Generate some points on the plane restricted by 3 points (triangle)

Assume that are the vertices of a triangle in space. How can i generate some points on this triangle?

Answer 1

[Ameer Hamza]

This is one of the way

n = 500; % number of random points
p1 = [1 1 2];
p2 = [5 7 3];
p3 = [8 2 1];
ps = [p1; p2; p3];

p12 = p2-p1;
p23 = p3-p2;
P = [p12; p23];
x = sqrt(rand(500, 1));
x = [x x.*rand(500, 1)];
P_new = x*P+p1;

ax = axes();
hold(ax);
view(3);
grid(ax);
plot3(ps(:,1), ps(:,2), ps(:,3), '+', 'MarkerSize', 10, 'LineWidth', 2)
plot3(P_new(:,1), P_new(:,2), P_new(:,3), 'r+', 'MarkerSize', 5, 'LineWidth', 1)

[Nima]

Thanks for your answer!

Answer 2

[Bruno Luong]

Another method:

n = 1000; % number of random points
p1 = [1 1 2];
p2 = [5 7 3];
p3 = [8 2 1];

w = -log(rand(3,n));
xyz = [p1; p2; p3].' * (w./sum(w));

plot3(xyz(1,:),xyz(2,:),xyz(3,:),'.')

[Nima]

Thanks for your answer too!