% intersections with a circle
clear
clc

x = []
y = []

colormap('default')

disp('check for 0 intercepts')
[px py] = intercept( 1, 0, -2 );
x = [x px];
y = [y py];
disp('check for 1 intercept')
[px py] = intercept( 1, 0, 1);
x = [x px];
y = [y py];
disp('check for 2 intercepts')
[px py] = intercept( 1, -1, 0);
x = [x px];
y = [y py];
[px py] = intercept( 1, -.5, 0);
x = [x px];
y = [y py];
[px py] = intercept( 1, 0, 0);
x = [x px];
y = [y py];
[px py] = intercept( 1, .5, 0);
x = [x px];
y = [y py];
[px py] = intercept( 1, 1, 0);
x = [x px];
y = [y py];
[px py] = intercept( 1, -1, -.5);
x = [x px];
y = [y py];
[px py] = intercept( 1, -.5, -.5);
x = [x px];
y = [y py];
[px py] = intercept( 1, 0, -.5);
x = [x px];
y = [y py];
[px py] = intercept( 1, .5, -.5);
x = [x px];
y = [y py];
[px py] = intercept( 1, 1, -.5);
x = [x px];
y = [y py];
[px py] = intercept( 1, -1, 0.5);
x = [x px];
y = [y py];
[px py] = intercept( 1, -.5, 0.5);
x = [x px];
y = [y py];
[px py] = intercept( 1, 0, 0.5);
x = [x px];
y = [y py];
[px py] = intercept( 1, .5, 0.5);
x = [x px];
y = [y py];
[px py] = intercept( 1, 1, 0.5);
x = [x px];
y = [y py];
[px py] = intercept( 1, -1, 1);
x = [x px];
y = [y py];
[px py] = intercept( 1, -.5, 1);
x = [x px];
y = [y py];
[px py] = intercept( 1, 0, 1);
x = [x px];
y = [y py];
[px py] = intercept( 1, .5, 1);
x = [x px];
y = [y py];
[px py] = intercept( 1, 1, 1);
x = [x px];
y = [y py];
[px py] = intercept( 1, -1, -1);
x = [x px];
y = [y py];
[px py] = intercept( 1, -.5, -1);
x = [x px];
y = [y py];
[px py] = intercept( 1, 0, -1);
x = [x px];
y = [y py];
[px py] = intercept( 1, .5, -1);
x = [x px];
y = [y py];
[px py] = intercept( 1, 1, -1);
x = [x px];
y = [y py];
plot(x,y,'rx')
axis equal
pause
hold on
th = 0:.01:2*pi;
plot(cos(th), sin(th))