How to add 'border' to Voronoi diagram

Update 2: An alternative way to specify the cropping region:

ClearAll[bsf, explode]
bsf = BSplineFunction[outerpoints[[FindShortestTour[outerpoints][[2]]]], 
   SplineDegree -> Automatic, SplineClosed -> True];

explode[f_] := f[#] + {{0, -#2}, {#2, 0}}.Normalize[f'[t] /. t -> #] &;

borderpoly = Polygon[explode[bsf][#, .2] & /@ Subdivide[100]];

pieces2 = BoundaryDiscretizeRegion[#, BaseStyle -> Opacity[.25,  RandomColor[]]] & /@ 
  (Graphics`PolygonUtils`PolygonIntersection[#, borderpoly] & /@ 
     MeshPrimitives[vm, 2]);

Show[pieces2, Graphics[{Red, Point[pts], Purple, PointSize[Medium], 
   Point @ outerpoints}], ImageSize -> Medium]

enter image description here

Use explode[bsf][#, .4] & when defining borderpoly to get

enter image description here

Update: Cropping frontier polygons and lines:

SeedRandom[1]
pts = RandomReal[{-1, 1}, {100, 2}];
vm = VoronoiMesh[pts];

mc = MeshCells[VoronoiMesh[pts], {1 | 2, "Frontier"}];

intm = RegionDifference[vm, MeshRegion[MeshCoordinates[vm], mc]];

borderpolygon = MeshPrimitives[BoundaryDiscretizeRegion[
     TransformedRegion[intm, ScalingTransform[1.3 {1, 1}]]], 2][[1]];

pieces = BoundaryDiscretizeRegion[#, 
  BaseStyle -> Opacity[.25, RandomColor[]]] & /@ 
    (Graphics`PolygonUtils`PolygonIntersection[#, borderpolygon] & /@ 
       MeshPrimitives[vm, 2]);

outerpoints = Select[pts, Not @* RegionMember[intm]];

Row[{Show[vm, pieces, Graphics[{Red, Point[pts], Purple, PointSize[Medium], 
    Point @ outerpoints}], ImageSize -> Medium], 
  Show[pieces, Graphics[{Red, Point[pts], Purple, PointSize[Medium], 
    Point @ outerpoints}], ImageSize -> Medium]}]

enter image description here

Original answer:

You can use the second argument of VoronoiMesh to specify coordinate bounds:

SeedRandom[1]
pts = RandomReal[{-1, 1}, {100, 2}];

Show[VoronoiMesh[pts, 1.1 {{-1, 1}, {-1, 1}}], Graphics[{Red, Point[pts]}]]

enter image description here


You can do it like this in Cropping a Voronoi diagram but the result is a bit ugly

pts = RandomReal[{-1, 1}, {100, 2}];
vmsh = VoronoiMesh[pts];

poly2disk[cell_, radius_] := 
 Block[{pts = MeshPrimitives[cell, 0][[All, 1]]},
  Return[Disk[Mean[pts], radius]]
 ]
disks = DiscretizeRegion[
   RegionUnion[poly2disk[#, 0.3] & /@ MeshPrimitives[vmsh, 2]]];

DeleteCases[
  RegionIntersection[DiscretizeGraphics@#, disks] & /@ 
   MeshPrimitives[vmsh, 2], _RegionIntersection] // 
 RegionPlot[#, AspectRatio -> Automatic] &

disks clipping voronoi mesh

You could also mask the mesh with the convex hull if you're happy with the points lying on the edge having no space around them. Here I show the result on top.

cvxh=ConvexHullMesh[pts];
Show[
 vmsh,
 DeleteCases[
   RegionIntersection[DiscretizeGraphics@#, cvxh] & /@ 
    MeshPrimitives[vmsh, 2], _RegionIntersection] // 
  RegionPlot[#, AspectRatio -> Automatic] &
 ,
 Graphics[Point[pts]]
 ]

voronoi mesh with convex hull

Maybe scaling up the new mesh about the center of all points would expand the convex hull enough to include some space around the edges too if that's desired.

Tags:

Mesh

Computational Geometry

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