How to plot under certain conditions ?

Hello guys, I want to plot every point (x element of [-4,4], y element of [-4,4]) that meets the following conditions:

• norm([x;y])<=4

The syntax is not right here, but I hope you understand what I'm looking for. For example the point x = 2, y = 2 would meet my requirements and therefore should be plotted.

I am aware of the fact that this is just another way of drawing a circle, but I want to dynamically change my norm (i.e. norm([x;y],1)). I am thankful for every bit of help I can get.

[Rik]

Have you taken a look at meshgrid?

[X,Y]=meshgrid(-4:4,-4:4);
D=sqrt(X.^2+Y.^2);

[DerMischa]

I know meshgrid but how do I plot my circle now ?

Answer 1

[Rik]

If you are not actually after plotting point, you can use fill.

radius=4;
theta=linspace(0,2*pi,200);
x=radius*cos(theta);
y=radius*sin(theta);
fill(x,y,'r')
axis([-radius radius -radius radius])
daspect([1 1 1])

If you want to plot the points:

radius=4;
[X,Y]=meshgrid(-radius:0.1:radius);
D=(X.^2+Y.^2);
plot(X(D<=radius^2),Y(D<=radius^2),'.')
axis([-radius radius -radius radius])
daspect([1 1 1])

[DerMischa]

Thank you this is almost perfect, and will do the job just fine.

Answer 2

[Jan]

Since Matlab R2016 with auto expanding:

x  = -4:4;
x2 = x.^2;
D  = x2 .* x2.' < 16;

Note: Comparing with 4^2 is cheaper than calculating the SQRT().