Esempio n. 1
0
        /// <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);
        }
Esempio n. 2
0
 /// <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));
 }