Messed up a transform while cleaning up my implementation of A Spherical Cap Preserving Parameterization for Spherical Distributions. I call it the Blackhole Sun effect.

Statistics: Posted by papaboo — Tue Dec 12, 2017 6:18 am

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My approximation to the solar emission spectrum might be inadequate in the blue wavelengths

EDIT:

Yeah that looks better!

https://www.dropbox.com/s/0jjsmpi5jvfmi ... 3.jpg?dl=0

https://www.dropbox.com/s/nh80qd93qnbje ... 4.jpg?dl=0

I changed two things at once: 36 bins instead of 10. sRGB output instead of CIE RGB 1931 because if I tell CIMG to write jpg it is probably going to be interpreted as sRGB.

Because I need RGB to spectrum conversions, I implemented the way of Smits (1999) but with more bins (kind of). The code is easily adaptable. I put it up on github: https://github.com/DaWelter/ToyTrace/bl ... sWay.ipynb

Statistics: Posted by dawelter — Mon Dec 11, 2017 12:42 pm

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Section 3.3 Eq 3.9.

As I understand, ultimately it is a matter of definition motivated by thermodynamics of a special case.

I imagine that the same particles that block light along some beam also emit light of their own. So it makes sense that emission and absorption strength have a common density-related prefactor.

The reverse view from the point of importance being emitted into the scene seems more intuitive to me: Importance particle have a chance to interact with particles of the medium in proportion to their cross section. If they interact, the medium transfers energy to the imaging sensor.

Statistics: Posted by dawelter — Sat Dec 09, 2017 9:30 am

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Unfortunately convergence stagnated after some 10k samples per pixel. Not unexpected since it is a difficult scene. Lit by two point lights through the holes in the ceiling. I haven't implemented area lights. The medium has chromatic collision coefficients with high scattering for blue wavelengths.

Cheers

Statistics: Posted by dawelter — Sat Dec 09, 2017 8:39 am

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However, the mental model behind radiance transfer is not one that considers the interaction of individual particles.

- Yes, I know.

1. eq. (1) says that contribution from source radiance Lm(x', w) is proportional to the extinction coefficient sigma_t(x').

- I can understand RTE of this form. Probability density with which light interact (one of scattering/absorption/emission) with medium at x' is proportional to particle density, that is sigma_t(x').

2. eq (3) says that once interaction happens, it is emission with probability (1 - \Lambda) and scattering with probability \Lambda.

- I can understand the latter because scattering albedo \Lambda is the probability that scattering happens out of some interaction. This is straightforward.

However I can't understand the former. The original question: Why is volumetric emission proportional to absorption coefficient?

I can understand absorption happens with the probability (1 - \Lambda), but cannot understand emission also happens with the probability (1 - \Lambda)

Now my question can be paraphrased as follows:

Shouldn't the probability emission happens be independent of absorption coefficient?

I'm sorry in case that the above explanation confuse you more and thank you for your kindness for detailed replying.

Statistics: Posted by shocker_0x15 — Fri Dec 08, 2017 6:34 pm

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I think it is required that emitting particles should not scatter light

I'm not quite sure if I understand how you come to this assumption and if I totally understand your question, but I don't see why particles that emit light shouldn't also scatter light.

However, the mental model behind radiance transfer is not one that considers the interaction of individual particles. The model rather derives the radiance in a density field due to emission, absorption, and scattering phenomena at certain sampling positions and in certain directions. So the question is: for position x, how much light is emitted by particles at or near x, how much light arrives there due to other particles scattering light into direction x ("in-scattering"), and conversely: how much light is absorbed due to local absorption phenomena at x, and how much light is scattered away from x ("out-scattering", distributed w.r.t. the phase function).

See e.g. Hadwiger et al. "Real-time Volume Graphics", p. 6:

Analogously, the total emission coefficient can be split into a source term q, which represents emission (e.g., from thermal excitation), and a scattering term

(https://doc.lagout.org/science/0_Comput ... aphics.pdf)

Out-scattering + heat dissipation etc. ==> total absorption at point x contributed to a viewing ray in direction w

In-scattering + emission ==> added radiance at point x along the viewing direction w

It is not about individual particles. The scattering equation is about the four effects contributing to the total radiance at a point x in direction w. There are no individual particles associated with the position x, you consider particle distributions and how they affect the radiance at x. The radiance increases if particles scatter light towards x, or if particles at (or near) x emit light. The radiance goes down due to absorption and out-scattering from the particle density at x. The point x is usually the sampling position that is encountered when marching a ray through the density field, and is not associated with individual particle positions.

I didn't find a more general source and am working with this paper anyway - the paper also shows the scattering equation and states that it has a combined emission+in-scattering term: http://www.vis.uni-stuttgart.de/~amentm ... eprint.pdf (cf. Eq. 3 on page 3).

Hope I'm not misreading your question?

Statistics: Posted by szellmann — Mon Dec 04, 2017 10:54 pm

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I can find the volumetric emission term which proportional to absorption coefficient for example in,

Jensen's Photon Mapping book, Spectral and Decomposition Tracking paper or Wojciech Jarosz's thesis.

In the Jarosz's thesis reference, there is the following sentence by the equation (4.12) in the page 60:

Media, such as fire, may also emit radiance, Le , by spontaneously converting other forms

of energy into visible light. This emission leads to a gain in radiance expressed as:

I think it is required that emitting particles should not scatter light in order L_e^V to be represented as a decomposed form \sigma_a(x) L_e(x, w).

Statistics: Posted by shocker_0x15 — Mon Dec 04, 2017 2:31 pm

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no perf. progress at all. all the vector ext. are simple crap. for graphics intel seems to be a dead end. gpus will dominate the next years.

so all the cpu stuff was wasted time.

mp

Statistics: Posted by mpeterson — Wed Nov 29, 2017 9:36 am

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With L_b(xb,w)+\int_xb^x L_e(x,w) sigma_a(x), b being the position of a constantly radiating background light and \int_xb^x meaning integration over the viewing ray from the backlight to the integration position, you get the classical emission+absorption model that is e.g. used for interactive DVR in SciVis. In- and out-scattering can be incorporated in the equation. See Nelson Max's '95 paper on optical models for DVR for the specifics: https://www.cs.duke.edu/courses/cps296. ... dering.pdf

Also note that those models usually don't consider individual particles, but rather particle densities, and then derive coefficients e.g. by considering the projected area of all particles inside an infinitesimally flat cylinder projected on the cylinder cap.

Emission and absorption are sometimes expressed with a single coefficient in code for practical reasons, e.g. so that a single coefficient in [0..1] can be used to look up an RGBA tuple in a single, pre-computed and optionally pre-integrated transfer function texture.

Statistics: Posted by szellmann — Tue Nov 28, 2017 9:17 pm

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I have a simple question as in the title.

Why is volumetric emission proportional to absorption coefficient?

I often see the volumetric emission term is written as

I can also see another representation, volumetric emittance function (e.g. in Mark Pauly's thesis: Robust Monte Carlo Methods for Photorealistic Rendering of Volumetric Effects)

, which has the unit of radiance divided by metre (that is W sr^-1 m^-3).

Do particles that emit light do not scatter light at all?

Thanks

Statistics: Posted by shocker_0x15 — Tue Nov 28, 2017 6:19 pm

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The sky is blue. It works!

Single Lambda.

Spectral. Same number of samples per pixel. Higher render time but the result is worth it.

Edit. I managed to do a crude derivation of why this works. Basically taking the delta-source from appendix B into the derivation of the scattering integral estimator.

Statistics: Posted by dawelter — Sun Nov 26, 2017 10:44 am

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Therefore, there are two steps until determining that the interaction is scattering in that implementation.

The first is whether the interaction is null-collision or not.

The second is whether the interaction is scattering out of scattering and absorption(emission).

The above expression shows how these steps form the weight.

The first fraction is division by the probability that the interaction is NOT null-collision.

The second fraction is division by the probability that the interaction is scattering out of scattering and absorption.

The denominator of the second fraction becomes scattering albedo in the standard delta tracking, and might be used for Russian roulette decision to continue constructing a light path.

Statistics: Posted by shocker_0x15 — Sat Nov 25, 2017 4:02 pm

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I made a quick implementation in python https://github.com/DaWelter/ToyTrace/bl ... racking.py.

It seems to work fine as you say, with the minor exception that I take 1/P_s instead of 1/(1-P_n). (Where did you get that from?)

Using two channels with different u_s and u_a (or sigma, as I named it). Reference:

The Integral = [ 0.60379031 0.04641034]

Transmission to the end = [ 0.33283447 0.86069506]

10k samples:

-----------------

spectral_tracking

-----------------

Interacting fraction: 0.4491

Escaping fraction: 0.5509

Integral estimate: 0.597721 +/- 0.008839, 0.046448 +/- 0.000701

Transmission estimate: 0.331000 +/- 0.004706, 0.879645 +/- 0.011789

-------------------------------

spectral_tracking_no_absorption

-------------------------------

Interacting fraction: 0.4186

Escaping fraction: 0.5814

Integral estimate: 0.609066 +/- 0.008566, 0.046662 +/- 0.000669

Transmission estimate: 0.329594 +/- 0.004540, 0.860574 +/- 0.010576

Looks good. I want to use it to simulate atmospheric scattering. If I understand correctly, strong variation of sigma_t across lambda causes high variance. But since my pathtracer was build for RGB channels I can change things to trace three nearby wavelengths simultaneously.

Statistics: Posted by dawelter — Sat Nov 25, 2017 2:45 pm

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In my understanding, T_r / p_surf becomes the weight computed by cumulatively multiplying the following single step weight:

as in the SD tracking paper.

If this is implemented by following PBRT's interface for example for GridDensityMedium::Sample(),

it returns the above weight if no interaction found, otherwise returns

, where w is the cumulative weight until this step.

In the conventional delta tracking,

P_n(x) = \mu_n(x) / \bar{\mu} (this leads the single step weight to 1.)

\bar{\mu} = \mu_a(x) + \mu_s(x) + \mu_n(x).

Therefore, this implementation matches the current PBRT-v3's implementation.

Statistics: Posted by shocker_0x15 — Sun Nov 19, 2017 11:49 am

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I read the recent paper on Spectral and Decomposition Tracking by Kutz et al.

http://drz.disneyresearch.com/~jnovak/p ... index.html

I want to use weighted tracking methods in my own toy path tracer.

Following the PBRT book pg 889, the incident radiance is composed of two terms: the radiance arriving from the distant hit point Tr*Lo and the inscattered radiance integrated along the viewing ray.

I evaluate only one of these terms probabilistically. The first, term if no collision was generated, otherwise there is a scattering or absorption even.

As per PBRT I need to weight Tr*Lo with the probability that no interaction takes place, i.e. the probability to hit the surface p_surf. Thus the estimator is Tr*Lo/p_surf.

However, I cannot figure out how to determine the weight Tr/p_surf.

So how is the inscattered radiance combined with the background?

I also took a brief look at Novak's Ratio Tracking paper but there I also failed to find an answer.

Cheers,

Statistics: Posted by dawelter — Sat Nov 11, 2017 3:57 pm

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