MATLAB: How to trim lines in plot

MATLABplot

Hello, I'm trying to plot several lines in a circle and need to trim the part of lines which are out of this circle. So how can I do that? Thank you in advance
 % plotting random lines
X1 = rand (8,8);
Y1 = rand (8,8);
figure
plot (X1,Y1)
hold on
 % plotting the circle
 R = 0.5;
 angle = linspace(0,2*pi,180);
 x= R*cos(angle);
 y= R*sin(angle); 
 plot(x,y,'r')
 axis equal

Best Answer

Not necessarily the best way, but a way that would work:
Take the coordinates of the random points, and subtract from them the coordinates of the center of the circle. Convert the result to polar coordinates. Now create a logical mask of the points that have r less than the radius of the circle.
Now you want to look at the boundaries between groups of points that are inside or not. Look for every transition between false (outside) and true (inside), and every transition between true (inside) and false (outside)
first_outside_in_group = [false, mask(1:end) & ~mask(2:end-1)];
last_outside_in_group = [mask(2:end) & ~mask(1:end-1), false];
keep = mask | first_outside_in_group | last_outside_in_group;
adjusted_theta = theta;
adjusted_r = r;
adjusted_r(first_outside_in_group) = R_circle;
adjusted_r(last_outside_in_group) = R_circle;
adjusted_theta(~keep) = nan;
adjusted_r(~keep) = nan;
[adjusted_x, adjusted_y] = pol2cart(adjusted_theta, adjusted_r);
adjusted_x = adjusted_x + circle_center_x;
adjusted_y = adjusted_y + circle_center_y;
and now you can plot(adjusted_x, adjusted_y)
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