Papers by Andrew Kensler


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Correlated Multi-Jittered Sampling

Andrew Kensler
March 2013

We present a new technique for generating sets of stratified samples on the unit square. Though based on jittering, this method is competitive with low-discrepancy quasi-Monte Carlo sequences while avoiding some of the structured artifacts to which they are prone. An efficient implementation is provided that allows repeatable, ... more

Paper (PDF)

Available as Pixar Technical Memo #13-01


Building an Orthonormal Basis, Revisited

Tom Duff, James Burgess, Per Christensen, Christophe Hery, Andrew Kensler, Max Liani, Ryusuke Villemin
March 2017

Frisvad [2012b] describes a widely-used computational method for augmenting a given single unit vector with two other vectors to produce an orthonormal frame in three dimensions, a useful operation for any physically based renderer. The implementation has a precision problem: as the z component of the input vector approaches -1, floating point cancellation causes ... more

Paper (PDF)


Progressive Multi-Jittered Sample Sequences

Per Christensen, Andrew Kensler, Charlie Kilpatrick
July 2018

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 ... more

Paper (PDF)

Additional materials: [pmj_slides.pdf], [pmj_suppl.pdf]

Computer Graphics Forum (Proceedings of the Eurographics Symposium on Rendering 2018)


RenderMan: An Advanced Path Tracing Architecture for Movie Rendering

Per Christensen, Julian Fong, Jonathan Shade, Wayne Wooten, Brenden Schubert, Andrew Kensler, Stephen Friedman, Charlie Kilpatrick, Cliff Ramshaw, Marc Bannister, Brenton Rayner, Jonathan Brouillat, Max Liani
July 2018

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 was extended over the years with ray tracing and several global illumination algorithms. This paper describes the modern version of ... more

Paper (PDF)


Orthogonal Array Sampling for Monte Carlo Rendering

Wojciech Jarosz, Afnan Enayet, Andrew Kensler, Charlie Kilpatrick, Per Christensen
July 2019

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 for integration. ... more

Paper (PDF)

Additional materials: [images.tar.xz], [supplemental.pdf]