Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.

This time.
What is...Fortune’s algorithm? Or: Parabolas and distance.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.
http://www.dtubbenhauer.com/youtube.html

Thumbnail.
https://img.freepik.com/premiumvecto...
Picture from https://demonstrations.wolfram.com/Fo...

Main discussion.
https://link.springer.com/article/10....
https://en.wikipedia.org/wiki/Fortune...
https://en.wikipedia.org/wiki/Sweep_l...
https://demonstrations.wolfram.com/Fo...
   • Fortune's Algorithm for Voronoi Diagrams  
https://jacquesheunis.com/post/fortun...
https://pvigier.github.io/2018/11/18/...
https://ieeexplore.ieee.org/document/...
https://www.cs.tufts.edu/comp/163/not...

Background.
https://en.wikipedia.org/wiki/Voronoi...
https://mathworld.wolfram.com/Voronoi...
https://plus.maths.org/content/maths...
https://www.et.byu.edu/~beard/papers/...
https://en.wikipedia.org/wiki/Voronoi...
https://www.irishtimes.com/news/scien...
https://en.wikipedia.org/wiki/Delauna...
https://www.newcastle.edu.au/__data/a...

Mathematica.
https://demonstrations.wolfram.com/Vo...
https://demonstrations.wolfram.com/Vo...
https://demonstrations.wolfram.com/Vo...

Pictures used.
Pictures from    • What is...a Voronoi diagram?  
https://www.aispotter.com/wpcontent/...
Picture from https://demonstrations.wolfram.com/Fo...
Picture created using https://reference.wolfram.com/languag...
Picture from https://www.cs.tufts.edu/comp/163/not...

YouTube and co.
   • Voronoi Diagrams [IB Math AI SL/HL]  
   • Voronoi Diagram Intro Part 1  Basic ...  
   • Delaunay Triangulation  
   • What is...a Voronoi diagram?   (shameful selfpromotion)

#combinatorics
#algorithms
#mathematics