How to associate edges of a triangles in a triangulation with numerical values?

I am trying to associate numerical values with the edges of each triangle of a triangulated mesh (Delaunay Triangulation) and I want to ensure that the sum of the associated values is equal to a fixed number. For Ex- Each triangle in the mesh is composed of two different types of materials (material 1 and material 2) such that there are 2 edges made of material 1 and the other made of material 2. I want to give a numerical value of 1 to material 1 and 0 to material 2, and thus constraint the sum of the edges of each triangle to be = 0+1+1=2.

[Fifteen12]

Can you provide information about how your data is encoded? Are you working with coordinate points?

[SABYASACHI DASH]

I have co-ordinates representing the vertices of a polygon, and few other co-ordinates representing points inside the polygon. I am using Delaunay's Triangulation to triagulate all the points, and I am extracting the triangle connectivity using DT.ConnectivityList. I also have the indices of the edges of the triangles using DT.edges.

Answer 1

[Karan Singh]

Hi Sabyasachi,

The points would be required to check if, after the triangulation, the constant sum is possible or not. So, more data would help. I have tried it with a random dataset; however, I was not able to find an example that satisfies the condition. Can you specify if you wish to have a condition to check or something else? Here is one of my attempts:

I have assigned the values at random, but there should also be a condition that checks if this assignment is correct or not.

% Define points (example polygon and inner points)
points = [0 0; 1 0; 2 0; 0 1; 1 1; 2 1; 0 2; 1 2; 2 2];

% Compute Delaunay triangulation
DT = delaunayTriangulation(points);

% Get triangle connectivity list
triangles = DT.ConnectivityList;

% Get edges of the triangulation
edges = edges(DT);

% Initialize edge values (0 for material 2, 1 for material 1)
edgeValues = zeros(size(edges, 1), 1);

% Define a function to check material type (for illustration)
% Assume material 1 for first two edges of each triangle and material 2 for the third
for i = 1:size(triangles, 1)
    tri_edges = [triangles(i, [1,2]); triangles(i, [2,3]); triangles(i, [3,1])]; % Triangle edges
    
    % Find index of edges in the edge list
    for j = 1:3
        edgeIndex = find(ismember(edges, tri_edges(j, :), 'rows') | ismember(edges, flip(tri_edges(j, :)), 'rows'));
        
        if j <= 2
            edgeValues(edgeIndex) = 1; % Material 1
        else
            edgeValues(edgeIndex) = 0; % Material 2
        end
    end
end

% Display results
disp('Edges and assigned values:');

Edges and assigned values:

disp([edges, edgeValues]);

     1     2     1
     1     4     0
     2     3     1
     2     4     0
     2     5     0
     3     5     1
     3     6     1
     4     5     1
     4     7     0
     5     6     0
     5     7     1
     5     8     1
     6     8     1
     6     9     1
     7     8     0
     8     9     0