Hello Jianan,
To exclude connections to seed points in boundary polygons of a Voronoi diagram, you need to identify the Voronoi regions that are unbounded and then remove connections to the seeds of those regions in the Delaunay triangulation. Follow below steps to achieve the same:
- Use the 'voronoiDiagram' function to get the Voronoi vertices and the corresponding regions. Unbounded regions will have vertices at infinity.
- Once you have identified which regions are unbounded, you can remove the corresponding points from the Delaunay triangulation.
Here is a modified version of your code to achieve this:
n = 100;
cre = 0.08;
rng(2);
x = zeros(n,1);
y = zeros(n,1);
i = 1;
while(x(n,1)==0 || y(n,1)==0)
if (i==1)
x(i,1) = rand;
y(i,1) = rand;
i = i+1;
else
x(i,1) = rand;
y(i,1) = rand;
for j=1:i-1
dist = sqrt((x(j,1)-x(i,1))^2+(y(j,1)-y(i,1))^2);
if dist < cre && i == length(x)
x(i) = 0;
y(i) = 0;
break
elseif dist < cre
break
elseif j == i-1
i = i+1;
end
end
end
end
% Create Delaunay Triangulation
DT = delaunayTriangulation(x, y);
% Get Voronoi diagram
[V, R] = voronoiDiagram(DT);
% Identify unbounded Voronoi regions
unbounded = cellfun(@(r) any(r == 1), R);
% Remove points with unbounded Voronoi regions
boundedPoints = DT.Points(~unbounded, :);
% Create new Delaunay triangulation with bounded points
DT_bounded = delaunayTriangulation(boundedPoints);
% Plot results
figure;
triplot(DT_bounded, 'b');
hold on;
scatter(boundedPoints(:,1), boundedPoints(:,2), 10, [1 0 0], 'filled');
title('Delaunay Triangulation Excluding Boundary Points');
xlabel('X');ylabel('Y');axis equal;grid on;
This approach efficiently removes connections to points in unbounded Voronoi regions and updates the Delaunay triangulation accordingly.
