Put area of Voronoi polygon to exact location

Hello

How to match area of each voronoi polygon with location of points used to create that polygon.

I calculate area of each polygon and when I plot it is not OK. For example (see attached picture) polygon around point T9 has area 5.389, but on the picture it is 5.2436.

X = [-1.5 3.2; 1.8 3.3; -3.7 1.5; -1.5 1.3; 0.8 1.2; ...
      3.3 1.5; -4.0 -1.0; -2.3 -0.7; 0 -0.5; 2.0 -1.5; ...
      3.7 -0.8; -3.5 -2.9; -0.9 -3.9; 2.0 -3.5; 3.5 -2.25];
[VX,VY] = voronoi(X(:,1),X(:,2));
h = plot(VX,VY,'-b',X(:,1),X(:,2),'.r');
xlim([-4,4])
ylim([-4,4])
[V,C,XY]=VoronoiLimit(X(:,1),X(:,2));

% Compute area of each voronoi polygon
A = zeros(length(C),1) ;
for i = 1:length(C)
    v1 = V(C{i},1) ; 
    v2 = V(C{i},2) ;
    patch(v1,v2,rand(1,3));
    A(i) = polyarea(v1,v2) ;
end
x=X(:,1);
y=X(:,2);
nump = size(x,1);
plabels = arrayfun(@(n) {sprintf('T%d', n)}, (1:nump)');
hold on
plot(x,y,'.')
text(x, y, plabels, ...
      'FontWeight', 'bold', 'HorizontalAlignment',...
      'right','BackgroundColor', 'none');
hold off

hold on
text(x,y,num2str(A),'fontsize',8,'HorizontalAlignment',...
      'left');
hold off
dt = delaunayTriangulation(X);
[V,R] = voronoiDiagram(dt);

% Assign labels to the Voronoi vertices V.
% By convention the first vertex is at infinity.
numv = size(V,1);
vlabels = arrayfun(@(n) {sprintf('V%d', n)}, (2:numv)');
hold on
Hpl = text(V(2:end,1), V(2:end,2)+.2, vlabels, ...
      'FontWeight', 'bold', 'HorizontalAlignment',...
      'center', 'BackgroundColor', 'none');
hold off

Answer 1

[Naga]

Hello Giometar,

I made the following modifications to your code:

1. Removed the call to 'VoronoiLimit' and instead used MATLAB's built-in 'voronoiDiagram' function directly with delaunayTriangulation. This is a direct approach to get the Voronoi vertices V and cells C.
2. Simplified the plotting and labeling by using a single loop to plot both the point labels (T1, T2, ..., Tn) and their corresponding area values. This reduces redundancy and makes the code more concise.
3. Consolidated the plotting commands with a single hold on and hold off pair, ensuring that all plotting operations happen within the same context and reducing potential errors.

X = [-1.5 3.2; 1.8 3.3; -3.7 1.5; -1.5 1.3; 0.8 1.2; ...
      3.3 1.5; -4.0 -1.0; -2.3 -0.7; 0 -0.5; 2.0 -1.5; ...
      3.7 -0.8; -3.5 -2.9; -0.9 -3.9; 2.0 -3.5; 3.5 -2.25];
[VX,VY] = voronoi(X(:,1),X(:,2));
h = plot(VX,VY,'-b',X(:,1),X(:,2),'.r');
xlim([-4,4])
ylim([-4,4])
[V,C] = voronoiDiagram(delaunayTriangulation(X));

% Compute area of each Voronoi polygon
A = zeros(length(C),1);
for i = 1:length(C)
    v1 = V(C{i},1);
    v2 = V(C{i},2);
    patch(v1,v2,rand(1,3));
    A(i) = polyarea(v1,v2);
end

% Plot points and labels
hold on
plot(X(:,1), X(:,2), '.r');
for i = 1:length(X)
    text(X(i,1), X(i,2), sprintf('T%d', i), 'FontWeight', 'bold', 'HorizontalAlignment', 'right');
    text(X(i,1), X(i,2), sprintf('%.4f', A(i)), 'FontSize', 8, 'HorizontalAlignment', 'left');
end
hold off

Please use the documentation links below to know more about the functions 'voronoiDiagram' and 'delaunayTriangulation':

1. voronoiDiagram: https://www.mathworks.com/help/matlab/ref/delaunaytriangulation.voronoidiagram.html
2. delaunayTriangulation:https://www.mathworks.com/help/matlab/ref/delaunaytriangulation.html