# Questions tagged [monte-carlo]

Algorithms generating large sets of random numbers to simulate real-world, usually optical systems.

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### Evaluating the Rendering Equation by hand (simple case)

I'm trying to make intuitive sense of the rendering equation and so I'm trying to work out a trivial example by hand, though ultimately I'm just trying to understand how monte carlo importance ...
1 vote
70 views

### Confusion about different sampling strategies in Monte Carlo Path Tracing

I am studying Monte Carlo Path Tracing from different sources. However, I have some confusion about the sampling part and dare to post here for experts' ...
1 vote
59 views

Equiangular sampling is a sampling method for point (sphere) emitter in scattering medium. While it claims to be very efficient when dealing with point (sphere) emitter in scattering medium (see this ...
1 vote
58 views

### Confusion about the bias during Monte Carlo integration

I recently stumbled into this question: Say, for example, we are doing mean-free-path sampling (distance sampling) in a scattering medium and to keep it simple, let's only consider the single ...
245 views

### Properties of the image reconstruction filter in rendering

Let $f$ denote the measurement contribution function for paths of length $k\in\mathbb N$, i.e. $$f(x)=g(x_0\leftrightarrow x_1)W_{\text e}(x_1\to x_0)t_k(x_0,\ldots,x_k)L_{\text e}(x_k\to x_{k-1}),$$ ...
1 vote
131 views

### Can anyone summarize in simple terms, how PSSMLT/MLT algorithms work?

I understand backwards path tracing and bidirectional path tracing (BDPT). However I'm failing to understand how Metrpolis Light Transport methods are even remotely feasible to run. My understanding ...
215 views

### Transforming between solid angle and spherical angle distribution in PBRT

In the Monte Carlo chapter of PBRT, in the section Transforming Between Distributions, they say "The density with respect to $\theta$ and $\phi$ can therefore be derived", but they start ...
112 views

### MSE & Variance of Monte Carlo Estimator

I am trying to prove the equality of $$\rm MSE(\langle I\rangle)=Var(\langle I \rangle)+Bias(\langle I \rangle)^2$$ but obviously I got something wrong as they don't equal in my calculation: So here ...
1 vote
155 views

### Applying Monte-Carlo methods in path tracing

I've noticed that I consistently get worse results in path-tracing when I try to do monte-carlo correctly compared to when I don't, and I think this might be because of a fundamental misunderstanding. ...
205 views

### importance sampling rectangular light

I have been struggling very much to wrap my head around this part of Peter Shirley's book. There is no explanation what the angle Alpha represents and to make things worse in the code the cos(Alpha) ...
86 views

106 views

### The variance for the Monte Carlo estimator

I was wondering about the variance for Monte Carlo. The book (Advanced Global Illumination 2ed, p.60) writes the equation as follows: $\sigma^2 = \frac{1}{N} \int(\frac{f(x)}{p(x)} - I)^2p(x)dx$ \$\...