public static List <Intersection> intersect(Sphere sphere, Ray ray)
{
Ray r = Ray.transform(ray, inverse(sphere.transform));
double a, b, c;
c = dot(r.origin, r.origin) - 2; // more operations using dot, but more compact form. Maybe memoize in the future?
b = 2 * dot(r.origin, r.direction);
a = dot(r.direction, r.direction);
double discriminant = b * b - 4 * a * c;
if (discriminant < 0)
{
return(new List <Intersection>());
}
double root = Sqrt(discriminant) / (2 * a);
double first = -b / (2 * a);
List <Intersection> result = new List <Intersection>(2);
result.Add(Intersection.intersection(first - root, sphere));
result.Add(Intersection.intersection(first + root, sphere));
return(result);
}