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Recreational Ruby tools for geometry. This ranges from simple functions like area calculation and line intersection, to Delaunay triangulation and Voronoi partitions. This is companion code to my educational video series about code and sound, and this code was featured in a video about Voronoi diagrams and Delaunay triangulations. I've also written more about this code on my blog.

XRES=960 YRES=540 bin/voronoi_transitions.rb /tmp/polygon.gif \
    test_data/3gon.yml 30 60 \
    test_data/square.yml 30 60 \
    test_data/pentagon.json 30 60 \
    test_data/zero.csv 30 0

Animation of Voronoi transitions

You might also be interested in mb-sound, mb-math, and mb-util.

This code is reasonably well-tested, but I recommend using it for non-critical tasks like fun and offline graphics, and not for making important decisions or mission-critical data modeling.


Check out all of the scripts in bin/; they usually have a header comment describing what they do.

Video or GIF of Voronoi transitions

The bin/voronoi_transitions.rb script will turn a sequence of Voronoi diagrams into an animation with smooth transitions.

See the documentation for MB::Geometry::Generators.generate in lib/mb/geometry/generators.rb for the syntax of the Voronoi diagram file format (.json, .yml, or .csv), with examples in test_data/. Also check out the MB::Geometry::VoronoiAnimator class.

Shuffling points

XRES=640 RANDOM_SEED=10 bin/voronoi_transitions.rb /tmp/shuffle.gif \
    test_data/lines.json 0 \
    __shuffle 60

Shuffling Voronoi points

60fps video transitions

XRES=960 YRES=540 bin/voronoi_transitions.rb /tmp/polygon.mp4 \
    test_data/3gon.yml 30 15 \
    test_data/square.yml 30 15 \
    test_data/pentagon.json 30 15 \
    test_data/zero.csv 30 0

Output of the voronoi_transitions.rb command


Static SVG image from Voronoi diagram

From the shell:

bin/voronoi_to_svg.rb test_data/pentagon.json /tmp/pentagon.svg

From code:

require 'mb-geometry'

# The Hash must be inside an Array to prevent it being interpreted as keyword args
# Rotation is in degrees
v =[{ generator: :polygon, sides: 5, rotate: 30 }]) ; nil

# You can save the Delaunay triangulation instead:

Voronoi diagram from image

You can generate a JSON points file for a Voronoi diagram from a PNG (or other) image, then generate a pixel-art SVG from that (16x16 or smaller images recommended):

bin/png_to_voronoi.rb image.png image.json
bin/voronoi_to_svg.rb image.json image.svg
Input Output
Smiley SVG Pixel Art Smiley

Voronoi points file format

The bin/triangulate.rb, bin/voronoi_to_svg.rb, and bin/voronoi_transitions.rb tools all use a common file format to describe a Voronoi partition. Any JSON, YAML, or CSV file that parses to an Array of X and Y coordinates is supported. There is also an abbreviated syntax for generating polygons or random points. The file format is documented below in the Voronoi points file format section. See MB::Geometry::Generators#generate_from_file for more info.

Raw array of points

Three simple points in a Voronoi diagram


  [-1, 1],
  [1.5, -0.5],
  [-1, 0],


- [-1, 1]
- - 1.5  
  - -0.5
- [-1, 0]



Raw array of point hashes

Point hashes may include a name and a color for a point.

Three points with custom colors


  { "x": -1, "y": 1, "name": "A", "color": [0.1, 0.2, 0.5, 0.9] },
  { "x": 1.5, "y": -0.5, "name": "B", "color": [0.6, 0.2, 0.5, 0.9] },
  { "x": -1, "y": 0, "name": "C", "color": [0.3, 0.8, 0.4, 0.9] }
bin/voronoi_to_svg.rb /tmp/hashes.json /tmp/hashes.svg


See the source code and files under test_data/ for details. Generators include :random, :segment, :polygon, :grid, :points, and :multi.

Random points

Colors and names may be specified in separate Arrays. Colors will be reused in a loop if there are more points than colors.

The anneal option controls how many times points are moved toward their cell's center. The bounding_box option controls the maximum space in which the points may expand. See MB::Geometry::Voronoi#anneal.

Random points with a deterministic seed


generator: :random
count: 10
seed: 3
anneal: 1
bounding_box: [-3, -2, 3, 2]
  - [0.1, 0.2, 0.5, 0.9]
  - [0.5, 0.3, 0.2, 0.9]
  - "P0"
  - "P1"
  - "P2"
  - "P3"
  - "P4"
  - "P5"
  - "P6"
  - "P7"
  - "P8"
  - "P9"
LABELS=1 bin/voronoi_to_svg.rb /tmp/random_points.yml /tmp/random_points.svg
Multiple generators combined

Voronoi diagram generated from the YML below


generator: :multi
  # Line segment generator
  - generator: :segment
    count: 5
    from: [-3, -0.1]
    to: [-2, -1]
  # Polygon generator
  - generator: :polygon
    sides: 7
    radius: 0.5
    rotate: 45
    clockwise: true
  # Random points generator
  - generator: :random
    count: 10
    seed: 3
    xmin: 1.5
    xmax: 3.25
    ymin: -1.5
    ymax: 1.5
    anneal: 1
  # Another segment
  - generator: :segment
    count: 5
    from: [-3, 0.1]
    to: [-2, 1]

Delaunay triangulation

The Voronoi diagrams generated by this code are all derived from Delaunay triangulation. There are three backends for Delaunay triangulation that can be switched by setting the DELAUNAY_ENGINE and DELAUNAY_DEBUG environment variables.

  • DELAUNAY_ENGINE=rubyvor -- Uses the RubyVor Gem's C extension for Delaunay triangulation. This is very fast, and the default.
  • DELAUNAY_ENGINE=delaunay -- My pure Ruby implementation of Lee and Schacter's 1980 divide and conquer algorithm. See and lib/mb/geometry/delaunay.rb for more info. This is reasonably fast.
  • DELAUNAY_ENGINE=delaunay_debug DELAUNAY_DEBUG=1 -- The same pure Ruby implementation, but with lots of debugging output and each step of the algorithm dumped to a .json file in /tmp (or the directory specified by the JSON_DIR environment variable, if set). This is slow.

Pure Ruby algorithm

The triangulate.rb command prints each input point's neighbors and the final list of triangles in Ruby Hash syntax.

DELAUNAY_ENGINE=delaunay bin/triangulate.rb test_data/square.yml

Rubyvor gem algorithm

DELAUNAY_ENGINE=rubyvor bin/triangulate.rb test_data/square.yml

Simple geometric functions

See MB::Geometry.

Area of a polygon

MB::Geometry.polygon_area([[0, 0], [1, 0], [1, 1], [0, 1]])
# => 1.0

Installation and usage

This project contains some useful programs of its own, or you can use it as a Gem (with Git source) in your own projects.

Standalone usage and development

First, install a Ruby version manager like RVM. Using the system's Ruby is not recommended -- that is only for applications that come with the system. You should follow the instructions from, but here are the basics:

gpg2 --recv-keys 409B6B1796C275462A1703113804BB82D39DC0E3 7D2BAF1CF37B13E2069D6956105BD0E739499BDB
\curl -sSL | bash -s stable

Next, install Ruby. RVM binary rubies are still broken on Ubuntu 20.04.x, so use the --disable-binary option if you are running Ubuntu 20.04.x.

rvm install --disable-binary 2.7.3

You can tell RVM to isolate all your projects and switch Ruby versions automatically by creating .ruby-version and .ruby-gemset files (already present in this project):

cd mb-geometry
cat .ruby-gemset
cat .ruby-version

Now install dependencies:

bundle install

You will also want ffmpeg if you want to make GIFs or videos:

# Debian/Ubuntu
sudo apt-get install ffmpeg

# macOS (might not be exactly right, but this is the gist)
brew install ffmpeg

Using the project as a Gem

To use mb-geometry in your own Ruby projects, add this Git repo to your Gemfile (plus the Git repos of other pre-release gems it depends on):

# your-project/Gemfile
gem 'mb-geometry', git: ''
gem 'mb-math', git: ''
gem 'mb-util', git: ''


Run rspec, or play with the included scripts under bin/.


Pull requests welcome, though development is focused specifically on the needs of my video series.


This project is released under a 2-clause BSD license. See the LICENSE file.

See also



See for Delaunay tringulation references.


Recreational Ruby tools for graphics and geometry.