The define of "dual" delaunay triangle from Voronoi diagram

p=dlmread('knot.pts'); where p is Nx3 ,matrix dt=DelaunayTri(p); [V R]=dt.voronoiDiagram(); According to Voronoi concepts ,"the delaunay triangle are dual to voronoi edge". It is possible I define the "dual triangle" of voronoi edge by based on R or V ? As i not wrong , the dt is based on dt.x and R is also based on dt.x. Second questions , [V R]=dt.voronoiDiagram() command has provide any method to define Voronoi edge? Thank you

Answer 1

[Ronit]

Hi Renoald,

To define the "Dual Triangle" of a Voronoi edge, it is essential to recognize that each Voronoi edge corresponds to an edge of a Delaunay triangle. The "Dual Triangle" of a Voronoi edge can be identified by finding the Delaunay triangle whose circumcenter is represented by the Voronoi vertex to which the edge is connected.

[V, R] = dt.voronoiDiagram()

The above function gives Voronoi vertices "V" and regions "R". To get Voronoi edges, connect consecutive vertices in each region from "R". This must be done manually since the function does not directly provide edges.

% Assuming V and R are obtained from the voronoiDiagram function
voronoiEdges = [];

for i = 1:length(R)
    region = R{i};
    if all(region ~= 1) % Ignore infinite regions
        % Connect each pair of consecutive vertices in the region
        edges = [region(:), region([2:end, 1])'];
        voronoiEdges = [voronoiEdges; edges];
    end
end
% voronoiEdges now contains pairs of indices into V that represent edges

Please refer to the MATLAB's documentation of "voronoiDiagram" for better undeerstanding:

https://www.mathworks.com/help/matlab/ref/delaunaytriangulation.voronoidiagram.html

Hope it helps!