Rendering along the Hilbert Curve

Based on the seminal work on Array-RQMC methods and rank-1 lattice sequences by Pierre L'Ecuyer and collaborators, we introduce efficient deterministic algorithms for image synthesis. Enumerating a low discrepancy sequence along the Hilbert curve superimposed on the raster of pixels of an image, we achieve noise characteristics that are desirable with respect to the human visual system, especially at very low sampling rates. As compared to the state of the art, our simple algorithms neither require randomization, nor costly optimization, nor lookup tables. We analyze correlations of space-filling curves and low discrepancy sequences, and demonstrate the benefits of the new algorithms in a professional, massively parallel light transport simulation and rendering system

Quasi-Monte Carlo Algorithms (not only) for Graphics Software

Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We then take a look at massively parallel quasi-Monte Carlo integro-approximation for image synthesis by light transport simulation. Beyond superior uniformity, low discrepancy points may be optimized with respect to additional criteria, such as noise characteristics at low sampling rates or the quality of low-dimensional projections

Filter-adapted spatiotemporal sampling for real-time rendering

Stochastic sampling techniques are ubiquitous in real-time rendering, where performance constraints force the use of low sample counts, leading to noisy intermediate results. To remove this noise, the post-processing step of temporal and spatial denoising is an integral part of the real-time graphics pipeline. The main insight presented in this paper is that we can optimize the samples used in stochastic sampling such that the post-processing error is minimized. The core of our method is an analytical loss function which measures post-filtering error for a class of integrands - multidimensional Heaviside functions. These integrands are an approximation of the discontinuous functions commonly found in rendering. Our analysis applies to arbitrary spatial and spatiotemporal filters, scalar and vector sample values, and uniform and non-uniform probability distributions. We show that the spectrum of Monte Carlo noise resulting from our sampling method is adapted to the shape of the filter, resulting in less noisy final images. We demonstrate improvements over state-of-the-art sampling methods in three representative rendering tasks: ambient occlusion, volumetric ray-marching, and color image dithering. Common use noise textures, and noise generation code is available at https://github.com/electronicarts/fastnoise.Comment: 18 pages, 12 figure

Editing and Advocacy

Good editors don’t just see the sentence that was written. They see the sentence that might have been written. They know how to spot words that shouldn’t be included and summon up ones that haven’t yet appeared. Their value comes not just from preventing mistakes but from discovering new ways to improve a piece of writing’s style, structure, and overall impact. This book— which is based on a popular course taught at the University of Chicago Law School, the University of Michigan Law School, and the UCLA School of Law— is designed to help you become one of those editors. You’ll learn how to edit with empathy. You’ll learn how to edit with statistics. You’ll learn, in short, a wide range of compositional skills you can use to elevate your advocacy and better champion the causes you care about the most. An All-American soccer player in college who holds both a PhD in English and a JD, Professor Patrick Barry joined the University of Michigan Law School after clerking for two federal judges and working in legal clinics devoted to combatting human trafficking and reforming the foster care system. He is the author of several books on advocacy—including Good with Words: Writing and Editing, The Syntax of Sports, and Notes on Nuance—and regularly puts on workshops for law firms, state governments, and nonprofit organizations. He also teaches at the University of Chicago Law School and has developed a series of online courses for the educational platform Coursera.https://repository.law.umich.edu/books/1116/thumbnail.jp

Klipsun Magazine, 2002, Volume 32, Issue 02 - January

Former New York Times Sunday editor Lester Markle once said, What you see is the news, what you know is background and what you feel is opinion. As a magazine staff, our job is to see the news — to scope with watchful eyes for newsworthy stories that will interest our readers. This quarter’s Klipsun staff sought stories with this mission in mind. In Pay Attention, a reporter interviewed a Western student who sells her own prescribed Attention Deficit Disorder drugs, Ritalin and Adderall, to students who decide they need the additional help while studying late at night. In The Lab Down Under, another reporter ventured into Western’s animal lab — a place many people have heard about, but few have actually seen. In lieu of these controversial topics, it s our hope that readers will have the background they need to establish a feeling or opinion about the stories in this issue.https://cedar.wwu.edu/klipsun_magazine/1211/thumbnail.jp