private double[] GetIntersectionsFromBook(Tuple4 origin, Tuple4 dir)
{
if (!Constants.EpsilonCompare(1.0, dir.Length()))
{
throw new ArgumentException("Direction should be normalized", nameof(dir));
}
var sphereToRay = Tuple4.Subtract(origin, Tuple4.ZeroPoint);
var a = Tuple4.DotProduct(dir, dir);
var b = 2 * Tuple4.DotProduct(dir, sphereToRay);
var c = Tuple4.DotProduct(sphereToRay, sphereToRay) - 1.0;
var discriminant = b * b - 4 * a * c;
if (discriminant < 0.0)
{
return(null);
}
var discriminantSqrt = Math.Sqrt(discriminant);
var t0 = (-b - discriminantSqrt) / (2 * a);
var t1 = (-b + discriminantSqrt) / (2 * a);
// Ray originates inside sphere
// When t > 0 that is intersection in the direction of the ray
// other intersection is in the opposite direction
return(new double[] { t0, t1 });
}
private double[] GetIntersections(Tuple4 origin, Tuple4 dir)
{
if (!Constants.EpsilonCompare(1.0, dir.Length()))
{
throw new ArgumentException("Direction should be normalized", nameof(dir));
}
var t = 0.0;
while (t < maxDistance)
{
var p = Tuple4.Geometry3D.MovePoint(origin, dir, t);
var d = DistanceFrom(p);
if (Math.Abs(d) < epsilon)
{
return(new double[] { t });
}
t += d;
}
return(null);
}
private double[] GetIntersections(Tuple4 origin, Tuple4 dir)
{
if (!Constants.EpsilonCompare(1.0, dir.Length()))
{
throw new ArgumentException("Direction should be normalized", nameof(dir));
}
var l = Tuple4.Subtract(Center, origin);
var tca = Tuple4.DotProduct(l, dir);
var d2 = Tuple4.DotProduct(l, l) - tca * tca;
if (d2 > radius2)
{
return(null);
}
var thc = Math.Sqrt(radius2 - d2);
var t0 = tca - thc;
var t1 = tca + thc;
// Ray originates inside sphere
// When t > 0 that is intersection in the direction of the ray
// other intersection is in the opposite direction
return(new double[] { t0, t1 });
}
