How do I detect intersections between a circle and any other circle in the same plane?

Question

I\'m looking for an algorithm to detect if a circle intersects with any other circle in the same plane (given that there can be more than one circle in a plane).

One

Answer 1

Swift 4 solution:

struct Circle {
    let radius: CGFloat
    let position: CGPoint
}

func circlesIntersect(circleA: Circle, circleB: Circle) -> Bool {
    let Δr² = pow(circleA.radius - circleB.radius, 2)
    let Δx² = pow(circleA.position.x - circleB.position.x, 2)
    let Δy² = pow(circleA.position.y - circleB.position.y, 2)
    let ΣΔx²Δy² = Δx² + Δy²
    let Σr² = pow(circleA.radius + circleB.radius, 2)
    return Δr² <= ΣΔx²Δy² && ΣΔx²Δy² <= Σr²
}