I have plotted two circles and I want to anything outside of the first circle (unit circle) to not be plotted or excluded.

So I have four 1D arrays for 2 circles that I plotted. One holds the x values, the other holds the y values for a circle and the other does the same for the other circle. The first circle is a unit circle. The second circle intersects with the unit circle. I want to remove any plotted points of the second circle that are not within the first unit circle.

I used this fx called RMap:

function [c,d] = RMap(a,b)
% A complex function that maps
%   R = (z - 1) /(z + 1)
% where
%   z = a + jb and R = c + jd
%   
%   Function inputes: a,b
%   Function outputs: c,d
c = (((a.*a)+ (b.*b) - 1) ./ ((a.*a) + (b.*b) + (2.*a) + 1));
d = ((-2.*b) ./ ((a.*a)+(b.*b)+ (2.*a) + 1));

end

And ran this scipt:

    np = 100000;
min = -pi*1000;
max = pi*1000;

hold on;

a = 0;
b = 0;
z = a + (1j*b);
e = linspace(z,z,np);     %both linspaces are used to create a line that is z=0
f = linspace(min,max,np); 
[c,d] = RMap(e,f);        %use fx RMap to compute the the line's position into the w-plane
plot(c,d);                %plot the result which is a unit circle
axis([-1 1 -1 1]);

hold on;

a = 0;
b = -10;
z = a + (1j*b);
h = linspace(imag(z),imag(z),np);  %both linspaces are used to create a line that is z= -j10
g = linspace(min,max,np);
[i,j] = RMap(g,h);                 %use fx RMap to compute the the line's position into the w-plane
plot(i,j);                         %plot the result which is a second circle circle


hold off;

Resulting in this figure: I have also attached a copy to this post.

I now want to limit exclude all the points in the samller circle that are outside of the blue unit circle.

I first tried something like

if sqrt((i.*i) + (j.*j)) > 1
    %I want to delete those the elements in the array where this condition
    %was true, but don't know how to or if there is a better solution.
end

Answer 1

[Alan Stevens]

Here's one way:

    np = 100000;
min = -pi*1000;
max = pi*1000;

hold on;

a = 0;
b = 0;
z = a + (1j*b);
e = linspace(z,z,np);     %both linspaces are used to create a line that is z=0
f = linspace(min,max,np); 
[c,d] = RMap(e,f);        %use fx RMap to compute the the line's position into the w-plane
plot(c,d);                %plot the result which is a unit circle
axis([-1 1 -1 1]);

hold on;

a = 0;
b = -10;
z = a + (1j*b);
h = linspace(imag(z),imag(z),np);  %both linspaces are used to create a line that is z= -j10
g = linspace(min,max,np);
[i,j] = RMap(g,h);                 %use fx RMap to compute the the line's position into the w-plane
[I,J] = find(i.^2+j.^2>1); %*******************
i(I) = nan; j(J) = nan;    %*******************
plot(i,j);                         %plot the result which is a second circle circle


hold off;

function [c,d] = RMap(a,b)
% A complex function that maps
%   R = (z - 1) /(z + 1)
% where
%   z = a + jb and R = c + jd
%   
%   Function inputes: a,b
%   Function outputs: c,d
c = (((a.*a)+ (b.*b) - 1) ./ ((a.*a) + (b.*b) + (2.*a) + 1));
d = ((-2.*b) ./ ((a.*a)+(b.*b)+ (2.*a) + 1));

end

[Salaheldin Elhadi]

Thanks! Helped me out a lot!