How do I detect intersections between a circle and

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 method I have found is to do the separating axis test. It says:

Two objects don't intersect if you can find a line that separates the two objects, i.e. a line such that all objects or points of an object are on different sides of the line.

However, I don't know how to apply this method to my case.

Can anybody help me?

Answer 1

XNA / C# solution

    class Circle
    {
        public Vector2 Center;
        public float Radius;

        public bool Intersects(Circle circle)
        {
            float distanceX = Center.X - circle.Center.X;
            float distanceY = Center.Y - circle.Center.Y;
            float radiusSum = circle.Radius + Radius;
            return distanceX * distanceX + distanceY * distanceY <= radiusSum * radiusSum;
        }
        public bool Contains(Circle circle)
        {
            if (circle.Radius > Radius)
                return false;
            float distanceX = Center.X - circle.Center.X;
            float distanceY = Center.Y - circle.Center.Y;
            float radiusD = Radius - circle.Radius;
            return distanceX * distanceX + distanceY * distanceY <= radiusD * radiusD;
        }
    }

Note that method Circle.Intersects() returns true even if one circle is within another (treats them as "filled" circles).