MATLAB: Uniformly distributed points generation inside quadrilateral with given points

rejection samplinguniform generation

I have a quadrilaterla with vertices (1,0),(1,2),(2,1) and (3,4). How can I generate uniformly distributed points inside it along with plot?

Best Answer

One of the way can be to find a rectangle enclosing all the vertices, create uniformly distributed random points inside the rectangle and then filter out the points using inpolygon()
x = [2 2 3 4];
y = [1 3 2 5];
% sort the vertices to create a convex polygon
X = [x.' y.'];
idx = convhull(X);
X = X(idx, :);
% find enclosing rectangle
ll_corner = [min(x) min(y)]; % lower_left corner
tr_corner = [max(x) max(y)]; % top_right corner
points = rescale(rand(10000, 2), ll_corner, tr_corner); % scale the random number
                                                       % to be inside the rectangle
idx = inpolygon(points(:,1), points(:,2), X(:,1), X(:,2));
points = points(idx, :);
figure();
ax = axes();
plot(X(:,1), X(:,2), 'LineWidth', 1)
hold on
plot(points(:,1), points(:,2), '.')
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