How to trim lines in plot?

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

[Rik]

Can you provide an example of what you mean? And what did you try already?

[Lisa Smith]

Hi Rik, As shown in the picture, I need to delete all lines that are out of the circle and keep that inside it.

[Walter Roberson]

Most of the time there will be a segment of the line in which one point is inside the circle and the other point is outside. Do you want to drop those segments, or do you want to calculate the intersection and draw just to the edge of the circle?

Will there be any line segments where both points are outside the circle but the line crosses the circle?

[Lisa Smith]

If a segment of line has one point inside the circle and the other point outside the circle then I want to calculate the intersection and draw just from the point located inside the circle to the circle's circumference. However, if the both points out the circle then I need to delete the whole line.

[Walter Roberson]

https://www.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections

https://www.mathworks.com/matlabcentral/fileexchange/11837-fast-and-robust-curve-intersections

https://www.mathworks.com/matlabcentral/fileexchange/8908-curve-intersect-2

[Lisa Smith]

Thank you Walter, still even if I get the intersection points how to draw it, because they are totally randomly generated lines.

Answer 1

[Walter Roberson]

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)

[Lisa Smith]

Thank you it works.