line and circle intersection

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intersection of line and circle with different slope

I have line which plotted by pp=randi([-400 400],2,2) then x=pp(:,1) and y=pp(:,2). I have a circle with centre (a,b) with radius r

I want to check the intersection point of circle and the line.

I have used polyfit command to check the slope and intercept. Then I used lincirc command but the problem is if the line crosses only one point then the other point is also shown.

For example, if the line crosses one side and stops in the middle, it shows the other point as well which will not cross the boundary

So when you get 2 points why not simply check to see if the endpoints of your line are inside the circle? If so, you have only 1 intersection point, if not then you have 2? You have the line equation and the circle equation so you have all the information you require. — mathematician1975, Jul 16 '12 at 17:02

mathematician1975 · Accepted Answer · 2012-07-16T17:19:06.847

1

You have a circle radius r centred at (a,b). You have a line. If you have plotted these points, you must have your data stored in x and y vectors, so you take the first and last of elements each as (x,y) coordinates. The first pair form the line start point and last pair the end point. Refer to these points as (c1,d1) and (c2,d2). Assuming that your lincirc function tells you there are 2 intersection points between line and circle, calculate

A1 = (c1-a,d1-b)
A2 = (c2-a,d2-b)

Now if

norm(A1,2) < r

then endpoint (c1,d1) is inside your circle, if

norm(A2,2) < r

then endpoint (c2,d2) is inside your circle.

If one of the points is inside the circle, then you only have one intersection point.

If neither point is inside the circle, then you know that your line crosses the circle twice (assuming that your lincirc function tells you there are 2 points)

If both points are inside the circle, then your lincirc function is lying to you.

edited Jul 16 '12 at 17:19

answered Jul 16 '12 at 17:11

mathematician1975

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I will post a picture in a new post. Sorry for that. I want to find the intersection point of a line and circle is there anyother way to do this. – Justin Oommen Jul 16 '12 at 17:37
@JustinOommen Do you know the coordinates of the end points of the line? – mathematician1975 Jul 16 '12 at 17:49
yes ..it is found by pp= randi([-500 500],2,2) ,and taking one point as pp(:,1) and other end point pp(:,2) . the centre of the circle and radius is also known. – Justin Oommen Jul 16 '12 at 17:51
@JustinOommen Your start and end should be pp(1,:) and pp(2,:) does that fix it??? – mathematician1975 Jul 16 '12 at 18:01
no it havn't .do you know anyother way to find the intersection very easily – Justin Oommen Jul 16 '12 at 18:02
where did you get the lincirc function from? is it part of matlab or did you write it yourself? – mathematician1975 Jul 16 '12 at 18:04
have you plotted the circle, the line and the intersections points returned by linecirc on the same graph? can you provide an image? – mathematician1975 Jul 16 '12 at 18:15
I cannot put image from here. I cant post.do you have an email id? – Justin Oommen Jul 16 '12 at 18:17
no sorry. i am not sure what else to suggest. my method will tell you if your line end points lie within your circle or not. but without seeing your code or an image i cant see what the problem is – mathematician1975 Jul 16 '12 at 18:23
I will post a program in next post .thanks – Justin Oommen Jul 16 '12 at 18:25

line and circle intersection

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