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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 with a euristic inspired by the A1.0 of [Huang-2006], then enclosed in a circle created around them using [MSW-1996] algorithm used in [Bostock-2017]. I hope to implement A1.5 at some point in the future but the results are good enough for my use case.


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 whose area is proportional to the corresponding input value.


>>> from pprint import pprint as pp
>>> import circlify as circ
>>> circles = circ.circlify([19, 17, 13, 11, 7, 5, 3, 2, 1], show_enclosure=True)
>>> pp(circles)
[Circle(x=0.0, y=0.0, r=1.0, level=0, ex=None),
 Circle(x=-0.633232604611031, y=-0.47732413442115296, r=0.09460444572843042, level=1, ex={'datum': 1}),
 Circle(x=-0.7720311587589236, y=0.19946176418549022, r=0.13379089020993573, level=1, ex={'datum': 2}),
 Circle(x=-0.43168871955473165, y=-0.6391381648617572, r=0.16385970662353394, level=1, ex={'datum': 3}),
 Circle(x=0.595447603036083, y=0.5168251295666467, r=0.21154197162246005, level=1, ex={'datum': 5}),
 Circle(x=-0.5480911056188739, y=0.5115139053491098, r=0.2502998363185337, level=1, ex={'datum': 7}),
 Circle(x=0.043747233552068686, y=-0.6848366902134195, r=0.31376744998074435, level=1, ex={'datum': 11}),
 Circle(x=0.04298737651230445, y=0.5310431146935967, r=0.34110117996070605, level=1, ex={'datum': 13}),
 Circle(x=-0.3375943908160698, y=-0.09326467617622711, r=0.39006412239133215, level=1, ex={'datum': 17}),
 Circle(x=0.46484095011516874, y=-0.09326467617622711, r=0.4123712185399064, level=1, ex={'datum': 19})]

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:

>>> from pprint import pprint as pp
>>> 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, show_enclosure=True)
>>> pp(circles)
[Circle(x=0.0, y=0.0, r=1.0, level=0, ex=None),
 Circle(x=-0.5658030759977484, y=0.4109778665114514, r=0.18469903125906464, level=1, ex={'datum': 0.05}),
 Circle(x=-0.5658030759977484, y=-0.4109778665114514, r=0.18469903125906464, level=1, ex={'id': 'a2', 'datum': 0.05}),
 Circle(x=-0.7387961250362587, y=0.0, r=0.2612038749637415, level=1, ex={'id': 'a1', 'datum': 0.1, 'children': [{'id': 'a1_1', 'datum': 0.05}, {'datum': 0.04}, 0.01]}),
 Circle(x=0.2612038749637414, y=0.0, r=0.7387961250362586, level=1, ex={'id': 'a0', 'datum': 0.8, 'children': [0.3, 0.2, 0.2, 0.1]}),
 Circle(x=-0.7567888163564135, y=0.1408782365133844, r=0.0616618704777984, level=2, ex={'datum': 0.01}),
 Circle(x=-0.8766762590444033, y=0.0, r=0.1233237409555968, level=2, ex={'datum': 0.04}),
 Circle(x=-0.6154723840806618, y=0.0, r=0.13788013400814464, level=2, ex={'id': 'a1_1', 'datum': 0.05}),
 Circle(x=0.6664952237042414, y=0.33692908734605553, r=0.21174557028487648, level=2, ex={'datum': 0.1}),
 Circle(x=-0.1128831469183017, y=-0.23039288135707192, r=0.29945345726929773, level=2, ex={'datum': 0.2}),
 Circle(x=0.1563193680487183, y=0.304601976765483, r=0.29945345726929773, level=2, ex={'datum': 0.2}),
 Circle(x=0.5533243963620487, y=-0.23039288135707192, r=0.3667540860110527, level=2, ex={'datum': 0.3})]

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.

[Huang-2006]WenQi HUANG, Yu LI, ChuMin LI, RuChu XU, New Heuristics for Packing Unequal Circles into a Circular Container,
[Bostock-2017]Mike Bostock, D3.js,,
  1. Matoušek, M. Sharir, and E. Welzl. A Subexponential Bound For Linear Programming. Algorithmica, 16(4/5):498–516, October/November 1996,

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