Marcos Fajardo

Importance Sampling Techniques for Path Tracing in Participating Media

We introduce a set of robust importance sampling techniques which allow efficient calculation of direct and indirect lighting from arbitrary light sources in both homogeneous and heterogeneous media. We show how to distribute samples along a ray proportionally to the incoming radiance for point and area lights. In heterogeneous media, we decouple ray marching from light calculations by computing a representation of the transmittance function that can be quickly evaluated during sampling, at the cost of a small amount of bias. This representation also allows the calculation of another probability density function which can direct samples to regions most likely to scatter light. These techniques are orthogonal and can be combined via multiple importance sampling to further reduce variance. Our method has very modest per‐ray memory requirements and does not require any preprocessing, making it simple to integrate into production ray tracing based renderers.

An area-preserving parametrization for spherical rectangles

We present an area‐preserving parametrization for spherical rectangles which is an analytical function with domain in the unit rectangle [0, 1]2 and range in a region included in the unit‐radius sphere. The parametrization preserves areas up to a constant factor and is thus very useful in the context of rendering as it allows to map random sample point sets in [0, 1]2 onto the spherical rectangle. This allows for easily incorporating stratified, quasi‐Monte Carlo or other sampling strategies in algorithms that compute scattering from planar rectangular emitters.

Unlighting the Parthenon

We present a method that extends techniques in [Yu and Malik 1998] and [Debevec 1998] to estimate the surface colors of a complex scene with diffuse surfaces lit by natural outdoor illumination. Given a model of the scene’s geometry, a set of photographs of the scene taken under natural illumination, and corresponding measurements of the illumination, we can calculate the spatially-varying diffuse surface reflectance. The process employs a simple iterative inverse global illumination technique to compute the surface colors for the scene which, when rendered under the recorded illumination, best reproduce the appearance in the photographs. The results can then be used to render the scene under novel illumination.

The path tracing revolution in the movie industry

As path tracing allows for more realistic and faster lighting, an increasing number of movies are created the physically based way. With examples from recent movies, the architectures and novel workflows of the next generation of production renderers are introduced to a wide audience including technical directors, artists, and researchers.

BSSRDF importance sampling

Light propagation within translucent materials can be described by a BSSRDF [Jensen et al. 2001]. The main difficulty in integrating this effect lies in the generation of well-distributed samples on the surface within the support of the rapidly decaying BSSRDF profile. Jensen suggested that these points could be importance sampled but did not provide implementation details. More recently, Walter et al. [2012] and Christensen et al. [2012] proposed other sampling methods which can still suffer from excessive variance.

Blue-noise dithered sampling

The visual fidelity of a Monte Carlo rendered image depends not only on the magnitude of the pixel estimation error but also on its distribution over the image. To this end, state-of-the-art methods use high-quality stratified sampling patterns, which are randomly scrambled or shifted to decorrelate the individual pixel estimates. While random pixel decorrelation yields an eye-pleasing whitenoise image error distribution, it is far from perceptually optimal. We show that visual fidelity can be substantially improved by instead correlating the samples among pixels in a way that minimizes the low-frequency content in the output noise. Inspired by digital halftoning, our blue-noise dithered sampling method can produce significantly more faithful images, especially at low sampling rates.

Recent advances in light transport simulation: some theory and a lot of practice

We are witnessing a renewed research interest in robust and efficient light transport simulation based on statistical methods. This research effort is propelled by the desire to accurately render general environments with complex materials and light sources, which is often difficult with the industry-standard ad hoc solutions. In addition, it has been recognized that advanced methods, which are able to render many effects in one pass without excessive tweaking, increase artists productivity and allow them to focus on their creative work. For this reason, the movie industry is shifting away from approximate rendering solutions towards physically-based rendering methods, which poses new challenges in terms of strict requirements on high image quality and algorithm robustness. Many of the recent advances in light transport simulation, such as new Markov chain Monte Carlo methods, the robust combination of bidirectional path tracing with photon mapping, or path space filtering are made possible by interpreting light transport as an integral in the space of light paths. However, there is a great deal of confusion among practitioners and researchers alike regarding these path space methods. The main contribution of the theoretical part of the course is a coherent review of the path integral formulation of light transport and its applications, including the most recent ones. We show that rendering algorithms that may seem complex at first sight, are in fact naturally derived from this general framework. We also show that the path integral framework makes the extension of the surface-based algorithm to volumetric media extremely simple. The course includes an extensive empirical comparison of the various light transport algorithms. A substantial part of the course is then devoted to the application of advanced light transport simulation and path sampling methods in practical rendering tasks in architectural visualization and VFX.

Importance sampling of area lights in participating media

We focus on the problem of single scattering in homogeneous volumes and develop a new importance sampling technique that avoids the singularity near point light sources. We then generalize our method to area lights of arbitrary shapes.

Path tracing in production - part 1: production renderers

The last few years have seen a decisive move of the movie making industry towards rendering using physically-based methods, mostly implemented in terms of path tracing. Increasing demands on the realism of lighting, rendering and material modeling, paired with a working paradigm that very naturally models the behaviour of light like in the real world mean that more and more movies each year are created the physically-based way. This shift has also been recently recognised by the Academy of Motion Picture Arts and Sciences, which in this years SciTech ceremony has awarded three ray tracing renderers for their crucial contribution to this move. While the language and toolkit available to the technical directors get closer and closer to natural language, an understanding of the techniques and algorithms behind the workings of the renderer of choice are still of fundamental importance to make efficient use of the available resources, especially when the hard-learned lessons and tricks from the previous world of rasterization-based rendering can introduce confusion and cause costly mistakes. In this course, the architectures and novel possibilities of the next generation of production renderers are introduced to a wide audience including technical directors, artists, and researchers. This is the first part of a two part course. While the first part focuses on architecture and implementation, the second one focuses on usage patterns and workflows.

Area-Preserving Parameterizations for Spherical Ellipses

We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area‐preserving mappings from the unit square [0,1]2 to a spherical ellipse (i.e. the projection of the disk onto the unit sphere). These mappings allow for low‐variance stratified sampling of direct illumination from disk‐shaped light sources. We discuss how to efficiently incorporate our methods into a production renderer and demonstrate the quality of our maps, showing significantly lower variance than previous work.