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### #ActualGeometrian

Posted 31 July 2012 - 03:01 AM

There is no PDF calculation in naive path tracing as your rays are already randomly bouncing around (which is equivalent to a diffuse BRDF), so the PDF is inherently taken into account through that random sampling.

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...bd/Lambert2.gif.  Am I missing something?

In BDPT, you instead force the connecting ray to go from one point to another, so you need to normalize the consequences of that event to its probability of actually happening - which is what the PDF does. This is assuming a random walk of course

Yes, I believe this is what I did for the BDPT.  I think in retrospect though that I should understand ordinary PT fully first.
Thanks,
-G

### #2Geometrian

Posted 31 July 2012 - 02:48 AM

There is no PDF calculation in naive path tracing as your rays are already randomly bouncing around (which is equivalent to a diffuse BRDF), so the PDF is inherently taken into account through that random sampling.

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...bd/Lambert2.gif.  Am I missing something?

In BDPT, you instead force the connecting ray to go from one point to another, so you need to normalize the consequences of that event to its probability of actually happening - which is what the PDF does. This is assuming a random walk of course

Yes, this is what I did for the BDPT.
Thanks,
-G

### #1Geometrian

Posted 31 July 2012 - 02:48 AM

There is no PDF calculation in naive path tracing as your rays are already randomly bouncing around (which is equivalent to a diffuse BRDF), so the PDF is inherently taken into account through that random sampling.

Are you sure?  Diffuse surfaces scatter light equally in all directions equally, but that's only true for an infinite number of points.  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.wikimedia.org/wikipedia/commons/b/bd/Lambert2.gif.  Am I missing something?

In BDPT, you instead force the connecting ray to go from one point to another, so you need to normalize the consequences of that event to its probability of actually happening - which is what the PDF does. This is assuming a random walk of course

Yes, this is what I did for the BDPT.
Thanks,
-G

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