Papers by Per Christensen


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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_suppl.pdf], [pmj_slides.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)


Progressive Sampling Strategies for Disk Light Sources

Per Christensen
June 2018

This technical memo compares six different strategies for sampling a disk area light source. We test padding the domain with zero values, rejection sampling, polar mapping, concentric mapping, and two new strategies we call polar4 and concentric4 mapping. We test the six strategies with nine different sample sequences ... more

Paper (PDF)

Available as Pixar Technical Memo #18-02


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)


Importance Resampling for BSSRDF

Ryusuke Villemin, Christophe Hery, Per Christensen
November 2016

We present a method to improve BSSRDF rendering, which reduces variance due to sampling of the scattering exit point. By using importance resampling, we are able to sample any arbitrary diffusion model, taking into account the geometry of the object at the same time. The new method is trivial to implement ... more

Paper (PDF)

Available as Pixar Technical Memo #16-05