# (Finite) Line-Circle Intersection

This topic is 5033 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

I'm writing a small collision detection library, but the math is taking longer than I planned. I'm currently doing circle with line, triangle and rectangle collision, but the Circle-Line page on MathWorld doesn't make much sense to me (plus, it's for infinite lines which is more work for me). I wonder how to implement a function that allows for the center of the circle to be other than (0, 0) - I can't think of anything with the MW explanation. Code prefered, but theory will do also.

##### Share on other sites
bool clIntersect(Circle c,Line l){	float x0 = c.x;	float y0 = c.y;	float x1 = l.s.x;	float y1 = l.s.y;	float x2 = l.e.x;	float y2 = l.e.y;	float n = fabs((x2-x1)*(y1-y0)-(x1-x0)*(y2-y1));	float d = sqrt((x2-x1)*(x2-x1)+(y2-y1)*(y2-y1));	float dist = n/d;	if(dist > c.r)return false;	float d1 = sqrt((x0-x1)*(x0-x1)+(y0-y1)*(y0-y1));	if((d1-c.r) > d)return false;	float d2 = sqrt((x0-x2)*(x0-x2)+(y0-y2)*(y0-y2));	if((d2-c.r) > d)return false;	return true;}

[Edited by - mike25025 on March 3, 2005 5:49:28 PM]

##### Share on other sites
It doesn't work? I have yet to find out why it doesn't.

##### Share on other sites
mike25025's code may be correct, but I'm a little confused as to what's happening in the last few lines. Anyway, if you're having trouble with it still, here's an alternate implementation to try:

bool IntersectCircleSegment(    const Vector2& c,        // center    float r,                            // radius    const Vector2& p1,     // segment start    const Vector2& p2)     // segment end{    Vector2 dir = p2 - p1;    Vector2 diff = c - p1;    float t = diff.Dot(dir) / dir.Dot(dir);    if (t < 0.0f)        t = 0.0f;    if (t > 1.0f)        t = 1.0f;    Vector2 closest = p1 + t * dir;    Vector2 d = c - closest;    float distsqr = d.Dot(d);    return distsqr <= r * r;}

Theory: Find the parametric projection of the circle center onto the line segment. Use this to find the point on the segment closest to the circle center. Find the squared distance between the closest point and the circle center. Compare to radius squared.

If you want a point of intersection rather than a simple boolean result, different (but equally straightforward) code will be required.

Note: the above code is untested and may not be error-free.

##### Share on other sites
it took me awhile but i found the error(s) in my code

it should work now

##### Share on other sites
Quote:
 I wonder how to implement a function that allows for the center of the circle to be other than (0, 0)

If that's the only holdup then you can just translate all your points before you jump into the algorithm. e.g. if a point on the line is at (Px, Py) and the circle is at (Cx, Cy) then use (Px - Cx, Py - Cy) and (0, 0) instead.

##### Share on other sites
Quote:
Original post by Anon Mike
Quote:
 I wonder how to implement a function that allows for the center of the circle to be other than (0, 0)

If that's the only holdup then you can just translate all your points before you jump into the algorithm. e.g. if a point on the line is at (Px, Py) and the circle is at (Cx, Cy) then use (Px - Cx, Py - Cy) and (0, 0) instead.

Yes, that's what I tried to do. But I don't know where to substitude the 0's since they are left out (?) on the MathWorld page.

@Jyk: Thanks, I'm going to look at the theory!

@mike25025: I'm going to replace that code immediately, you'll hear from me!

##### Share on other sites
MMkay.. The collision works partly now. When the circle is on the line, all is okay, but when the circle is around the starting- and endingpoints, it gets stuck sometimes, while not even touching the line.

I'm using mike25025's code.

[update edit whatever]
YAEAAAAAAH!! I implemented jyk's code and it works like a super charm! I'll work out the theory later when I have time, currently I'm just so happy that the code works!

Thanks for everyone's attempt on helping, all++!

[Edited by - Pipo DeClown on March 4, 2005 3:02:58 AM]

1. 1
2. 2
3. 3
Rutin
15
4. 4
5. 5

• 26
• 11
• 9
• 9
• 11
• ### Forum Statistics

• Total Topics
633701
• Total Posts
3013440
×