Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 ApproximateGeneralizedVoronoiMesh

Source Notebook

Approximate the generalized Voronoi mesh for non-overlapping geometries

Contributed by: Lakshay Garg

ResourceFunction["ApproximateGeneralizedVoronoiMesh"][{g1,g2,…}]

gives a MeshRegion that approximates the Voronoi mesh of curves approximated by the 2D points in lists g1,g2,….

ResourceFunction["ApproximateGeneralizedVoronoiMesh"][{g1,g2,…},{{xmin,xmax},{ymin,ymax}}]

clips the mesh to the bounds [xmin,xmax]⨯ [ymin,ymax].

Details and Options

ResourceFunction["ApproximateGeneralizedVoronoiMesh"] takes the same options as MeshRegion.

Examples

Basic Examples (1) 

Generate the Voronoi mesh for some points, lines and a parabola:

In[1]:=
With[ {parabola = Table[{t, 1.7 - t*t}, {t, -0.5, 0.5, 0.1}], line1 = Table[{t, t}, {t, 0, 1, 0.1}], line2 = Table[{t - 0.7, -0.5 - 0.1 t}, {t, 0, 1, 0.1}], point1 = {1, 0}, point2 = {0, 1}}, Show[ ResourceFunction["ApproximateGeneralizedVoronoiMesh"][ {parabola, line1, line2, {point1}, {point2}}, {{-1, 2}, {-1, 2}}], ListLinePlot[parabola], ListLinePlot[line1], ListLinePlot[line2], ListPlot[{point1, point2}]]]
Out[1]=

Possible Issues (1) 

Since MeshRegion cannot contain polygons with holes, the Voronoi meshes which contain such polygons will contain edges so that such polygons can be represented without holes:

In[2]:=
With[ {circle = Table[AngleVector[t], {t, 0, 2 Pi + 0.1, 0.1}], point1 = {{-0.5, 0}}, point2 = {{0.5, 0}}}, Show[ ResourceFunction["ApproximateGeneralizedVoronoiMesh"][ {circle, point1, point2}, {{-1.2, 1.2}, {-1.2, 1.2}}], ListLinePlot[circle], ListPlot[point1], ListPlot[point2]]]
Out[2]=

Publisher

Lakshay Garg

Version History

  • 1.0.0 – 31 March 2020

Related Resources

Author Notes

If one is not interested in a MeshRegion but only the polygons, here’s an alternative approach which handles polygons with holes gracefully

License Information