31

The term "distributed ray tracing" was originally coined by Robert Cook in this 1984 paper. His observation was that in order to perform anti-aliasing in a ray-tracer, the renderer needs to perform spatial upsampling - that is, to take more samples (i.e. shoot more rays) than the number of pixels in the image and combine their results. One way to do this is ...


24

In order to understand Russian Roulette, let's look at a very basic backward path tracer: void RenderPixel(uint x, uint y, UniformSampler *sampler) { Ray ray = m_scene->Camera.CalculateRayFromPixel(x, y, sampler); float3 color(0.0f); float3 throughput(1.0f); // Bounce the ray around the scene for (uint bounces = 0; bounces < 10; +...


13

The next step up from a pinhole camera model is a thin lens model, where we model the lens as being an infinitely thin disc. This is still an idealization that pretty far from modeling a real camera, but it will give you basic depth of field effects. The image above, from panohelp.com, shows the basic idea. For each point on the image, there are multiple ...


10

You always need to multiply by the cosine term indeed (that's part of the rendering equation). Though when you do indirect diffuse using ray-tracing and thus monte-carol integration (which is the most common technique in this case), you have to divide the contribution of each sample by your PDF. This is well exampled here. Note also that in the mentioned ...


10

Generally speaking, path tracing removes a number of assumptions that ray tracing makes. Ray tracing usually assumes that there is no indirect lighting (or that indirect lighting can be approximated by a constant function), because handling indirect lighting would require casting many additional rays whenever you shade an intersection point. Ray tracing ...


9

The Russian roulette technique itself is a way of terminating paths without introducing systemic bias. The principle is fairly straightforward: if at a particular vertex you have a 10% chance of arbitrarily replacing the energy with 0, and if you do that an infinite number of times, you will see 10% less energy. The energy boost just compensates for that. If ...


8

There is one important distinction to make. Markov Chain Monte Carlo (such as Metropolis Light Transport) methods fully acknowledge the fact that they produce lots of highly correlated, it is actually the backbone of the algorithm. On other hand there are algorithms as Bidirectional Path Tracing, Many Light Method, Photon Mapping where the crucial role ...


7

Overview Here is a short overview of the most used space representations, MLT variants and mutation strategies for these MLT variants. As you can see, there are quite some papers dating back to 2017 (e.g., three papers explore combining the Path Space and the Primary Sample Space by jumping back and forth between the two). Path Space (PS) representation, ...


7

First of all, a good reference for Monte Carlo path tracing in participating media is these course notes from Steve Marschner. The way I like to think about volume scattering is that a photon traveling through a medium has a certain probability per unit length of interacting (getting scattered or absorbed). As long as it doesn't interact, it just goes in a ...


7

Just to expand on some of the other answers, the proof that Russian Roulette does not give a biassed result is very simple. Suppose that you have some random variable $F$ which is the sum of several terms: $$F = F_1 + \cdots + F_N$$ Replace each term with: $$F'_i = \left\{ \begin{array}{ll} \frac{1}{p_i} F_i & \hbox{with probability } p_i \\ ...


7

Sample locations with a uniform pattern will create aliasing in the output, whenever there are geometric features of size comparable to or smaller than the sampling grid. That's the reason why "jaggies" exist: because images are made of a uniform square pixel grid, and when you render (for example) an angled line without antialiasing, it crosses rows/columns ...


6

Monte Carlo methods rely on the law of large numbers, which states that the average of a random event repeated a large number of times converges toward the expected value (if you flip a coin a gazillion times, on average you will obtain each side half the time). Monte Carlo integration uses that law to evaluate an integral by averaging a large number of ...


5

In Distributed ray tracing, You stochastically sample many rays in directions which may or may not be preferred by the BRDF. Whereas, in Monte Carlo ray tracing or simply path tracing, you sample only one ray in a direction preferred by the BRDF. So, there are two obvious advantages Path Tracing would have: Computationally less expensive. Which means with ...


5

This is a very good question. There is a common misconception that Monte Carlo, or integration is applied "recursively" on the rendering equation. That is not what's happening. Numerical integration methods are tailored to problems of the form: $$I = \int_{\Omega}{f(x)d\mu(x)} \approx \sum_{k=0}^{N-1}w(x_k)f(x_k)$$ Note that this is not the case for the ...


4

I've seen both, unfortunately. I'm not fond of rays per second as meaning exclusively primary rays and I'd suggest "paths per second" or better yet "samples per second" instead. "Complete ray" is not a common term: a ray is a (potentially unbounded) line segment and a sequence of rays is a path. Rays per second in your second sense of total ray casts is not ...


4

See Kolb, et al., A Realistic Camera Model for Computer Graphics, SIGGRAPH 95. However, do bear in mind that camera models which mimic real-world cameras aren't necessarily what you want for the rendering phase. In a visual effects/post-production scenario, the more blur/vignetting/distortion that the camera model introduces, the worse it is for the ...


4

The hemispherical intensity function, i.e. the hemispherical function of incident light multiplied by the BRDF, correlates to the number of samples required per solid angle. Take the sample distribution of any method and compare it to that hemispherical function. The more similar they are, the better the method is in that particular case. Note that since ...


4

I don't have that book to check the context of this, but from the equations you posted, yes, it looks like you're right. The $1/N$ factor should be applied to both terms. That agrees with the formula for variance from statistics, which is $E[X^2] - E[X]^2$.


4

I think you're right and the subtraction is a mistake. The code should rather be multiplying the fraction of photons not absorbed into the weight. Something like: float fraction_absorbed = sigma_a / sigma_t; absorption += w * fraction_absorbed; w *= (1.0f - fraction_absorbed); This makes absorption the total fraction of photons absorbed so far, and w the ...


3

In Monte Carlo integration, the samples $x_1, x_2, \ldots x_N$ are independent, identically-distributed random variables. This implies they all have the same expectation value. The derived quantities $f(x_i)/p(x_i)$ also all have the same expectation value. So the expectation of a sum of $N$ of these is the same as $N$ times the expectation of any one of ...


3

The classic method is to uniformly sample the disc at the base of your hemisphere and to project your samples upwards on the hemisphere (eg. compute z from x and y). This yields a cosine weighted distribution. As the projection preserves stratification, you need only use stratified sampling of the disc to get a stratified cosine distribution.


3

I can find two possible reasons for the image not converging. #1. Every sample is the same For every sample, you generate random rays. You do that when you shoot the ray through a pixel (for anti-aliasing and DoF) and when you sample the hemisphere (for a new indirect bounce). The problem would be if for every sample, it would generate the same direction, ...


3

The general idea for sampling half vector based distributions is that you generate $H$ and then compute $w_i$ by reflecting $w_o$ about $H$. This is so $H$ will be the half vector of your $w_i$ and $w_o$ pair. It is standard reflection: $$w_i = -w_o + 2(w_o\cdot H)H $$ How you generate $H$ depends on the specific distribution. Generally, it is done in polar ...


3

It's not that hard. If you have just planar or angular light sources, you can think of them as one light source split into multiple chunks and the only thing to deal with is how to sample this multi-light and how to compute the PDF of the resulting samples. Picking probability First, you need to setup the picking probability $P(l)$ for each light source $l$...


3

Throughout my answer I'll sometimes refer to some results in https://sites.fas.harvard.edu/~cs278/papers/veach.pdf by using [MIS,section_number]. You can skip the following derivation if you don't care about the mathematical explanation of why using MIS to combine estimators is valid. I'll have to start with what the purpose of MIS is. The general idea is ...


2

If you have a deterministic mapping function which transforms uniformly distributed samples into the desired PDF (cosine shaped in your case), just feed it directly with stratified uniformly distributed samples. The mapping will keep the strata separated. Usually one sample per stratum is used and the number of strata is set according to the total amount of ...


2

PSSMT operates directly on the space of random numbers that generate valid light paths. As such, mutations in the unit hypercube lose their physical interpretation since they do not have direct knowledge of the actual light path constructed. Recent research in rendering has shown that it is possible to bridge the gap between path space (that acts directly on ...


2

Specular surfaces which use MIS are not perfectly specular like a mirror. They have a small amount of blur, otherwise there is indeed no point in sampling the light as all the samples will evaluate the BRDF as 0. In fact, you would only need to trace a single reflection ray. A small amount of blur means that a given camera ray will see a small area of the ...


1

This approximation is typically done by running a bidirectional path tracer with a modest amount of samples per pixel. This means multiple paths per pixel to approximate the integral of $f_j$, the measurement contribution function. Veach's original MLT paper explains how it can be done in a way that eliminates start-up bias (see Section 5.1).


1

Yes, in the simple case, primary rays conform to the frustum. If you're doing depth-of-field optically, then the rays don't quite conform to the frustum, because you need to vary the ray origins slightly as well as the directions. How exactly the variation works depends on how closely you're simulating the lens system and aperture. You can picture it as ...


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