# Per H. Christensen's research while affiliated with Pixar Animation Studios and other places

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## Publications (13)

We generalize N‐rooks, jittered, and (correlated) multi‐jittered sampling to higher dimensions by importing and improving upon a class of techniques called orthogonal arrays from the statistics literature. Renderers typically combine or “pad” a collection of lower‐dimensional (e.g. 2D and 1D) stratified patterns to form higher‐dimensional samples f...

Pixar’s RenderMan renderer is used to render all of Pixar’s films and by many film studios to render visual effects for live-action movies. RenderMan started as a scanline renderer based on the Reyes algorithm, and it was extended over the years with ray tracing and several global illumination algorithms.
This article describes the modern version o...

We introduce three new families of stochastic algorithms to generate progressive 2D sample point sequences. This opens a general framework that researchers and practitioners may find useful when developing future sample sequences. Our best sequences have the same low sampling error as the best known sequence (a particular randomization of the Sobol...

Path tracing is one of several techniques to render photorealistic images by simulating the physics of light propagation within a scene. The roots of path tracing are outside of computer graphics, in the Monte Carlo simulations developed for neutron transport. A great strength of path tracing is that it is conceptually, mathematically, and often-ti...

Path tracing is one of several techniques to render photorealistic images by simulating the physics of light propagation within a scene. The roots of path tracing are outside of computer graphics, in the Monte Carlo simulations developed for neutron transport. A great strength of path tracing is that it is conceptually, mathematically, and often-Ti...

Computer graphics researchers have developed increasingly sophisticated and accurate physically-based subsurface scattering BSSRDF models: from the simple dipole diffusion model [Jensen et al. 2001] to the quantized diffusion [d'Eon and Irving 2011] and beam diffusion [Habel et al. 2013] models. We present a BSSRDF model based on an empirical refle...

We present photon beam diffusion, an efficient numerical method for accurately rendering translucent materials. Our approach interprets incident light as a continuous beam of photons inside the material. Numerically integrating diffusion from such extended sources has long been assumed computationally prohibitive, leading to the ubiquitous single-d...

We describe a multiresolution radiosity caching method that enables efficient computation of global illumination (GI) in a single pass in complex CG movie production scenes.

Photon-density estimation techniques are a popular choice for simulating light transport in scenes with complicated geometry and materials. This class of algorithms can be used to accurately simulate inter-reflections, caustics, color bleeding, scattering in participating media, and subsurface scattering. Since its introduction, photon-density esti...

This paper describes how we extended Pixar's RenderMan renderer with ray tracing abilities. In order to ray trace highly complex scenes we use multiresolution geometry and texture caches, and use ray differentials to determine the appropriate resolution. With this method we are able to efficiently ray trace scenes with much more geometry and textur...

In this talk I will describe how we extended Pixar Animation Studios' RenderMan renderer with ray tracing abilities. In order to ray trace highly complex scenes we use multiresolution geometry and texture caches, and use ray differentials to determine the appropriate resolution. With this method we are able to efficiently ray trace scenes with much...

We introduce a tiled 3D MIP map representation of global illumination data. The representation is an adaptive, sparse octree with a ìbrickî at each octree node; each brick consists of 83 voxels with sparse irradiance values. The representation is designed to enable efcient caching. Combined with photon tracing and recent advances in distribution ra...

When rendering only directly visible objects, ray tracing a few levels of specular reflection from large, low-curvaturesurfaces, and ray tracing shadows from point-like light sources, the accessed geometry is coherentand a geometry cache performs well. But in many other cases, the accessed geometry is incoherent and a standardgeometry cache perform...

## Citations

... There has been other progress on combining the integration speed of low-discrepancy sequences, while keeping the pleasing error pattern from blue noise in "Low-Discrepancy Blue Noise Sampling" [1], "A Low-Discrepancy Sampler That Distributes Monte Carlo Errors as a Blue Noise in Screen Space" [10], "Screen-Space Blue-Noise Diffusion of Monte Carlo Sampling Error via Hierarchical Ordering of Pixels" [2], "Orthogonal Array Sampling for Monte Carlo Rendering" [12], and "Progressive Multi-jittered Sample Sequences" [4]. ...

Reference: Using Blue Noise for Ray Traced Soft Shadows

... The control over the appearance of the hair color is based on physical parameters of indi-vidual hair fibers, such as natural melanin concentration/ratio or other artificial dye colorants. In order to improve the user friendliness in production, visual attributes such as the albedo have been introduced in [2] and implemented in Renderman [3] to favor the artistic expression. However, the tuning of these parameters to match the appearance of a physical hair sample is almost impossible without a psycho-visual match. ...

... These sampling techniques are common in computer graphics to attenuate aliasing artifacts while controlling the gap size of unrendered data [6]. ...

Reference: Graph Spectrum Based Seismic Survey Design

... Both direct (Kajiya, 1986;Kalos & Whitlock, 2008;Veach, 1997) and Markov-chain Monte Carlo (Hastings, 1970;Metropolis et al., 1953;Veach & Guibas, 1997) avoid the curse of dimensionality this way when constructing random walks. Moreover, this strategy can even be the most efficient one, as documented, for instance, by the ubiquity of path tracing methods for simulating light transport in the visual effects industry (Christensen & Jarosz, 2016;Fong et al., 2017). Indeed, our method draws significant inspiration from these works. ...

... We have presented the classical building blocks of a state of the art volumetric path tracer which are resumed in Algorithm 2. Note this is a very simplified version to showcase the simplicity of the main unidirectional path tracing loop. Several blocks were omitted such as spectral wavelength discretization [Wilkie et al. 2014, Evans andMcCool 1999] or subsurface scattering for skin and translucent materials [Jensen et al. 2001, Christensen 2015] -which is a simplified version of volumetric light transport. ...

... The resulting 3D heterogeneous diffusion problem can be computed using classical deterministic solvers [Arbree et al. 2011;Koerner et al. 2014], but these methods have seen limited use in rendering due to their need for meshing, global solves, and great care in coupling the diffusion solver with the overarching Monte Carlo rendering algorithm. Practical approaches have typically relied on approximations like homogeneity and local planarity via the dipole and its variants [d'Eon and Irving 2011;Donner et al. 2008;Habel et al. 2013;]-which typically introduce more error than the diffusion assumption itself. Our approach instead allows us to couple a Monte Carlo VRE solver with a fully heterogeneous 3D diffusion solver while avoiding many of these compromises. ...

... Linear motion blur can easily be handled by linearly interpolating the bounding boxes during traversal according to the ray time [3], which yields much tighter bounds than growing the bounding boxes to contain the entire motion path. Because de Casteljau's algorithm is an iterated version of linear interpolation, this can easily be extended to higher-order Bézier interpolation: the control points can be used to define control bounding boxes that are Bézier-interpolated during the traversal (see Figure 35-3). ...

Reference: Ray Tracing of Blobbies

... Photon mapping. Photon mapping is a popular technique of global illumination rendering, which is based on photon density estimation [10]. Arvo [11] first combined density estimation with light transport simulation by introducing particle tracing algorithm. ...

... The last few years have seen a decisive move of the movies making industry towards rendering utilizing physicallybased approaches, mostly implemented in terms of path tracing algorithm [1][2][3] . Besides, because of their generality, fast start-up, and progressive nature, path tracing has been an important method in many applications in scientific visualization, such as video, games et al. [4][5] . Unfortunately, such method takes a prohibitive a lot of time to obtain the images with better quality because of the large number of samples required per pixel [6] . ...

... Wide BVHs. Ray traversal using wide BVHs is common with CPU SIMD ray traversal [Christensen et al. 2006;Dammertz et al. 2008;Ernst and Greiner 2008]. Here, multiple bounding volumes are tested simultaneously with single rays without the need for using ray packets [Benthin et al. 2007;Gunther et al. 2007]. ...

Reference: CPU-style SIMD ray traversal on GPUs