geometry - Line Segment Circle Intersection

Question

I am trying to determine the point at which a line segment intersect a circle. For example, given any point between P0 and P3 (And also assuming that you know the radius), what is the easiest method to determine P3?

Answer 1

Generally,

• find the angle between P0 and P1
• draw a line at that angle from P0 at a distance r, which will give you P3

In pseudocode,

theta = atan2(P1.y-P0.y, P1.x-P0.x)
P3.x = P0.x + r * cos(theta)
P3.y = P0.y + r * sin(theta)