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geometry - Line Segment Circle Intersection

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?

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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)

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