SharpVoronoiLib

C# implementation of generating a Voronoi diagram from a set of points in a plane (using Fortune's Algorithm) with edge clipping and border closure. This implementation guarantees O(n×ln(n)) performance.

The key differences from the original VoronoiLib repo

• Borders can be closed, that is, edges generated along the boundary
• Edges and points/sites contain additional useful data
• Multiple critical and annoyingly-rare bugs and edge cases fixes
• LOTS more unit testing

Known issues:

• The algorithm uses a lot of allocations, forcing garbage collection
• There is no visual output/example since the original used MonoGame

Examples

TODO: several pretty pictures here

Use

Quick-start:

List<VoronoiSite> sites = new List<VoronoiSite>
{
    new VoronoiSite(300, 300),
    new VoronoiSite(300, 400),
    new VoronoiSite(400, 300)
};

List<VoronoiEdge> edges = VoronoiPlane.TessellateOnce(
    sites, 
    0, 0, 
    600, 600
);

The tesselation result for the given VoronoiSites contains VoronoiEdges and VoronoiPoints. The returned collection contains the generated edges.

• VoronoiEdge.Start and .End are the start and end points of the edge.
• VoronoiEdge.Right and .Left are the sites the edge encloses. Border edges move clockwise and will only have the .Right site. And if no points are within the region, both will be null.
• Edge end VoronoiPoints also contain a .BorderLocation specifying if it's on a border and which one.
• VoronoiEdge.Neighbours (on-demand) are edges directly "connecting" to this edge, basically creating a traversable edge graph.
• VoronoiEdge.Length (on-demand) is the distance between its end points.
• VoronoiSite.Cell contains the edges that enclose the site (the order is not guaranteed).
• VoronoiSite.ClockwiseCell (on-demand) contains these edges sorted clockwise (starting from the bottom-right "corner" end point).
• VoronoiSite.Neighbors contains the site's neighbors (in the Delaunay Triangulation), that is, other sites across its edges.
• VoronoiSite.Points (on-demand) contains points of the cell, that is, edge end points / edge nodes.
• VoronoiSite.ClockwisePoints (on-demand) contains these points sorted clockwise (starting from the bottom-right "corner").

If closing borders around the boundary is not desired (leaving sites with unclosed cells/polygons):

List<VoronoiEdge> edges = VoronoiPlane.TessellateOnce(
    sites, 
    0, 0, 
    600, 600,
    BorderEdgeGeneration.DoNotMakeBorderEdges
);

Full syntax (leaving a reusable VoronoiPlane instance):

VoronoiPlane plane = new VoronoiPlane(0, 0, 600, 600);

plane.SetSites(sites);

List<VoronoiEdge> edges = plane.Tessellate();

Sites can be quickly randomly-generated:

VoronoiPlane plane = new VoronoiPlane(0, 0, 600, 600);

plane.GenerateRandomSites(1000, PointGenerationMethod.Uniform);

plane.Tessellate();

Lloyds relaxation algorithm can be applied to "smooth" cells:

VoronoiPlane plane = new VoronoiPlane(0, 0, 600, 600);

plane.SetSites(sites);

plane.Tessellate();

List<VoronoiEdge> edges = plane.Relax();
// List<VoronoiEdge> edges = plane.Relax(3, 0.7f); // relax 3 times with 70% strength each time 

Dependencies

The main library is compiled for .NET (Core) 6.0 and .NET Standard 2.0 at C# 8.0 and targets compatible OSes - Windows, Linux & macOS - and frameworks like Xamarin, Mono, UWP, or Unity.

Credits

• Originally written by Logan Lembke as VoronoiLib
• Updated with unit tests and nuget package by Sean Esopenko
• Improvements by Jeffrey Jones
• Various code pieces attributed inline

Original implementation inspired by:

• Ivan Kuckir's project
• Raymond Hill's project