how can i calculate the surface of delaunay triangulation???????

I want to calculate the area(the surface) of a zone(2D) using the delaunay triangulation how can i do ?plzzzzzzzz i need help

Answer 1

[Naga]

Hello Ali,

To calculate the area of a 2D zone using Delaunay triangulation in MATLAB, use the delaunayTriangulation function to create a triangulation of your points. Calculate the area of each triangle using the vertex indices from the triangulation, then sum these areas to obtain the total area. MATLAB script for the same:

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];
dt = delaunayTriangulation(X);

% Extract the list of triangles
triangles = dt.ConnectivityList;

totalArea = 0;

for i = 1:size(triangles, 1)
    % Get the indices and coordinates of the triangle vertices
    tri = triangles(i, :);
    v = X(tri, :);
    % Calculate the area using the determinant method
    totalArea = totalArea + 0.5 * abs(det([v(1,:) 1; v(2,:) 1; v(3,:) 1]));
end

disp(['Total area of the zone: ', num2str(totalArea)]);