VoronoiCells use the VoronoiDelaunay package to compute the vertices and areas of the Voronoi cells in a tessellation.
In Julia, run
The two main functions of VoronoiCells are
Both functions have a method where the input is a vector of
IndexablePoint2D's -- a subtype of the
AbstractPoint2D from the GeometricalPredicates package.
Such a vector can be created with e.g.
using VoronoiCells pts = [IndexablePoint2D(1+rand(), 1+rand(), n) for n in 1:10]
Note that an
AbstractPoint2D must be in [1,2]x[1,2].
The last entry in an
IndexablePoint2D is used to associate it with the corners of its Voronoi cells in the output from
C = voronoicells(pts)
C is a Dict where the keys are integers representing the indices of the generator points in
C[n] is a vector with the corners of the
n'th Voronoi cell.
voronoiarea computes the areas of a point set in the same order as the input.
A = voronoiarea(C)
A[n] is the area of the
IndexablePoint2D with index
There is also a method of
voronoiarea that accepts two vectors with
y coordinates, respectively.
y have entries that are not in the unit square a suitable bounding box must be specified.
x = rand(10) y = rand(10) A = voronoiarea(x,y)
The window is specified as a vector with
[xmin, xmax, ymin, ymax].
Consider e.g. points in the rectangle [0,1]x[-1,1]:
x = rand(10) y = 2*rand(10) - 1 A = voronoiarea(x, y, [0.0, 1.0, -1.0, 1.0])
A third function is
If one wish to cover the bounding box with cirlces of equal radii and centers specified by vectors
density(x,y) returns the minimum such radius.
Just as in
voronoiarea the default bounding box is the unit square and a different box can be specified as a third argument.
For technical reasons (that I don't fully understand) VoronoiDelaunay includes the corner points of the default bounding box, i.e., (1,1), (2,1), (2,2) and (1,2) in the set of generators. This means that these corners also get their own Voronoi cell and the cells of the generators closest to the corners are a priori incorrect.
The way VoronoiCells removes the corner cells and update the affected neighbor cells are explained in the attached document.
doc folder also includes the script
plots.jl used to make the plots in the document.
3 months ago