public void TupleDotProductTest()
{
var t1 = new Tuple4(-1, 7, 3, TupleFlavour.Vector);
var t2 = new Tuple4(4, 5, 6, TupleFlavour.Vector);
Assert.Equal(49.0, Tuple4.DotProduct(t1, t2));
}
protected override Intersection[] GetBaseIntersections(Ray ray)
{
var dir_cross_e2 = Tuple4.CrossProduct(ray.dir, E2);
var det = Tuple4.DotProduct(E1, dir_cross_e2);
if (Constants.EpsilonZero(Math.Abs(det)))
{
return(null);
}
var f = 1.0 / det;
var p1_to_origin = Tuple4.Subtract(ray.origin, P1);
var u = f * Tuple4.DotProduct(p1_to_origin, dir_cross_e2);
if ((u < 0.0) || (u > 1.0))
{
return(null);
}
var origin_cross_e1 = Tuple4.CrossProduct(p1_to_origin, E1);
var v = f * Tuple4.DotProduct(ray.dir, origin_cross_e1);
if ((v < 0.0) || ((u + v) > 1.0))
{
return(null);
}
var t = f * Tuple4.DotProduct(E2, origin_cross_e1);
return(new Intersection[] { new Intersection(t, this) });
}
public static double Schlick(HitResult hit, double refractiveIndexEntering, double refractiveIndexExiting)
{
// find the cosine of the angle between the eye and normal vectors
double cosI = Tuple4.DotProduct(hit.EyeVector, hit.SurfaceNormal);
// total internal reflection can only occur if n1 > n2
if (refractiveIndexEntering > refractiveIndexExiting)
{
double ration = refractiveIndexEntering / refractiveIndexExiting;
double sinTheta2 = ration * ration * (1.0 - cosI * cosI);
if (sinTheta2 > 1.0)
{
return(1.0);
}
// compute cosine of theta_t using trig identity
var cosTheta = Math.Sqrt(1.0 - sinTheta2);
// when n1 > n2, use cos(theta_t) instead
cosI = cosTheta;
}
var r0 = Math.Pow((refractiveIndexEntering - refractiveIndexExiting) / (refractiveIndexEntering + refractiveIndexExiting), 2);
return(r0 + (1 - r0) * Math.Pow((1 - cosI), 5));
}
private static Lighting GetIntensity(IMaterial material, Tuple4 lightDirection, double intensity, Tuple4 eyeVector, Tuple4 pointOnSurface, Tuple4 surfaceNormal)
{
var diffuse = 0.0;
var specular = 0.0;
var cosine = Tuple4.DotProduct(lightDirection, surfaceNormal);
if (cosine >= 0)
{
diffuse = cosine * material.Diffuse;
if (material.IsShining())
{
// var reflected = Tuple4.Subtract(Tuple4.Scale(surfaceNormal, 2 * Tuple4.DotProduct(surfaceNormal, lightDirection)), lightDirection);
var reflected = Tuple4.Reflect(Tuple4.Negate(lightDirection), surfaceNormal);
var reflectedDotDir = Tuple4.DotProduct(reflected, eyeVector);
if (reflectedDotDir > 0)
{
specular = material.Specular * Math.Pow(reflectedDotDir / (reflected.Length() * eyeVector.Length()), material.Shininess);
}
}
}
return(diffuse, specular, intensity);
}
public virtual HitResult[] AllHits(Tuple4 origin, Tuple4 dir)
{
var intersections = GetIntersections(new Ray(origin, dir));
if (intersections == null)
{
return(new HitResult[] { HitResult.NoHit });
}
var result = new HitResult[intersections.Length];
for (int i = 0; i < intersections.Length; ++i)
{
var figure = intersections[i].figure;
var distance = intersections[i].t;
var pointOnSurface = Tuple4.Geometry3D.MovePoint(origin, dir, distance); // orig + dir*dist
// TODO: Remove this cast to BaseFigure
(var surfaceNormal, var objectPoint) = ((BaseFigure)figure).GetTransformedNormal(figure, pointOnSurface, intersections[i].u, intersections[i].v);
var eyeVector = Tuple4.Negate(dir);
var isInside = false;
if (Tuple4.DotProduct(surfaceNormal, eyeVector) < 0)
{
isInside = true;
surfaceNormal = Tuple4.Negate(surfaceNormal);
}
var pointOverSurface = Tuple4.Add(pointOnSurface, Tuple4.Scale(surfaceNormal, Constants.Epsilon));
var pointUnderSurface = Tuple4.Subtract(pointOnSurface, Tuple4.Scale(surfaceNormal, Constants.Epsilon));
var reflectionVector = Tuple4.Reflect(dir, surfaceNormal);
result[i] = new HitResult(true,
figure,
distance,
intersections[i].u,
intersections[i].v,
objectPoint,
pointOnSurface,
pointOverSurface,
pointUnderSurface,
surfaceNormal,
eyeVector,
reflectionVector,
isInside);
}
return(result);
}
private Tuple4 CalculateRefractedColorAt(HitResult hit, double refractiveIndexEntering, double refractiveIndexExiting, int remaining)
{
if (!hit.IsHit || remaining <= 0)
{
return(colors.Black);
}
var material = hit.Figure.Material;
if (Constants.EpsilonZero(material.Transparency))
{
return(colors.Black);
}
// Calculations are based on Snell's law
var ration = refractiveIndexEntering / refractiveIndexExiting;
var cosI = Tuple4.DotProduct(hit.EyeVector, hit.SurfaceNormal);
// sin(t) * sin(t) = (ration * ration) * (1 - cos(I) * cos(I))
var sinTheta2 = ration * ration * (1 - cosI * cosI);
if (sinTheta2 > 1.0)
{
// Total internal reflection
return(colors.Black);
}
var cosTheta = Math.Sqrt(1 - sinTheta2);
var dir = Tuple4.Subtract(Tuple4.Scale(hit.SurfaceNormal, ration * cosI - cosTheta),
Tuple4.Scale(hit.EyeVector, ration));
var refractedRay = new Ray(hit.PointUnderSurface, dir);
var refractedColor = CastRay(refractedRay, remaining - 1);
return(Tuple4.Scale(refractedColor, material.Transparency));
}
public void Then_dot(string a, string b, double expected)
{
Assert.True(Constants.EpsilonCompare(expected, Tuple4.DotProduct(cache[a], cache[b])));
}