## Plotting the area defined by (x,y), where x=a^2-b^2 , y=a*b , 0<=a<=1 & 0<=b<=1?

on 13 Oct 2018 at 14:08
Latest activity Commented on by Sultan Al-Hammadi

on 14 Oct 2018 at 1:50

I tried plotting the area defined by (x,y), where x=a^2-b^2 , y=a*b , 0<=a<=1 & 0<=b<=1: in MATLAB, but I don't know how to do it probably. Here is what I have done so far:

```a=0:0.0001:1;
b=0:0.0001:1;
x=a.^2-b.^2;
y=a.*b;
plot(x,y);
```

Please help me 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!!

### John D'Errico (view profile)

on 13 Oct 2018 at 14:15

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.)

on 13 Oct 2018 at 14:30

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

John D'Errico

### John D'Errico (view profile)

on 13 Oct 2018 at 15:06

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.

on 14 Oct 2018 at 1:50

Thank you so much, it looks quite right

### Bruno Luong (view profile)

on 13 Oct 2018 at 14:19
Edited by Bruno Luong

### Bruno Luong (view profile)

on 13 Oct 2018 at 15:03

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');
```

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Bruno Luong

### Bruno Luong (view profile)

on 13 Oct 2018 at 14:37

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

on 13 Oct 2018 at 14:44

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

### Bruno Luong (view profile)

on 13 Oct 2018 at 15:03

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

### Bruno Luong (view profile)

on 13 Oct 2018 at 14:50

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');
```