Colouring patches from a voronoi tessalation

5 views (last 30 days)
I want to color patches generated from a Voronoi tessellation. However, some of the elements stay white. You can see the midpoints and the elements in the first figure below. Some elements (patches) remain white.
In the second figure you can see the assumable reason for this, the elements corresponding to the outer points are not closed and therefore do not form a valid patch.
Do you guys have a solution for how I can color all patches? Maybe by closing the outer ones artificially?
Here is my MWE:
%MWE Voronoi tesselation cell colouring
sample_set = randn(100,2);
figure
[vMGFPoints, vMGFcells] = voronoin(sample_set);
[vMGFx, vMGFy] = voronoi(sample_set(:,1), sample_set(:,2));
hold on
color = randn(100,1);
for vcell = 1:length(sample_set)
patch(vMGFPoints(vMGFcells{vcell},2),vMGFPoints(vMGFcells{vcell},1), color(vcell))
plot(sample_set(vcell,2),sample_set(vcell,1),'k.')
end
plot(vMGFy,vMGFx, 'k')
colorbar_obj = colorbar;
colorbar_obj.Label.String = 'Weighting';
xlim([-3 3])
ylim([-3 3])
Generating this image:
Zooming out shows this
  3 Comments
mbvoyager
mbvoyager on 18 Nov 2022
Sorry, I failed to replace one variable, now it should work. Thanks for pointing out the issue!

Sign in to comment.

Accepted Answer

mbvoyager
mbvoyager on 19 Nov 2022
Edited: mbvoyager on 19 Nov 2022
Inspired by Star striders boundary approach, I searched for these terms and found this idea (stackoverflow-python-voronoi). In the second answer in StackOverflow the idea is to artificially bound my 2D space by simply adding far away points in the "corners of the 2D space". These artificially added points will likely change the Voronoi cells and the tessellation but for my purpose this might still be alright.
%MWE Voronoi tesselation cell colouring
sample_set = randn(100,2);
bound_point = 999; %adding 4 artificial boundary points
sample_set = [sample_set; [-bound_point, -bound_point]; [-bound_point, bound_point]; [bound_point, -bound_point]; [bound_point, bound_point]];
figure
[vMGFPoints, vMGFcells] = voronoin(sample_set);
[vMGFx, vMGFy] = voronoi(sample_set(:,1), sample_set(:,2));
hold on
color = randn(length(sample_set),1);
for vcell = 1:length(sample_set)
patch(vMGFPoints(vMGFcells{vcell},2),vMGFPoints(vMGFcells{vcell},1), color(vcell))
plot(sample_set(vcell,2),sample_set(vcell,1),'k.')
end
plot(vMGFy,vMGFx, 'k')
colorbar_obj = colorbar;
colorbar_obj.Label.String = 'Weighting';
xlim([-3 3])
ylim([-3 3])
  1 Comment
Bjorn Gustavsson
Bjorn Gustavsson on 19 Nov 2022
You better test how this affect your results. One suggestion is to put your "dummy-points" further and further away and see if and how the effect varies. It should have a very small (I think even no) effect inside the outermost patches.

Sign in to comment.

More Answers (1)

Star Strider
Star Strider on 18 Nov 2022
Edited: Star Strider on 18 Nov 2022
It may be possible to close the exterior of the plot using the boundary function. I was able to do that reasonably well with:
v1 = vMGFx(:); % Column Vector For 'boundary' Call
v2 = vMGFy(:); % Column Vector For 'boundary' Call
bidx = boundary(v1,v2, 0.95);
vxf = ismember(vMGFx, v1(bidx));
[r,cx] = find(vxf);
vyf = ismember(vMGFy, v2(bidx));
[r,cy] = find(vyf);
Vx = vMGFx(:,cx) % Boundary Points
Vy = vMGFx(:,cy) % Boundary Points
However, I do not understand your code well enough to incorporate these points into it. Also, since the data are random, it may be necessary to adjust the ‘shrink factor’ in the boundary call each time. (That would not be necessary with fixed values.)
I am not not certain how to use these results with the patch function to close the patch areas. It may require a separate patch call to use them. I will help as I can to work with you to solve this.
.
  1 Comment
mbvoyager
mbvoyager on 19 Nov 2022
Thanks for your help and your time, really appreciated!
Honestly, I do not really understand your approach (most likely because I've never worked with boundary), so the pounts Vx and Vy are suppose to be the boundary points for the outer elements generated by the MATLAB voronoi function?Is the second line here correct, shouldn't vMGFy be accessed in the second line?
Vx = vMGFx(:,cx) % Boundary Points
Vy = vMGFx(:,cy) % Boundary Points
If I edit this line to include
Vy = vMGFy(:,cy) % Boundary Points
and run the following,
plot(vMGFy,vMGFx, 'k') % Plot original points from voroin
hold on
scatter(Vx, Vy, '+r')
I receive this:
These additional points could help but some of them are not really useful.

Sign in to comment.

Categories

Find more on Voronoi Diagram in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!