Searching for line and circle intersection.

Hello,

I have two circles and a line that connects the centers. I am trying to find only the closest intersections of the line and the circles(A and B) , but the "linecirc" function gives me all the four.

And this is my code:

Center1=[0.68,3.17];
Center3=[3.82,0.28];
Xline1_3=[0.68 3.82];
Yline1_3=[3.17 0.28];
p1_3=polyfit(Xline1_3,Yline1_3,1);
[X_L1_3_C1,Y_L1_3_C1] = linecirc(p1_3(:,1),p1_3(:,2),0.68,3.17,2);
[X_L1_3_C3,Y_L1_3_C3] = linecirc(p1_3(:,1),p1_3(:,2),3.82,0.28,1);

%http://www.mathworks.com/matlabcentral/fileexchange/2876-draw-a-circle
s1=circle(Center1,2,1000);
hold on
s3=circle(Center3,1,1000);
hold on
plot(Xline1_3,Yline1_3)
hold on 
scatter(X_L1_3_C1,Y_L1_3_C1)
scatter(X_L1_3_C3,Y_L1_3_C3)

[Pawel Ladosz]

Does it have to work on this case only or on any generic case?

[Miro Mitev]

I need it in any case :)

Answer 1

[Thorsten]

If P11 and P12 are the intersection points with circle 1, and P21, P22 are those with circle 2, you compute the distances between each pair

d(P11, P21)
d(P11, P22)
d(P12, P21)
d(P12, P22)

an then select the points with the smallest distance. Note that for some configurations, e.g., two concentric circles and a line through the common center, you get two pairs with the same minimal distance.

[Miro Mitev]

Hi Thorsten, Yes I already did that. I was thinking if there is some shorter way but this one also works for me. Thanks