Uniformly distributed points generation inside quadrilateral with given points

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?

[John D'Errico]

Is this a one time problem with this specific quad? Or tomorrow will you have some different quadrilateral? Or will you have a more general polygon? The reason I ask is the solution would depend on what you really need to do next.

The simple solution would be to triangulate the quadrilateral. Then generate points randomly inside the triangles, based on their area. Not difficult.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Ameer Hamza]

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), '.')

Answer 2

[Matt J]

I haven't used it, but this FEX tool claims to be able to do it:

https://www.mathworks.com/matlabcentral/fileexchange/71398-random-point-inside-a-polygone