Plot closed convex set in 2D

Hello,

this seems like a pretty basic question, but I have not found an answer yet.

I want to plot a set S in 2D, such that

S = { (x1,x2): f(x1, x2) <= 0 }

where f is a given convex function, so that S will be convex. S will also be closed.

Say, x1 and x2 both should go from say -10 to 10 in increments of 0.1

I can easily write a code to evaluate f, for a given x1 and x2, but f is complicated enough, so it is not easy to ``vectorize" it. It is more complicated, than say x1^2 + x2^2-1 (which would give a closed disk.

Similar question is posted for

https://www.mathworks.com/matlabcentral/answers/1687074-how-to-plot-a-set-as-the-constraint-in-2d?s_tid=srchtitle

but that is not quite what I want.

A first approximation is this code, but it is slow, and the plot it generates looks jagged.

lb1=-5; %lower bound of x1

ub1=5; %upper bound of x1

N1=(ub1-lb1)/0.1;

lb2=-5; %lower bound of x2

ub2=5; %upper bound of x2

N2=(ub2-lb2)/0.1;

syms x1 x2

f(x1, x2)=x1^2+x2^2-1;

A=[]; % x1 of points in feasible set

B=[]; % x2 of points in feasible set

for i=0:N1

a=lb1+i*0.1;

for j=0:N2

b=lb2+j*0.1;

if f(a,b)<=0

A=[A,a];

B=[B,b];

end

end

end

scatter(A,B,'filled');

-----------------------------------------------------

Thank you

Answer 1

[Torsten]

If f is only one function and not a vector of functions, use "fimplicit".

fimplicit(@(x,y) x.^2+y.^2-1);

[gabor pataki]

Thank you, but my f is more complicated. It may be computed by an involved computation for a given x and y.

[Torsten]

Doesn't matter. The f doesn't need to be given as a "one-liner". You can define your f in a separate function file.

Then just do

fimplicit(@fun)

function value = fun(x,y)
  value = x.^2+y.^2-1;
end

[gabor pataki]

Thanks! And if I want the set itself to be say blue ?

[Torsten]

https://de.mathworks.com/matlabcentral/answers/805046-how-can-we-fill-a-region-defined-by-a-implicit-function