/// <summary>
/// Computes an intersection of the spheres
/// </summary>
/// <returns>True if the spheres intersect or one sphere is contained within the other</returns>
public static bool SphereSphere(Vector3 centerA, float radiusA, Vector3 centerB, float radiusB,
out IntersectionSphereSphere intersection)
{
Vector3 fromBtoA = centerA - centerB;
float distanceFromBtoASqr = fromBtoA.sqrMagnitude;
if (distanceFromBtoASqr < Geometry.Epsilon)
{
if (Mathf.Abs(radiusA - radiusB) < Geometry.Epsilon)
{
// Spheres are coincident
intersection = IntersectionSphereSphere.Sphere(centerA, radiusA);
return(true);
}
// One sphere is inside the other
intersection = IntersectionSphereSphere.None();
return(true);
}
// For intersections on the sphere'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 = IntersectionSphereSphere.Point(centerB + fromBtoA * (radiusB / sumOfRadii));
return(true);
}
if (distanceFromBtoA > sumOfRadii)
{
// No intersections, spheres are separate
intersection = IntersectionSphereSphere.None();
return(false);
}
float differenceOfRadii = radiusA - radiusB;
float differenceOfRadiiAbs = Mathf.Abs(differenceOfRadii);
if (Mathf.Abs(distanceFromBtoA - differenceOfRadiiAbs) < Geometry.Epsilon)
{
// One intersection inside
intersection = IntersectionSphereSphere.Point(centerB - fromBtoA * (radiusB / differenceOfRadii));
return(true);
}
if (distanceFromBtoA < differenceOfRadiiAbs)
{
// One sphere is contained within the other
intersection = IntersectionSphereSphere.None();
return(true);
}
// Circle intersection
float radiusASqr = radiusA * radiusA;
float distanceToMiddle = 0.5f * (radiusASqr - radiusB * radiusB) / distanceFromBtoASqr + 0.5f;
Vector3 middle = centerA - fromBtoA * distanceToMiddle;
float discriminant = radiusASqr / distanceFromBtoASqr - distanceToMiddle * distanceToMiddle;
float radius = distanceFromBtoA * Mathf.Sqrt(discriminant);
intersection = IntersectionSphereSphere.Circle(middle, -fromBtoA.normalized, radius);
return(true);
}
/// <summary>
/// Computes an intersection of the spheres
/// </summary>
/// <returns>True if the spheres intersect or one sphere is contained within the other</returns>
public static bool SphereSphere(Sphere sphereA, Sphere sphereB, out IntersectionSphereSphere intersection)
{
return(SphereSphere(sphereA.center, sphereA.radius, sphereB.center, sphereB.radius, out intersection));
}