Plotting the area defin

Iluating x & y, I don't want a & b to be always the same as long as 0<=a<=1 & 0<=b<=1. But I have no idea to resolve this issue!!

Answer 1

[John D'Errico]

You know how to use meshgrid! In fact, I know that, because you used it in your other question.

So it you want to plot something over all combinations of a and b, then why not use meshgrid? (10000 points in each dimensions will be wild overkill of course.)

[Image Analyst]

So he can use linspace() to reduce the number of points and get something like this:

numPoints = 50;
a=linspace(0, 1, numPoints);
b=linspace(0, 1, numPoints);
[a, b] = meshgrid(a,b);
x=a.^2-b.^2;
y=a.*b;
plot(x, y, '-', 'LineWidth', 2);
grid on;
xlabel('x', 'FontSize', 20);
ylabel('y', 'FontSize', 20);

[Sultan Al-Hammadi]

 The problem is that when evaluating x & y, I don't want a & b to be always the same as long as 0<=a<=1 & 0<=b<=1. But I have no idea to resolve this issue!!

[madhan ravi]

You need to be clear in what you want to do? Still your statement is not clear

[John D'Errico]

As I said, you resolve the issue by using meshgrid. meshgrid generates ALL combinations of the two variables, a & b.

[a,b] = meshgrid(0:.01:1,0:.01:1);

So a and b are now TWO dimensional arrays, here, each of size 101x101. Now compute x and y as directed.

x = a.^2 - b.^2;
y = a.*b;

plot(x,y,'.')

The result is a sort of triangular domain, with curved edges along the top.

Are you asking how to generate the boundary of that domain? From what you have said, I don't think so.

edgeind = convhull(x(:),y(:));
plot(x(edgeind),y(edgeind),'r-')

But you need to understand that when you want to generate all combinations of two variables like this, USE MESHGRID.

[Sultan Al-Hammadi]

Thank you so much, it looks quite right

Answer 2

[Bruno Luong]

almost right, you need to make a & b oriented in 2 different dimensions (here row for a and column for b)

a=linspace(0,1,101); 
b=linspace(0,1,101)'; % <= make a column
x=a.^2-b.^2; 
y=a.*b; 
plot(x,y,'.b');

[Sultan Al-Hammadi]

The problem is that when evaluating x & y, I don't want a & b to be always the same. But I have no idea to resolve this issue!!

[Bruno Luong]

you do not need to have same a and b, simply make them oriented differently

[Sultan Al-Hammadi]

Is there a way to get it every possible value of a & b, and hence evaluating all possible values of x & y? [for example, a could equal to 0.1 while b=1, etc]

[Bruno Luong]

??? x, y are already computed from all combination of a, b with resolutions of 0.01.

So what your question is about? Might be your should slow down think, then ask a real question.

Answer 3

[Bruno Luong]

Or perhaps you want this?

a=linspace(0,1,100)';
b=linspace(0,1,100)';

rect = [a 0+0*a;
    1+0*b b;
    flip(a) 1+0*a;
    0+0*b flip(b)];
a = rect(:,1);
b = rect(:,2);
x=a.^2-b.^2;
y=a.*b;
plot(x,y,'-b');