SDS problem solved

[zio]

Hi all.
I decided to change my previous name (ior) to zio to not to be confused with refraction index.

It seems like the SDS problem got at least partially solved by merging photon mapping with BiDir or PT.
http://cgg.mff.cuni.cz/~jaroslav/papers/2012-vcm/
http://www.iliyan.com/publications/Vert ... omparison/

Looks like it does not solve caustics on glossy surfaces nor volumetrics on reflections and refractions.

Can indigo take advantage of this method? Or there are other methods in the forge?

I think that there are solutions to this problems, the goal is to find them.

[Juju]

aaaah solutions...

[galinette]

SDS is solved for a long time and the name of the solution is... photon mapping.

However, SDS is solved only with bias. There's actually a mathematical proof that SDS cannot be solved with an unbiased solution.

Cheers,

Etienne

[lycium]

SDS is solved for a long time and the name of the solution is... photon mapping.

However, SDS is solved only with bias. There's actually a mathematical proof that SDS cannot be solved with an unbiased solution.

Cheers,

Etienne

I would be very interested to read more about this, if you have a reference please share!

We are aware of the recent methods in this biased category ("solved" is definitely an overstatement), however bidirectional path tracing still has a higher convergence order than photon mapping and is unbiased, so in the end what's needed is a judicious combination... something we are thinking about for sure

[galinette]

I would be very interested to read more about this, if you have a reference please share!

Which one, first statement or second?

Etienne

[lycium]

Proof that bias is necessary to overcome the SDS problem (without regularisation).

[galinette]

I'll try to find the paper and send you the reference.

However, it's not that difficult to understand the principle.

Imagine a SDS path with a point light source and point camera.
Trace from the camera until the diffuse surface. To successfully continue to the source, you must find a ray over the hemisphere that must be specularly reflected towards a point. That's a zero size set over the set of possible directions, with the solid angle measure. This means you cannot find it by sampling. The only solution is solving analytically and globally vs all specular surfaces the rays that are reflected to the point light. Which is feasible with some surfaces (sphere, plane), maybe with smoothed triangles (which behave in a similar way to a quadric) but expensive, and becomes non analytically solvable with an arbitrary surface or as soon as you need two or more specular reflections to reach the source.
If the point light is not a perfect point but has a small size, and if you find a ray by luck, then you can find another local solution by using the equation's differentials, that's the essence of Manifold-based mutations.

Starting from the light to the cam has the same problem, since the cam is point-size.

[Oscar J]

Why is the camera point sized? Can't you, somehow, simulate a film on which the rays are traced?

[galinette]

Why is the camper point size? Can't you, somehow, emulate a film on which the rays are traced?

Renderers such as Indigo actually simulate the real lens and film size.

The point size camera model is in fact an ingredient of the worst-case scenario for reflected caustics rendering algorithms. This is why it is discussed in theoretical papers. But as real world camera apertures are a few mm wide in most cases, they can be considered as point-size regarding the SDS issue in most cases.

[zio]

There's actually a mathematical proof that SDS cannot be solved with an unbiased solution.

I do not believe in a proof that discards all possible workarounds that can be created still maintaining the thing unbiased. I think that that proof does not consider saving all traced data and if you can simplify the saved data, voila.

I can think of a solution that needs to be consolidated (might not be correct or feasible) that solves the problem of caustics hidden from the light or hidden from the camera, the problem still arises when the caustics are hidden from the camera and the light at the same time. But that can have a solution too, I believe.

Glare have been working on this for more than three years as it was said in a previous post and I can see lycium curiosity on the paper because they have already a working prototype solution

Cant wait for that.

[galinette]

There's actually a mathematical proof that SDS cannot be solved with an unbiased solution.

I do not believe in a proof that discards all possible workarounds that can be created still maintaining the thing unbiased

For the point light / point cam, arbitrary surface SDS case, that's like saying that you know a finite decimal representation of Pi. That would be a breakthrough.

However, more practical cases with area lights may be improved and I'm sure glare can. But titles such as "SDS problem solved" sound like hoaxes.