# lloydsAlgorithm(Px,​Py, crs, numIterations, showPlot)

Version 1.6.0.0 (7.16 KB) by
Starts with a point set, repeatedly moves each point to centroid of Voronoi cell.
Updated 11 Feb 2015

LLOYDSALGORITHM runs Lloyd's algorithm on the particles at xy positions
(Px,Py) within the boundary polygon crs for numIterations iterations
showPlot = true will display the results graphically.

Lloyd's algorithm starts with an initial distribution of samples or
points and consists of repeatedly executing one relaxation step:
1. The Voronoi diagram of all the points is computed.
2. Each cell of the Voronoi diagram is integrated and the centroid is computed.
3. Each point is then moved to the centroid of its Voronoi cell.
Inspired by http://www.mathworks.com/matlabcentral/fileexchange/34428-voronoilimit
Requires the Polybool function of the mapping toolbox to run.
Run with no input to see example. To initialize a square with 50 robots
in left middle, run:
lloydsAlgorithm(0.01*rand(50,1),zeros(50,1)+1/2, [0,0;0,1;1,1;1,0], 200, true)

### Cite As

Aaron T. Becker's Robot Swarm Lab (2024). lloydsAlgorithm(Px,Py, crs, numIterations, showPlot) (https://www.mathworks.com/matlabcentral/fileexchange/41507-lloydsalgorithm-px-py-crs-numiterations-showplot), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2012a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Categories
Find more on Voronoi Diagram in Help Center and MATLAB Answers
##### Acknowledgements

Inspired by: VoronoiLimit(varargin)

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Version Published Release Notes
1.6.0.0

corrected error about some vertices not being in clockwise error by sorting the vertices

1.5.0.0

Corrected error when called as a function by adding a calculation for n, removed warning about order of vertices by sorting them in CW order, added example call as a function. Thanks for the feedback Kirill Smirnov!

1.3.0.0

When run with no arguments, starts the robots in a small grid pattern.

1.1.0.0

removed dependency on www.mathworks.com/matlabcentral/fileexchange/34428 (which sometimes miscalculates the Voronoi cell boundaries), robots never leave the boundary, reduces to a single file.

1.0.0.0