/// <summary>
/// Tests for an intersection between a ray and a sphere
/// </summary>
public static Line3Intersection GetRayIntersection( Ray3 ray, Sphere3 sphere )
{
Vector3 originToCentre = ray.Origin - sphere.Centre;
float a0 = originToCentre.SqrLength - ( sphere.SqrRadius );
float a1 = ray.Direction.Dot( originToCentre );
float discriminant;
Point3 intersectionPt;
if ( a0 <= 0 )
{
// 1 intersection: The origin of the ray is inside the sphere
discriminant = ( a1 * a1 ) - a0;
float t = -a1 + Functions.Sqrt( discriminant );
intersectionPt = ray.GetPointOnRay( t );
return new Line3Intersection( intersectionPt, ( intersectionPt - sphere.Centre ).MakeNormal( ), t );
}
if ( a1 >= 0 )
{
// No intersections: Ray origin is outside the sphere, ray direction points away from the sphere
return null;
}
discriminant = ( a1 * a1 ) - a0;
if ( discriminant < 0 )
{
// No intersections: Ray/sphere equation has no roots
return null;
}
if ( discriminant < 0.0001f ) // TODO: Magic number
{
// 1 intersection: Discriminant is close to zero - there's only root to the ray/sphere equation
float t = -a1;
intersectionPt = ray.GetPointOnRay( t );
return new Line3Intersection( intersectionPt, ( intersectionPt - sphere.Centre ).MakeNormal( ), t );
}
// 2 intersections: 2 roots to the ray/sphere equation. Choose the closest
float root = Functions.Sqrt( discriminant );
float t0 = -a1 - root;
float t1 = -a1 + root;
float closestT = ( t0 < t1 ) ? t0 : t1;
intersectionPt = ray.GetPointOnRay( closestT );
return new Line3Intersection( intersectionPt, ( intersectionPt - sphere.Centre ).MakeNormal( ), closestT );
}