Circle line-segment collision detection algorithm?

Question

I have a line from A to B and a circle positioned at C with the radius R.

What is a good alg

Answer 1

In this post circle line collision will be checked by checking distance between circle center and point on line segment (Ipoint) that represent intersection point between normal N (Image 2) from circle center to line segment.

(https://i.stack.imgur.com/3o6do.png)

On image 1 one circle and one line are shown, vector A point to line start point, vector B point to line end point, vector C point to circle center. Now we must find vector E (from line start point to circle center) and vector D (from line start point to line end point) this calculation is shown on image 1.

(https://i.stack.imgur.com/7098a.png)

At image 2 we can see that vector E is projected on Vector D by "dot product" of vector E and unit vector D, result of dot product is scalar Xp that represent the distance between line start point and point of intersection (Ipoint) of vector N and vector D. Next vector X is found by multiplying unit vector D and scalar Xp.

Now we need to find vector Z (vector to Ipoint), its easy its simple vector addition of vector A (start point on line) and vector X. Next we need to deal with special cases we must check is Ipoint on line segment, if its not we must find out is it left of it or right of it, we will use vector closest to determine which point is closest to circle.

(https://i.stack.imgur.com/p9WIr.png)

When projection Xp is negative Ipoint is left of line segment, vector closest is equal to vector of line start point, when projection Xp is greater then magnitude of vector D then Ipoint is right of line segment then closest vector is equal to vector of line end point in any other case closest vector is equal to vector Z.

Now when we have closest vector , we need to find vector from circle center to Ipoint (dist vector), its simple we just need to subtract closest vector from center vector. Next just check if vector dist magnitude is less then circle radius if it is then they collide, if its not there is no collision.

(https://i.stack.imgur.com/QJ63q.png)

For end, we can return some values for resolving collision , easiest way is to return overlap of collision (subtract radius from vector dist magnitude) and return axis of collision, its vector D. Also intersection point is vector Z if needed.