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Circle packing algorithm for Python

Project description

PyPi version Python compatibility Build Status Coverage Codacy


Pure Python implementation of circle packing layout algorithm.

Circles are first arranged via a version of A1.0 by Huang et al (see for details) and then enclosed in a circle created around them using Matoušek-Sharir-Welzl algorithm used in d3js (see,, and


Using pip:

pip install circlify

or using the source:

git clone git://
cd circlify
python install

The last step may require sudo if you don’t have root access.


The main function circlify is supported by a small data class circlify.Circle and takes 3 parameters:

  • A list of positive values sorted from largest to smallest.
  • (optional) A target enclosure where the packed circles should fit. It defaults to the unit circle (0, 0, 1).
  • (optional) A boolean indicating if the target enclosure should be appended to the output.

The function returns a list of circlify.Circle objects, each one corresponding to the coordinates and radius of cirlces proportional to the corresponding input value.


import circlify as circ

data = [19, 17, 13, 11, 7, 5, 3, 2, 1]
circles = circ.circlify(data, with_enclosure=True)

The variable circles contains (level 0 is the enclosure):

    circ.Circle(x=0.0, y=0.0, r=1.0, level=0),
    circ.Circle(x=0.09222041925800777, y=0.8617116738294696,
    circ.Circle(x=-0.40283175658099674, y=0.7512387781681531,
    circ.Circle(x=0.3252787490004198, y=0.7776370388468007,
    circ.Circle(x=0.48296614887228806, y=0.4541723195782383,
    circ.Circle(x=-0.6132109517981927, y=0.4490810687795324,
    circ.Circle(x=-0.045884607890591435, y=-0.6977206243364218,
    circ.Circle(x=-0.04661299415374866, y=0.4678014425767657,
    circ.Circle(x=-0.411432317820337, y=-0.13064957525245907,
    circ.Circle(x=0.35776879346704843, y=-0.13064957525245907,

A simple matplotlib representation. See circlify.bubbles helper function (requires matplotlib):

visualization of circlify circle packing of first 9 prime numbers.

Starting with version 0.10, circlify also handle hierarchical input so that:

import circlify as circ

data = [0.05, {'id': 'a2', 'datum': 0.05},
        {'id': 'a0', 'datum': 0.8, 'children': [0.3, 0.2, 0.2, 0.1], },
        {'id': 'a1', 'datum': 0.1, 'children':
          [ {'id': 'a1_1', 'datum': 0.05}, {'datum': 0.04}, 0.01],},
circles = circ.circlify(data, with_enclosure=True)


    circ.Circle(level=0, r=1.0),
    circ.Circle(x=-0.565803075997749, y=0.41097786651145324,
    circ.Circle(x=-0.3385727489559141, y=0.7022188441650276,
                r=0.18469903125906464, ex={'id': 'a2', 'datum': 0.05}),
    circ.Circle(x=-0.7387961250362587, r=0.2612038749637415,
                ex={'id': 'a1', 'datum': 0.1,
                    'children': [{'id': 'a1_1', 'datum': 0.05},
                                 {'datum': 0.04},
                                 {'id': 'a1_2', 'datum': 0.01}]}),
    circ.Circle(x=0.2612038749637414, r=0.7387961250362586,
                ex={'id': 'a0', 'datum': 0.8,
                    'children': [0.3, 0.2, 0.2, 0.1]}),
    circ.Circle(level=2, x=-0.7567888163564136,
                y=0.14087823651338607, r=0.0616618704777984,
                ex={'id': 'a1_2', 'datum': 0.01}),
    circ.Circle(level=2, x=-0.8766762590444033, y=0.0,
                ex={'datum': 0.04}),
    circ.Circle(level=2, ex={'id': 'a1_1', 'datum': 0.05},
                x=-0.6154723840806618, y=0.0, r=0.13788013400814464),
    circ.Circle(level=2, x=0.6664952237042423,
                y=0.3369290873460549, r=0.2117455702848763),
    circ.Circle(level=2, x=-0.11288314691830154,
                y=-0.230392881357073, r=0.2994534572692975),
    circ.Circle(level=2, x=0.15631936804871832,
                y=0.30460197676548245, r=0.2994534572692975),
    circ.Circle(level=2, x=0.5533243963620484,
                y=-0.230392881357073, r=0.36675408601105247),

A simple matplotlib representation. See circlify.bubbles helper function (requires matplotlib):

visualization of circlify nested circle packing for a hierarchical input.

Note that the area of the circles are proportional to the values passed in input only if the circles are at the same hierarchical level. For instance: circles a1_1 and a2 both have a value of 0.05, yet a1_1 is smaller than a2 because a1_1 is fitted within its parent circle a1 one level below the level of a2. In other words, the level 1 circles a1 and a2 are both proportional to their respective values but a1_1 is proportional to the values on level 2 witin a1.

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