/// <summary>
/// Computes an intersection of the circles
/// </summary>
/// <returns>True if the circles intersect or one circle is contained within the other</returns>
public static bool IntersectCircleCircle(Circle circleA, Circle circleB, out IntersectionCircleCircle intersection)
{
return(IntersectCircleCircle(circleA.center, circleA.radius, circleB.center, circleB.radius, out intersection));
}
/// <summary>
/// Computes an intersection of the circles
/// </summary>
/// <returns>True if the circles intersect or one circle is contained within the other</returns>
public static bool IntersectCircleCircle(Vector2 centerA, float radiusA, Vector2 centerB, float radiusB,
out IntersectionCircleCircle intersection)
{
intersection = new IntersectionCircleCircle();
Vector2 fromBtoA = centerA - centerB;
float distanceFromBtoASqr = fromBtoA.sqrMagnitude;
if (distanceFromBtoASqr < EpsilonSqr)
{
if (Mathf.Abs(radiusA - radiusB) < Epsilon)
{
// Circles are coincident
intersection.type = IntersectionType.Circle;
return(true);
}
// One circle is inside the other
intersection.type = IntersectionType.None;
return(true);
}
float sumOfRadii = radiusA + radiusB;
float sumOfRadiiSqr = sumOfRadii * sumOfRadii;
if (distanceFromBtoASqr > sumOfRadiiSqr)
{
// No intersections, circles are separate
intersection.type = IntersectionType.None;
return(false);
}
if (Mathf.Abs(distanceFromBtoASqr - sumOfRadiiSqr) < EpsilonSqr)
{
// One intersection outside
intersection.type = IntersectionType.Point;
intersection.pointA = centerB + fromBtoA * (radiusB / sumOfRadii);
return(true);
}
float differenceOfRadii = radiusA - radiusB;
float differenceOfRadiiSqr = differenceOfRadii * differenceOfRadii;
if (distanceFromBtoASqr < differenceOfRadiiSqr)
{
// One circle is contained within the other
intersection.type = IntersectionType.None;
return(true);
}
if (Mathf.Abs(distanceFromBtoASqr - differenceOfRadiiSqr) < EpsilonSqr)
{
// One intersection inside
intersection.type = IntersectionType.Point;
intersection.pointA = centerB - fromBtoA * (radiusB / differenceOfRadii);
return(true);
}
// Two intersections
intersection.type = IntersectionType.TwoPoints;
float radiusASqr = radiusA * radiusA;
float distanceToMiddle = 0.5f * (radiusASqr - radiusB * radiusB) / distanceFromBtoASqr + 0.5f;
Vector2 middle = centerA - fromBtoA * distanceToMiddle;
float discriminant = radiusASqr / distanceFromBtoASqr - distanceToMiddle * distanceToMiddle;
if (discriminant < 0)
{
discriminant = 0;
}
Vector2 offset = fromBtoA.Perp() * Mathf.Sqrt(discriminant);
intersection.pointA = middle + offset;
intersection.pointB = middle - offset;
return(true);
}
/// <summary>
/// Computes an intersection of the circles
/// </summary>
/// <returns>True if the circles intersect or one circle is contained within the other</returns>
public static bool CircleCircle(Vector2 centerA, float radiusA, Vector2 centerB, float radiusB,
out IntersectionCircleCircle intersection)
{
Vector2 fromBtoA = centerA - centerB;
float distanceFromBtoASqr = fromBtoA.sqrMagnitude;
if (distanceFromBtoASqr < Geometry.Epsilon)
{
if (Mathf.Abs(radiusA - radiusB) < Geometry.Epsilon)
{
// Circles are coincident
intersection = IntersectionCircleCircle.Circle();
return(true);
}
// One circle is inside the other
intersection = IntersectionCircleCircle.None();
return(true);
}
// For intersections on the circle's edge magnitude is more stable than sqrMagnitude
float distanceFromBtoA = Mathf.Sqrt(distanceFromBtoASqr);
float sumOfRadii = radiusA + radiusB;
if (Mathf.Abs(distanceFromBtoA - sumOfRadii) < Geometry.Epsilon)
{
// One intersection outside
intersection = IntersectionCircleCircle.Point(centerB + fromBtoA * (radiusB / sumOfRadii));
return(true);
}
if (distanceFromBtoA > sumOfRadii)
{
// No intersections, circles are separate
intersection = IntersectionCircleCircle.None();
return(false);
}
float differenceOfRadii = radiusA - radiusB;
float differenceOfRadiiAbs = Mathf.Abs(differenceOfRadii);
if (Mathf.Abs(distanceFromBtoA - differenceOfRadiiAbs) < Geometry.Epsilon)
{
// One intersection inside
intersection = IntersectionCircleCircle.Point(centerB - fromBtoA * (radiusB / differenceOfRadii));
return(true);
}
if (distanceFromBtoA < differenceOfRadiiAbs)
{
// One circle is contained within the other
intersection = IntersectionCircleCircle.None();
return(true);
}
// Two intersections
float radiusASqr = radiusA * radiusA;
float distanceToMiddle = 0.5f * (radiusASqr - radiusB * radiusB) / distanceFromBtoASqr + 0.5f;
Vector2 middle = centerA - fromBtoA * distanceToMiddle;
float discriminant = radiusASqr / distanceFromBtoASqr - distanceToMiddle * distanceToMiddle;
Vector2 offset = fromBtoA.RotateCCW90() * Mathf.Sqrt(discriminant);
intersection = IntersectionCircleCircle.TwoPoints(middle + offset, middle - offset);
return(true);
}
