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

Another solution, first considering the case where you don't care about collision location. Note that this particular function is built assuming vector input for xB and yB but can easily be modified if that is not the case. Variable names are defined at the start of the function

#Line segment points (A0, Af) defined by xA0, yA0, xAf, yAf; circle center denoted by xB, yB; rB=radius of circle, rA = radius of point (set to zero for your application)
def staticCollision_f(xA0, yA0, xAf, yAf, rA, xB, yB, rB): #note potential speed up here by casting all variables to same type and/or using Cython
    
    #Build equations of a line for linear agents (convert y = mx + b to ax + by + c = 0 means that a = -m, b = 1, c = -b
    m_v = (yAf - yA0) / (xAf - xA0)
    b_v = yAf - m_v * xAf
    rEff = rA + rB #radii are added since we are considering the agent path as a thin line

    #Check if points (circles) are within line segment (find center of line segment and check if circle is within radius of this point)
    segmentMask = np.sqrt( (yB - (yA0+yAf)/2)**2 + (xB - (xA0+xAf)/2)**2 ) < np.sqrt( (yAf - yA0)**2 + (xAf - xA0)**2 ) / 2 + rEff

    #Calculate perpendicular distance between line and a point
    dist_v = np.abs(-m_v * xB + yB - b_v) / np.sqrt(m_v**2 + 1)
    collisionMask = (dist_v < rEff) & segmentMask

    #return True if collision is detected
    return collisionMask, collisionMask.any()

If you need the location of the collision, you can use the approach detailed on this site, and set the velocity of one of the agents to zero. This approach works well with vector inputs as well: http://twobitcoder.blogspot.com/2010/04/circle-collision-detection.html