Bidirectional Path Tracer Theory and Importance Sampling

Ian Mallett · 2012-07-31T10:06:08

Hi, I've written a standard path tracer, GPU accelerated with OpenCL. It fails for small area lights (and of course point light sources fail entirely). Using direct light sampling doesn't work, because that can't handle caustics correctly, if at all. I want to write a bidirectional path tracer, but I'm not sure how. My understanding: 1: Two paths are generated--one from the light and one from the camera. 2: The vertices of the paths are connected in all possible ways to form a number of complete paths from the light to the camera (paths that pass through opaque objects are discarded). I.e., all paths that use some light path vertices, jump somewhere on the camera path, and then use the rest of the camera path vertices. 3: Each path is evaluated by weighting the probability of each interaction occurring, producing a sample. 4: The sample is averaged into the final pixel's color. I would like to make sure that the above is correct. Continuing on the assumption that it is: In standard path tracing, I use importance sampling (e.g., for a diffuse surface I generate random rays with a cosine weighted distribution, then just weight all samples equally). For bidirectional path tracing, I speculate that both the light subpath and the camera subpath could be generated in this way, but the interactions at both ends of the connecting step would need to be weighted manually (because you can't just choose the endpoints randomly) by the interactions' PDF. This all sound good? Thanks, -G

Graphics and GPU Programming Programming

Started by Geometrian July 28, 2012 08:52 AM

9 comments, last by Bacterius 11 years, 9 months ago

Bacterius

13,181

July 31, 2012 10:06 AM

Are you sure? Diffuse surfaces scatter light equally in all directions equally, but a single point scatters light with a cosine-weighted BRDF. When viewed from above, each point reflects strongly. When viewing at an angle, the reflectance is weaker by a factor of cos(theta), but there are more points per unit area by the same factor, so it appears the same reflectance. You get diagrams like: http://upload.wikime...d/Lambert2.gif. Am I missing something?

Actually, the diffuse BRDF is constant at 1/pi, the cos(theta) term is in fact universal, but you are right, I've been spending too much time around diffuse-only algorithms haha (where the diffuse PDF cancels out that term, so I forgot about it). But I think I've found out where you went wrong - you should be dividing by the PDF, not multiplying (obviously - if an event has a 0.01 probability of occuring, its contribution should be scaled by 1/0.01 = 100, not 0.01).

Did you read this? (slide 9)

To be fair I'm now confused. I had a lot of trouble understanding this in the past and it seems I've forgotten how it works, once again

I will need to read over it later. Sorry...