Edge extraction from a voronoi tessellation

Hello everyone,

I'm having a lot of problems about extracting edges from a random Voronoi tessellation.

Would any of you know how? Is there any function that allows you to do this?

Thank you.

Answer 1

[Sarvani Panguluri]

Hi,

can you specify what you mean by "a random voronoi tesselation"?

Are you creating a 3D voronoi tesselation and trying to extract its edges?If so, Using voronoin /VoronoiDiagram functions output arguments,

[v,c]= voronoin(P); % P is matrix with coordinates

returns matrix v which represent Vertices of edges and a cell array c where each element of c containes the row indices of the Voronoi vertices v that make up a Voronoi cell.

v(c{i},:) 

would return the vertices corresponding to cell number 'i'

You can refer to this Computing the Voronoi Diagram for more insight

Hope this helps!

[Tonino Nucifora]

Hi, yes I generated a Voronoi tessellation with random seeds. The problem is to try to extract the sides of the polygons generated by the tessellation. Is there a way to reorder the indexes of the vertices so that I can work on every single polygon? The sides, once extracted, I need to assign them a thickness. Thank you.

[Sarvani Panguluri]

Can you post the code that you have used to create voronoi diagram.

[Tonino Nucifora]

Vcub=[0 0 0; 1 0 0; 0 1 0; 0 0 1;

1 1 1; 0 1 1; 1 0 1; 1 1 0];

% Vcub(:,2)=2*Vcub(:,2);

N=100;

seeds=1.5*rand(N,3)-0.25;

[Ver,Cel,C_tst]=voronoi3d_cuboid(seeds,Vcub);

figure

hold on

axis('equal')

view([-36 27])

for k = 1:length(Cel)

if ~isempty(Cel{k})

col=rand(1,3);

Vk = Ver(Cel{k},:); Fk = convhull(Vk);

if exist('mergeCoplanarFaces.m','file')==2

[Vk, Fk] = mergeCoplanarFaces(Vk, Fk);

for i=1:length(Fk)

patch('Vertices',Vk,'Faces',Fk{i},'FaceColor',col,'FaceAlpha',0,'EdgeAlpha',1)

end

else

trisurf(Fk,Vk(:,1),Vk(:,2),Vk(:,3),'FaceColor',col, ...

'FaceAlpha', 1,'EdgeAlpha',1,'EdgeColor','k')

end

end

end

[Sarvani Panguluri]

For assigning thickness values to edges, There is a property 'LineWidth' for patch and trisurf functions .Refer this.

[Tonino Nucifora]

So the edges are already contained within the patch? Don't need a matrix to extract the sides of the various polygons? And also is it possible to convert this into an STL file? Thank you.

[HG]

https://www.mathworks.com/matlabcentral/answers/855885-color-voronoi-diagram-and-coresponding-matrix?s_tid=prof_contriblnk

please answer my question if it's possible for you.