applications.

Development

Build tools

This project uses cibuildwheel to build wheels on multiple platforms.