In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane. That set of points (called seeds, sites, or generators) is specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than to any other. These regions are called Voronoi cells. The Voronoi diagram of a set of points is dual to its Delaunay triangulation.
It is named after Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi diagrams have practical and theoretical applications to a large number of fields, mainly in science and technology but also including visual art.
The simplest case
In the simplest case, shown in the first picture, we are given a finite set of points {p1, …, pn} in the Euclidean plane. In this case each site pk is simply a point, and its corresponding Voronoi cell Rk consists of every point whose distance to pk is less than or equal to its distance to any other pk. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The line segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites.
Revision Village - Voted #1 IB Math Resource! New Curriculum 2021-2027.
This video covers Voronoi Diagrams. Part of the IB Mathematics Applications & Interpretation SL & HL course in Topic 3, Geometry & Trigonometry.
More IB Math Videos & Exam Questions can be found at:
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published: 01 Jun 2020
Constructing Voronoi Diagrams
How to create a Voronoi diagram given the position of two or more sites
published: 18 May 2020
Why this pattern shows up everywhere in nature || Voronoi Cell Pattern
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0:00 Voronoi Patterns in nature
0:53 Crystallization
3:03 Proving Cholera is waterborne
4:10 Greatest Circle Problem
6:21 The Kolmogorov-Avrami model
13:30 Brilliant.org/TreforBazett
Voronoi cell patterns are ubiquitous in nature with many applications in engineering, computer science, and economics.
Check out my MATH MERCH line in collaboration with Beautiful Equations
►https://beautifulequations.net/pages/trefor
COURSE PLAYLISTS:
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
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►CALCULUS I: https:...
Computational Geometry
Lecture 07: Voronoi Diagram
Part I: The Post Office Problem
Philipp Kindermann
Playlist: https://www.youtube.com/playlist?list=PLubYOWSl9mIuUsLBKM4NIzPrmBA5jKL-r
Slides: https://algo.uni-trier.de/lectures/algeo/slides/
Full course: https://www.youtube.com/channel/UCuAzKw_VngkAsQh7ummYq0A/playlists?view=50&sort=dd&shelf_id=5
In this video we will learn a simple algorithm for generating Voronoi diagrams. Given a set of points on the plane, the idea is to create, for each point, a polygon that encloses the region of the plane that is closest to that point.
Voronoi diagrams are a type of spatial partitioning diagram that divide a plane into regions based on the distance to a set of points. They are used in a variety of applications, including computer graphics, image processing, and machine learning.
By the end of this video, you will be able to understand and implement the Voronoi diagram algorithm in your own code.
Pseudocode (short version): https://gist.github.com/isedgar/d445248c9ff6c61cef44fc275cb2398f
Pseudocode (long version): https://gist.github.com/isedgar/adbf6b035f8cce62e87998a825ba4294
JavaScript...
published: 21 Sep 2023
Intro to Voronoi diagrams [IB Maths AI SL/HL]
Are you preparing for your IB maths exams? We've got you covered! OSC Study features exams created by IB experts in mathematics, showing you every step of every solution. Try it out for free here: https://app.oscstudy.com/
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Cheers, Mitch
published: 24 Feb 2021
United States of Voronoi
Is there a better way to choose US state boundaries? Voronoi diagrams can do the job.
Voronoi Diagrams by Jason Davies:
United States of Voronoi: https://www.jasondavies.com/maps/voronoi/us-capitals/
World Airports Voronoi: https://www.jasondavies.com/maps/voronoi/airports/
Music: "Daily Beetle" Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 License http://creativecommons.org/licenses/by/3.0/
Street maps by OpenStreetMap contributors. Tiles courtesy of Andy Allan.
Picture of Don Knuth - By Flickr user Jacob Appelbaum, uploaded to en.wikipedia by users BeSherman, Duozmo (Flickr.com (via en.wikipedia)) [CC BY-SA 2.5 (http://creativecommons.org/licenses/by-sa/2.5)], via Wikimedia Commons
Voronoi diagram - By Balu Ertl (Own work) [CC BY-SA 4.0...
published: 03 Jul 2017
Voronoi Explained!
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In this video I will explain the very common voronoi pattern. This pattern is very common in nature and is not too complicated to make so it makes a great building block for making cool effects.
Revision Village - Voted #1 IB Math Resource! New Curriculum 2021-2027.
This video covers Voronoi Diagrams. Part of the IB Mathematics Applications & Interpre...
Revision Village - Voted #1 IB Math Resource! New Curriculum 2021-2027.
This video covers Voronoi Diagrams. Part of the IB Mathematics Applications & Interpretation SL & HL course in Topic 3, Geometry & Trigonometry.
More IB Math Videos & Exam Questions can be found at:
Revision Village - IB Math
https://www.revisionvillage.com
Revision Village - Voted #1 IB Math Resource! New Curriculum 2021-2027.
This video covers Voronoi Diagrams. Part of the IB Mathematics Applications & Interpretation SL & HL course in Topic 3, Geometry & Trigonometry.
More IB Math Videos & Exam Questions can be found at:
Revision Village - IB Math
https://www.revisionvillage.com
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription!
...
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription!
0:00 Voronoi Patterns in nature
0:53 Crystallization
3:03 Proving Cholera is waterborne
4:10 Greatest Circle Problem
6:21 The Kolmogorov-Avrami model
13:30 Brilliant.org/TreforBazett
Voronoi cell patterns are ubiquitous in nature with many applications in engineering, computer science, and economics.
Check out my MATH MERCH line in collaboration with Beautiful Equations
►https://beautifulequations.net/pages/trefor
COURSE PLAYLISTS:
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX
OTHER PLAYLISTS:
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https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
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Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription!
0:00 Voronoi Patterns in nature
0:53 Crystallization
3:03 Proving Cholera is waterborne
4:10 Greatest Circle Problem
6:21 The Kolmogorov-Avrami model
13:30 Brilliant.org/TreforBazett
Voronoi cell patterns are ubiquitous in nature with many applications in engineering, computer science, and economics.
Check out my MATH MERCH line in collaboration with Beautiful Equations
►https://beautifulequations.net/pages/trefor
COURSE PLAYLISTS:
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX
OTHER PLAYLISTS:
► Learning Math Series
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Cool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
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Computational Geometry
Lecture 07: Voronoi Diagram
Part I: The Post Office Problem
Philipp Kindermann
Playlist: https://www.youtube.com/playlist?list=PLubYOWSl...
Computational Geometry
Lecture 07: Voronoi Diagram
Part I: The Post Office Problem
Philipp Kindermann
Playlist: https://www.youtube.com/playlist?list=PLubYOWSl9mIuUsLBKM4NIzPrmBA5jKL-r
Slides: https://algo.uni-trier.de/lectures/algeo/slides/
Full course: https://www.youtube.com/channel/UCuAzKw_VngkAsQh7ummYq0A/playlists?view=50&sort=dd&shelf_id=5
Computational Geometry
Lecture 07: Voronoi Diagram
Part I: The Post Office Problem
Philipp Kindermann
Playlist: https://www.youtube.com/playlist?list=PLubYOWSl9mIuUsLBKM4NIzPrmBA5jKL-r
Slides: https://algo.uni-trier.de/lectures/algeo/slides/
Full course: https://www.youtube.com/channel/UCuAzKw_VngkAsQh7ummYq0A/playlists?view=50&sort=dd&shelf_id=5
In this video we will learn a simple algorithm for generating Voronoi diagrams. Given a set of points on the plane, the idea is to create, for each point, a pol...
In this video we will learn a simple algorithm for generating Voronoi diagrams. Given a set of points on the plane, the idea is to create, for each point, a polygon that encloses the region of the plane that is closest to that point.
Voronoi diagrams are a type of spatial partitioning diagram that divide a plane into regions based on the distance to a set of points. They are used in a variety of applications, including computer graphics, image processing, and machine learning.
By the end of this video, you will be able to understand and implement the Voronoi diagram algorithm in your own code.
Pseudocode (short version): https://gist.github.com/isedgar/d445248c9ff6c61cef44fc275cb2398f
Pseudocode (long version): https://gist.github.com/isedgar/adbf6b035f8cce62e87998a825ba4294
JavaScript code: https://gist.github.com/isedgar/ac26c58e3eb2934623a8b8bc89611b64
https://www.instagram.com/edgardocpu/
In this video we will learn a simple algorithm for generating Voronoi diagrams. Given a set of points on the plane, the idea is to create, for each point, a polygon that encloses the region of the plane that is closest to that point.
Voronoi diagrams are a type of spatial partitioning diagram that divide a plane into regions based on the distance to a set of points. They are used in a variety of applications, including computer graphics, image processing, and machine learning.
By the end of this video, you will be able to understand and implement the Voronoi diagram algorithm in your own code.
Pseudocode (short version): https://gist.github.com/isedgar/d445248c9ff6c61cef44fc275cb2398f
Pseudocode (long version): https://gist.github.com/isedgar/adbf6b035f8cce62e87998a825ba4294
JavaScript code: https://gist.github.com/isedgar/ac26c58e3eb2934623a8b8bc89611b64
https://www.instagram.com/edgardocpu/
Are you preparing for your IB maths exams? We've got you covered! OSC Study features exams created by IB experts in mathematics, showing you every step of every...
Are you preparing for your IB maths exams? We've got you covered! OSC Study features exams created by IB experts in mathematics, showing you every step of every solution. Try it out for free here: https://app.oscstudy.com/
We're so excited to be able to share our exams with you!
Cheers, Mitch
Are you preparing for your IB maths exams? We've got you covered! OSC Study features exams created by IB experts in mathematics, showing you every step of every solution. Try it out for free here: https://app.oscstudy.com/
We're so excited to be able to share our exams with you!
Cheers, Mitch
Is there a better way to choose US state boundaries? Voronoi diagrams can do the job.
Voronoi Diagrams by Jason Davies:
United States of Voronoi: https://w...
Is there a better way to choose US state boundaries? Voronoi diagrams can do the job.
Voronoi Diagrams by Jason Davies:
United States of Voronoi: https://www.jasondavies.com/maps/voronoi/us-capitals/
World Airports Voronoi: https://www.jasondavies.com/maps/voronoi/airports/
Music: "Daily Beetle" Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 License http://creativecommons.org/licenses/by/3.0/
Street maps by OpenStreetMap contributors. Tiles courtesy of Andy Allan.
Picture of Don Knuth - By Flickr user Jacob Appelbaum, uploaded to en.wikipedia by users BeSherman, Duozmo (Flickr.com (via en.wikipedia)) [CC BY-SA 2.5 (http://creativecommons.org/licenses/by-sa/2.5)], via Wikimedia Commons
Voronoi diagram - By Balu Ertl (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Picture of Beijing National Aquatics Centre - By Morio (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Picture of Alibaba headquarters - By HASSELL [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Thiessen Polygons - By Emilio Gomez Fernandez (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons
Voronoi Fortune Droite Balayage Tangente Cercle - By Cdang (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Sound effects obtained from www.zapsplat.com
Sources:
Delaunay triangulation. (2017, July 1). In
Wikipedia, The Free Encyclopedia.
Retrieved from https://en.wikipedia.org/w/index.php?title=Delaunay_triangulation&oldid=789148708.
Drysdale, S. (1993, July 19).
Voronoi diagrams: applications from archaeology to zoology.
Retrieved from https://www.ics.uci.edu/~eppstein/gina/scot.drysdale.html.
Kadish, S. (n.d.).
Voronoi map of the USA.
Retreived from http://vizual-statistix.tumblr.com/post/48625446909/these-are-voronoi-maps-of-the-contiguous-usa.
Voronoi diagram. (2017, June 19). In
Wikipedia, The Free Encyclopedia.
Retrieved
from
https://en.wikipedia.org/w/index.php?title=Voronoi_diagram&oldid=786507557.
Is there a better way to choose US state boundaries? Voronoi diagrams can do the job.
Voronoi Diagrams by Jason Davies:
United States of Voronoi: https://www.jasondavies.com/maps/voronoi/us-capitals/
World Airports Voronoi: https://www.jasondavies.com/maps/voronoi/airports/
Music: "Daily Beetle" Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 License http://creativecommons.org/licenses/by/3.0/
Street maps by OpenStreetMap contributors. Tiles courtesy of Andy Allan.
Picture of Don Knuth - By Flickr user Jacob Appelbaum, uploaded to en.wikipedia by users BeSherman, Duozmo (Flickr.com (via en.wikipedia)) [CC BY-SA 2.5 (http://creativecommons.org/licenses/by-sa/2.5)], via Wikimedia Commons
Voronoi diagram - By Balu Ertl (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Picture of Beijing National Aquatics Centre - By Morio (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Picture of Alibaba headquarters - By HASSELL [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Thiessen Polygons - By Emilio Gomez Fernandez (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons
Voronoi Fortune Droite Balayage Tangente Cercle - By Cdang (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Sound effects obtained from www.zapsplat.com
Sources:
Delaunay triangulation. (2017, July 1). In
Wikipedia, The Free Encyclopedia.
Retrieved from https://en.wikipedia.org/w/index.php?title=Delaunay_triangulation&oldid=789148708.
Drysdale, S. (1993, July 19).
Voronoi diagrams: applications from archaeology to zoology.
Retrieved from https://www.ics.uci.edu/~eppstein/gina/scot.drysdale.html.
Kadish, S. (n.d.).
Voronoi map of the USA.
Retreived from http://vizual-statistix.tumblr.com/post/48625446909/these-are-voronoi-maps-of-the-contiguous-usa.
Voronoi diagram. (2017, June 19). In
Wikipedia, The Free Encyclopedia.
Retrieved
from
https://en.wikipedia.org/w/index.php?title=Voronoi_diagram&oldid=786507557.
Twitter: @The_ArtOfCode
Facebook: https://www.facebook.com/groups/theartofcode/
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PayPal Donation: https://paypal.me/theartofcode
In this video I will explain the very common voronoi pattern. This pattern is very common in nature and is not too complicated to make so it makes a great building block for making cool effects.
Twitter: @The_ArtOfCode
Facebook: https://www.facebook.com/groups/theartofcode/
Patreon: https://www.patreon.com/TheArtOfCode
PayPal Donation: https://paypal.me/theartofcode
In this video I will explain the very common voronoi pattern. This pattern is very common in nature and is not too complicated to make so it makes a great building block for making cool effects.
Revision Village - Voted #1 IB Math Resource! New Curriculum 2021-2027.
This video covers Voronoi Diagrams. Part of the IB Mathematics Applications & Interpretation SL & HL course in Topic 3, Geometry & Trigonometry.
More IB Math Videos & Exam Questions can be found at:
Revision Village - IB Math
https://www.revisionvillage.com
Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription!
0:00 Voronoi Patterns in nature
0:53 Crystallization
3:03 Proving Cholera is waterborne
4:10 Greatest Circle Problem
6:21 The Kolmogorov-Avrami model
13:30 Brilliant.org/TreforBazett
Voronoi cell patterns are ubiquitous in nature with many applications in engineering, computer science, and economics.
Check out my MATH MERCH line in collaboration with Beautiful Equations
►https://beautifulequations.net/pages/trefor
COURSE PLAYLISTS:
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw
►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX
OTHER PLAYLISTS:
► Learning Math Series
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Cool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
BECOME A MEMBER:
►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join
MATH BOOKS I LOVE (affilliate link):
► https://www.amazon.com/shop/treforbazett
SOCIALS:
►Twitter (math based): http://twitter.com/treforbazett
►Instagram (photography based): http://instagram.com/treforphotography
Computational Geometry
Lecture 07: Voronoi Diagram
Part I: The Post Office Problem
Philipp Kindermann
Playlist: https://www.youtube.com/playlist?list=PLubYOWSl9mIuUsLBKM4NIzPrmBA5jKL-r
Slides: https://algo.uni-trier.de/lectures/algeo/slides/
Full course: https://www.youtube.com/channel/UCuAzKw_VngkAsQh7ummYq0A/playlists?view=50&sort=dd&shelf_id=5
In this video we will learn a simple algorithm for generating Voronoi diagrams. Given a set of points on the plane, the idea is to create, for each point, a polygon that encloses the region of the plane that is closest to that point.
Voronoi diagrams are a type of spatial partitioning diagram that divide a plane into regions based on the distance to a set of points. They are used in a variety of applications, including computer graphics, image processing, and machine learning.
By the end of this video, you will be able to understand and implement the Voronoi diagram algorithm in your own code.
Pseudocode (short version): https://gist.github.com/isedgar/d445248c9ff6c61cef44fc275cb2398f
Pseudocode (long version): https://gist.github.com/isedgar/adbf6b035f8cce62e87998a825ba4294
JavaScript code: https://gist.github.com/isedgar/ac26c58e3eb2934623a8b8bc89611b64
https://www.instagram.com/edgardocpu/
Are you preparing for your IB maths exams? We've got you covered! OSC Study features exams created by IB experts in mathematics, showing you every step of every solution. Try it out for free here: https://app.oscstudy.com/
We're so excited to be able to share our exams with you!
Cheers, Mitch
Is there a better way to choose US state boundaries? Voronoi diagrams can do the job.
Voronoi Diagrams by Jason Davies:
United States of Voronoi: https://www.jasondavies.com/maps/voronoi/us-capitals/
World Airports Voronoi: https://www.jasondavies.com/maps/voronoi/airports/
Music: "Daily Beetle" Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 License http://creativecommons.org/licenses/by/3.0/
Street maps by OpenStreetMap contributors. Tiles courtesy of Andy Allan.
Picture of Don Knuth - By Flickr user Jacob Appelbaum, uploaded to en.wikipedia by users BeSherman, Duozmo (Flickr.com (via en.wikipedia)) [CC BY-SA 2.5 (http://creativecommons.org/licenses/by-sa/2.5)], via Wikimedia Commons
Voronoi diagram - By Balu Ertl (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Picture of Beijing National Aquatics Centre - By Morio (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Picture of Alibaba headquarters - By HASSELL [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Thiessen Polygons - By Emilio Gomez Fernandez (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons
Voronoi Fortune Droite Balayage Tangente Cercle - By Cdang (Own work) [CC BY-SA 4.0 (http://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons
Sound effects obtained from www.zapsplat.com
Sources:
Delaunay triangulation. (2017, July 1). In
Wikipedia, The Free Encyclopedia.
Retrieved from https://en.wikipedia.org/w/index.php?title=Delaunay_triangulation&oldid=789148708.
Drysdale, S. (1993, July 19).
Voronoi diagrams: applications from archaeology to zoology.
Retrieved from https://www.ics.uci.edu/~eppstein/gina/scot.drysdale.html.
Kadish, S. (n.d.).
Voronoi map of the USA.
Retreived from http://vizual-statistix.tumblr.com/post/48625446909/these-are-voronoi-maps-of-the-contiguous-usa.
Voronoi diagram. (2017, June 19). In
Wikipedia, The Free Encyclopedia.
Retrieved
from
https://en.wikipedia.org/w/index.php?title=Voronoi_diagram&oldid=786507557.
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In this video I will explain the very common voronoi pattern. This pattern is very common in nature and is not too complicated to make so it makes a great building block for making cool effects.
In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane. That set of points (called seeds, sites, or generators) is specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than to any other. These regions are called Voronoi cells. The Voronoi diagram of a set of points is dual to its Delaunay triangulation.
It is named after Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi diagrams have practical and theoretical applications to a large number of fields, mainly in science and technology but also including visual art.
The simplest case
In the simplest case, shown in the first picture, we are given a finite set of points {p1, …, pn} in the Euclidean plane. In this case each site pk is simply a point, and its corresponding Voronoi cell Rk consists of every point whose distance to pk is less than or equal to its distance to any other pk. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The line segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites.