Various links on ray tracing

Here are some links related to ray tracing, and more specifically, path tracing.

Some ray tracing related projects or blogs:

Some major publications:

  • The rendering equation, SIGGRAPH 1986, James T. Kajiya. From the paper:

    We present an integral equation which generalizes a variety of known rendering algorithms.
    We mention that the idea behind the rendering equation is hardly new.
    However, the form in which we present this equation is well suited for computer graphics, and we believe that this form has not appeared before.

  • Bi-directional path tracing, Compugraphics 1993, Eric P. Lafortune and Yves D. Willems. From the paper:

    The basic idea is that particles are shot at the same time from a selected light source and from the viewing point, in much the same way. All hit points on respective particle paths are then connected using shadow rays and the appropriate contributions are added to the flux of pixel  in question.

  • Optimally Combining Sampling Techniques for Monte Carlo Rendering, SIGGRAPH 1995, Eric Veach and Leonidas J. Guibas. From the abstract:

    We present a powerful alternative for constructing robust Monte Carlo estimators, by combining samples from several distributions in a way that is provably good.

  • Metropolis Light Transport, SIGGRAPH 1997, Eric Veach and Leonidas J. Guibas. From the abstract:

    To render an image, we generate a sequence of light transport paths by randomly mutating a single current path (e.g. adding a new vertex to the path).

  • Robust Monte Carlo methods for light transport simulation, 1998, Erich Veach PhD thesis (432 pages pdf): it presents bidirectional path tracing, and introduces Metropolis Light Transport and Multiple Importance Sampling. From the abstract:

    Our statistical contributions include a new technique called multiple importance sampling, which can greatly increase the robustness of Monte Carlo integration. It uses more than one sampling technique to evaluate an integral, and then combines these samples in a way that is provably close to optimal. This leads to estimators that have low variance for a broad class of integrands. We also describe a new variance reduction technique called efficiency-optimized Russian roulette.


    The second algorithm we describe is Metropolis light transport, inspired by the Metropolis sampling method from computational physics. Paths are generated by following a random walk through path space, such that the probability density of visiting each path is proportional to the contribution it makes to the ideal image.


On a slightly different topic, fxguide had a great series of articles on the state of rendering in the film industry, which I previously mentioned.

A GLSL version of smallpt

smallpt is a bare minimum path tracer written under 100 lines of C++, featuring diffuse, and specular reflection, and refraction. Using the detailed explanation slides by David Cline, I experimented porting it to GLSL on Shadertoy.

This proved to be an interesting experiment that brought a few lessons.

You can see the shader and tweak it here. By default it uses 6 samples per pixel, and 3 bounces, which allows it to run smoothly on average hardware. I found 40 samples per pixel and 5 bounces to give nice results while maintaining interactive framerate.

Path tracing, 40 samples per pixel, 5 bounces

Path tracing, 40 samples per pixel, 5 bounces

Update: since GLSL Sandbox has a feature, reading from the previous frame buffer, that Shadertoy is missing at the moment, I thought it’d be interesting try it to have the image converging over time. A little hacking later, a minute or so worth of rendering got me this kind of result: Given the effort, I am really pleased by the result.

Path tracing, 40 samples per pixel, 5 bounces

Path tracing, unknown number of samples per pixel, 7 bounces

A raytracer under a hundred lines of C++

On his website Kevin Beason presents a Monte Carlo ray tracer written with 99 lines of C++, generating a picture of a Cornell box with global illumination. Beyond the interesting experiment and the fact it can generate a binary of 4kB, I find very valuable the fact there are slides explaining all the code.