How to generate all the possible data points in this 2D triangle?

Hi,

I have a blue triangle in a 2-D V-S space.

How can I know the [s v] values of all the possible points within the blue triangle area?

[Torsten]

These are all:

s>=0 intersect v>=0 intersect s+v <= 1

[Salad Box]

Thank you for your comment. I don't fully understand what it means. Could you explain a little bit please?

[Torsten]

s >=0
v >= 0
s + v <= 1

The blue region is characterized as the set of pairs (s,v) that satisfy all three constraints.

Never heard of linear programming ? Simplex algorithm ? Optimization under constraints ? Linprog ?

[Salad Box]

Sorry I am a beginner to Matlab and programming in general. I haven't heard of any of those terms before but I will find out.

But I think now I understand your algorithm/conditions.

I wrote something based on the logic you put down here.

s = linspace(0,1,20);
v = linspace(0,1,20);
sv = cartprod(s,v); % generate all the points in the square

% condition
idx = (sv(:,1) + sv(:,2))<=1; % s+v<=1
idx = find(idx == 1);
sv = sv(idx,:);

figure
plot(sv(:,1), sv(:,2),'.r')

and I plotted the sv it also worked perfectly.

I would like to thank you for your advice and its really valuable to me.

Answer 1

[KSSV]

P = [0 0 ; 0 1 ; 1 0] ;  % vertices of triangle 
m = 20 ; n = 20 ; 
x = linspace(min(P(:,1)),max(P(:,1)),m) ;
y = linspace(min(P(:,2)),max(P(:,2)),n) ;
[X,Y] = meshgrid(x,y) ; 

idx = inpolygon(X,Y,P(:,1),P(:,2)) ;


patch(P(:,1),P(:,2),'b')
hold on
plot(X(idx),Y(idx),'.r')

[Salad Box]

That is perfect. All I need to do is to modify the number 20 to another number depends on how many points I want. Thank you for your answer.:)