how i can calculate the surface(2D) of delaunay triangulation ??????????????????

I want to calculate the area(the surface) of a zone(2D) using the delaunay triangulation or convex hull, how can i do ?plzzzzzzzz i need help net = [1:n;rand([1,n])*x;rand([1,n])*y]; net1 = net; xx=net(2,:); yy=net(3,:); dt = DelaunayTri(xx',yy'); P = [xx',yy']; K = convexHull(dt); triplot(dt,'cyan');

Answer 1

[Gautam]

Hello @ali hadjer

Delaunay triangulation divides the 2D area into triangles without any overlapping. Once you have the triangulation, you can calculate the area of each triangle and sum them up to get the total area using the "polyarea" function.

% Sample data points
points = [0, 0; 1, 0; 1, 1; 0, 1; 0.5, 0.5];

% Perform Delaunay triangulation
tri = delaunay(points(:, 1), points(:, 2));

% Plot the triangulation
figure;
triplot(tri, points(:, 1), points(:, 2));
hold on;
plot(points(:, 1), points(:, 2), 'r*');
title('Delaunay Triangulation');
xlabel('X');
ylabel('Y');
grid on;

% Calculate the area of each triangle
area = 0;
for i = 1:size(tri, 1)
    x = points(tri(i, :), 1);
    y = points(tri(i, :), 2);
    area = area + polyarea(x, y);
end

% Display the total area
fprintf('Total Area using Delaunay Triangulation: %.2f\n', area);