/// <summary>
/// Computes an intersection of the segment and the sphere
/// </summary>
public static bool SegmentSphere(Vector3 segmentA, Vector3 segmentB, Vector3 sphereCenter, float sphereRadius,
out IntersectionSegmentSphere intersection)
{
Vector3 segmentAToCenter = sphereCenter - segmentA;
Vector3 fromAtoB = segmentB - segmentA;
float segmentLength = fromAtoB.magnitude;
if (segmentLength < Geometry.Epsilon)
{
float distanceToPoint = segmentAToCenter.magnitude;
if (distanceToPoint < sphereRadius + Geometry.Epsilon)
{
if (distanceToPoint > sphereRadius - Geometry.Epsilon)
{
intersection = IntersectionSegmentSphere.Point(segmentA);
return(true);
}
intersection = IntersectionSegmentSphere.None();
return(true);
}
intersection = IntersectionSegmentSphere.None();
return(false);
}
Vector3 segmentDirection = fromAtoB.normalized;
float centerProjection = Vector3.Dot(segmentDirection, segmentAToCenter);
if (centerProjection + sphereRadius < -Geometry.Epsilon ||
centerProjection - sphereRadius > segmentLength + Geometry.Epsilon)
{
intersection = IntersectionSegmentSphere.None();
return(false);
}
float sqrDistanceToLine = segmentAToCenter.sqrMagnitude - centerProjection * centerProjection;
float sqrDistanceToIntersection = sphereRadius * sphereRadius - sqrDistanceToLine;
if (sqrDistanceToIntersection < -Geometry.Epsilon)
{
intersection = IntersectionSegmentSphere.None();
return(false);
}
if (sqrDistanceToIntersection < Geometry.Epsilon)
{
if (centerProjection < -Geometry.Epsilon ||
centerProjection > segmentLength + Geometry.Epsilon)
{
intersection = IntersectionSegmentSphere.None();
return(false);
}
intersection = IntersectionSegmentSphere.Point(segmentA + segmentDirection * centerProjection);
return(true);
}
// Line intersection
float distanceToIntersection = Mathf.Sqrt(sqrDistanceToIntersection);
float distanceA = centerProjection - distanceToIntersection;
float distanceB = centerProjection + distanceToIntersection;
bool pointAIsAfterSegmentA = distanceA > -Geometry.Epsilon;
bool pointBIsBeforeSegmentB = distanceB < segmentLength + Geometry.Epsilon;
if (pointAIsAfterSegmentA && pointBIsBeforeSegmentB)
{
Vector3 pointA = segmentA + segmentDirection * distanceA;
Vector3 pointB = segmentA + segmentDirection * distanceB;
intersection = IntersectionSegmentSphere.TwoPoints(pointA, pointB);
return(true);
}
if (!pointAIsAfterSegmentA && !pointBIsBeforeSegmentB)
{
// The segment is inside, but no intersection
intersection = IntersectionSegmentSphere.None();
return(true);
}
bool pointAIsBeforeSegmentB = distanceA < segmentLength + Geometry.Epsilon;
if (pointAIsAfterSegmentA && pointAIsBeforeSegmentB)
{
// Point A intersection
intersection = IntersectionSegmentSphere.Point(segmentA + segmentDirection * distanceA);
return(true);
}
bool pointBIsAfterSegmentA = distanceB > -Geometry.Epsilon;
if (pointBIsAfterSegmentA && pointBIsBeforeSegmentB)
{
// Point B intersection
intersection = IntersectionSegmentSphere.Point(segmentA + segmentDirection * distanceB);
return(true);
}
intersection = IntersectionSegmentSphere.None();
return(false);
}
/// <summary>
/// Computes an intersection of the segment and the sphere
/// </summary>
public static bool SegmentSphere(Segment3 segment, Sphere sphere, out IntersectionSegmentSphere intersection)
{
return(SegmentSphere(segment.a, segment.b, sphere.center, sphere.radius, out intersection));
}