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Refraction not working (path tracing, Pascal)


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#1 Bacterius   Crossbones+   -  Reputation: 8870

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Posted 13 January 2012 - 08:29 PM

Hi,
I've been working on a path tracer and I just implemented the four basic BRDF's (well, three, one is just a combination of two), and I'm using recursive radiance accumulation. I've got the specular, diffuse, and specular+diffuse BRDF's working well:

Posted Image
Posted Image

(do these look correct by the way? the distorted spheres and odd shadowing come from the pinhole camera which warps the image at the edges)

But I can't seem to get the refraction BRDF working, it just seems to reflect everything. This is my code (in Pascal Object):

function TRefractive.BRDF(Ray: TRay; Normal: TVector; Distance: Double; Rand: TPRNG): TRay;
Var
N1, N2, Index: Double;
Theta, Phi: Double;
Fresnel: Double;
begin
{ Choose the correct index of refraction. }
Theta := DotVector(Normal, Ray.Direction);
if Theta > 0 then
  begin
   N1 := 1;
   N2 := FRefractiveIndex;
   Normal := MulVector(Normal, -1);
  end
else
  begin
   N1 := FRefractiveIndex;
   N2 := 1;
   Theta := -Theta;
  end;

{ Compute the medium change index. }
Index := N2 / N1;

{ Check for total internal reflection. }
Phi := Index * Index * (1 - Theta * Theta);
if (Phi > 1) then
  begin
   { Total internal reflection - fall back to specular BRDF. }
   Result.Origin := AddVector(Ray.Origin, MulVector(Ray.Direction, Distance - SELF_INTERSECTION_EPSILON));
   Result.Direction := NormalizeVector(AddVector(Ray.Direction, MulVector(Normal, 2 * Theta)));
  end
else
  begin
   { Compute the Fresnel term. }
   Phi := Sqrt(1 - Phi); // Phi is the sine in Snell's law
   Fresnel := (Sqr((N1 * Theta - N2 * Phi) / (N1 * Theta + N2 * Phi)) + Sqr((N2 * Theta - N1 * Phi) / (N2 * Theta + N1 * Phi))) * 0.5;

   { Perform a random trial to decide if the ray will reflect or refract. }
   if (Rand.random <= Fresnel) then
	begin
	 { The ray is reflected, fall back to specular BRDF. }
	 Result.Origin := AddVector(Ray.Origin, MulVector(Ray.Direction, Distance - SELF_INTERSECTION_EPSILON));
	 Result.Direction := NormalizeVector(AddVector(Ray.Direction, MulVector(Normal, 2 * Theta)));
	end
   else
	begin
     { The ray is refracted - use Snell Law. }
	 Result.Origin := AddVector(Ray.Origin, MulVector(Ray.Direction, Distance + SELF_INTERSECTION_EPSILON));
	 Result.Direction := NormalizeVector(AddVector(MulVector(Ray.Direction, Index), MulVector(Normal, Index * Theta - Phi)));
	end;
end;
end;

The normal is assumed to by pointing outwards of the geometric primitive (assume this is for a sphere, so the normal points away from the center). So I first decide whether the ray is going into the sphere or out of it, and switch the refractive index and normal vector appropriately. Then I check for total internal reflection. If there is no total internal reflection I go ahead and compute the Fresnel term, and do a random trial to reflect or refract the ray. But even if the ray gets refracted, it just seems to get reflected anyhow by the refraction formula, and I'm not sure why. I hope my code is understandeable, does anyone have a clue what's going on?

Thanks!

Edit: hmm code syntax highlighting doesn't work very well for pascal Posted Image I hope it's still readable

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

 

- Pessimal Algorithms and Simplexity Analysis


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#2 Bacterius   Crossbones+   -  Reputation: 8870

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Posted 14 January 2012 - 02:05 PM

Solved! It turns out I needed to raise the recursion depth slightly, to account for multiple reflections inside the sphere (otherwise refracted rays eventually get discarded as they reach the maximum recursion depth, resulting in only reflected rays being taken into account). If anyone has that problem in the future, that might be your solution too!

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

 

- Pessimal Algorithms and Simplexity Analysis





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