Shlomi Steinberg

CS370 Numerical Computation — Spring 2026

Mon, 11 May 2026 12:00:00 +0000

On the Accuracy of Surface Scattering Theories

Wed, 01 Apr 2026 12:00:00 +0000

CS888 Advanced Topics in Computer Graphics — Winter 2026

Thu, 30 Oct 2025 12:00:00 +0000

Course Overview

This seminar-style course will consist primarily of paper presentations and discussions. Students will take turns presenting papers, followed by a group discussion of the relative merits and limitations of the paper in question. Students are also expected to study the presented papers, prepare paper reviews/reports and engage in discussion.

Students will encounter and use a variety of numerical, computational, and mathematical techniques and tools, such as numerical integration, efficient spatial queries, integral equations, stochastic models, signal processing, optics, parallel computation, efficient memory accesses, and so on.

High-Performance Elliptical Cone Tracing

Thu, 28 Aug 2025 12:00:00 +0000

Wave Tracing: Generalizing The Path Integral To Wave Optics

Thu, 28 Aug 2025 12:00:00 +0000

From ray optics to wave optics. In this paper we analyze the classical path integral formulation of light transport, and rigorously study what wave-optical phenomena can be reproduced by it. We show that some effects, like dispersion and scattering by a restricted class of statistical surface models (rendered in image A), fall under its regime. We generalize the classical path integral to a formulation that is able to account for a much wider variety of wave effects, and based on that generalized path integral present a unified framework that is able to: (B) simulate long-wave radiation and its propagation and diffraction in complex environments, for example to compute its signal strength (visualized color-coded); and (C) render optical wave effects, such as diffraction by arbitrary geometry

CS488 Introduction to Computer Graphics — Spring 2025

Wed, 05 Mar 2025 12:00:00 +0000

Class website

CS888 Theoretical Foundations of Light Transport Simulations — Winter 2025

Mon, 05 Aug 2024 12:00:00 +0000

Course Overview

This class will cover the theoretical foundations of light transport, from the perspective of a computer scientist that wishes to perform light transport simulations. The aim is to develop a strong understanding of the fundamentals of modern light transport formulations, their domains of applicability and the accompanying assumptions.

List of topics:

Fermat’s Principle
Ray optics (Hamiltonian optics) & the optical phase space
The transition from ray to wave theories
Diffraction
Polarization
Locality & incoherence in light transport simulations
Optical coherence
Incoherence due to uncertainty

Required prerequisites:

Calculus, linear algebra and ODEs on an undergraduate level

Supplemental text books:

Optics, Hecht
Linear Ray and Wave Optics in Phase Space, Torre
Introduction to the Theory of Coherence and Polarization of Light, Wolf

Text books are not mandatory, but recommended.

A Free-Space Diffraction BSDF

Fri, 05 Apr 2024 12:00:00 +0000

Path tracing simulation of signal coverage. (a) We simulate the propagation of cellular radiation (λ = 10 cm) in an urban scene, consisting of various buildings. The light source is placed on top of the highlighted antenna. (b) Also shown is a top-down view upon the region shadowed by the large buildings. Visualized is the colour-coded irradiance impinging upon the visible surfaces. The scene consists of 181 000 triangles, and the meshes were not optimized for long-wavelength rendering: they admit many small details and wavelength-scale edges, making the computations of free-space diffractions expensive. For comparison, displayed are the ray optics-only renderings. Observe the difference (compared with ray optics) insets: the long-wavelength radiation diffracts around the building edge’s into the shadow regions, yielding a signal distribution that deviates sharply from the ray optics-only simulation. Also notice the multiple interactions (reflections and diffractions) of radiation with the scene—effects which are very difficult to simulate with existing methods.

CS488 Introduction to Computer Graphics — Spring 2024

Tue, 05 Mar 2024 12:00:00 +0000

Class website

CS888 Advanced Topics in Computer Graphics — Rendering — Winter 2024

Fri, 05 Jan 2024 12:00:00 +0000

Course Overview

Rendering is widely used for synthesizing realistic images that we all see in movies, TV commercials, and industrial design. This seminar-style course will consist primarily of paper presentations and discussions. We will primarily focus on offline rendering techniques for physics-based light transport simulation. Students will encounter and use a variety of numerical, computational, and mathematical techniques and tools, such as numerical integration, efficient spatial queries, integral equations, stochastic models, signal processing, optics, parallel computation, efficient memory accesses, and so on. The course takes the style of a seminar: students will take turns presenting papers, followed by a group discussion of the relative merits and limitations of the paper in question. Students are also expected to read each paper and engage in discussion.

On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions

Tue, 23 May 2023 00:00:01 +0000

A Generalized Ray Formulation For Wave-Optical Light Transport

Mon, 27 Mar 2023 12:00:00 +0000

From ray optics to wave optics. In this paper we present the generalized ray: an extension of the classical ray to wave optics. The generalized ray retains the defining characteristics of the ray-optical ray: locality and linearity. These properties allow the generalized ray to serve as a ``point query'' of light's behaviour---the same purpose that the classical ray fulfils in rendering. By using such generalized rays, we enable the rendering of complex scenes, like the ones shown, under rigorous wave-optical light transport. Materials admitting diffractive optical phenomena are visible: e.g., a diffraction grated Aluminium strip dispersing light; a Bornite ore with a layer of copper oxide causing interference; a Brazilian Rainbow Boa, whose scales are biological diffraction grated surfaces; and, a Chrysomelidae beetle, whose colour arises due to naturally-occurring multilayered interference reflectors in its elytron. Our formalism serves as a link between path tracing techniques and wave optics, and admits a highly general validity domain. Therefore, we are able to apply sophisticated sampling techniques, and achieve performance that surpasses the state-of-the-art by orders-of-magnitude. We indicate resolution and samples-per-pixel (spp) count in all figures rendered using our method. While these figures showcase converged (high spp) results, our implementation also allows interactive rendering of all these scenes at 1 spp. Frame times (at 1 spp) for interactive rendering are indicated. Implementation, as well as additional renderings and videos are available in our supplemental material.

Towards Practical Physical-Optics Rendering

Sun, 03 Apr 2022 12:00:00 +0000

Scene rendered with our framework, viewed through a polarization filter (e.g., sunglasses) and lit by sunlight and afternoon sky light. Multiple diffraction optical effects are visible: (a) the glass window and (b) moulded plastic spoke guard admit stress birefringence, which results in iridescence depending on viewing direction; and (c) the metal brake surface on the bicycle's wheels acts as an imperfect diffraction grating, dispersing scattered light. Unlike the state-of-the-art which still depends on classical materials for performance, all the materials in this scene are coherence-aware, physical optics materials, nevertheless, our rendering performance is close to classical radiometric renderers. The appearance of these materials depends on the radiometric, polarimetric, and coherence properties of light.

Two-Mirror Compact System for Ideal Concentration of Diffuse Light

Tue, 15 Feb 2022 12:00:01 +0000

Rendering of Subjective Speckle Formed by Rough Statistical Surfaces

Wed, 26 Jan 2022 12:00:00 +0000

A Stanford Dragon made of chromium rendered under a D65 illuminant. The light source is moderately coherent with a coherence radius of roughly $\sim30$ μm on average when incident upon the Dragon’s surface. The surface was modelled statistically only, therefore the scattered intensity, $I$, can be considered as a stochastic process. In order to render this scattered intensity we decompose it, in a physically and mathematically consistent manner, into its ensemble average, $\langle I\rangle$, and a fluctuating intensity, $\mathfrak{I}$: (left) The ensemble average of the process, $\langle I\rangle$, dominates the scattered energy and is the averaged scattered intensity over all possible realizations of the surface. (middle) The fluctuating intensity is a zero-mean process (only positive values were visualised) that gives rise to diffraction patterns—known as subjective optical speckle—that depend on the statistical properties of the light, surface and the imaging device. (right) The final intensity is then the superposition of the ensemble averaged lobe and fluctuating field.

Physical Light-Matter Interaction in Hermite-Gauss Space

Sat, 31 Jul 2021 12:00:00 +0000

Partially-coherent light transport in a scene with diffractive materials. The insets visualise the shape of the coherence area (see Fig. 4) of light that is sourced from a light source or scattered by matter. A spherical source gives rise to light with (a) highly isotropic spatial coherence, while a cylindrical source produces light that is (b) significantly more coherent in one transverse direction than in the other (a phenomenon we term coherence anisotropy). Light then propagates away from the source and interacts with matter. These physical processes—the coherence of light and light-matter interaction—are mutually-dependant processes: Coherence drives the optical response of the interaction of light with matter, and, conversely, the properties of matter alter the coherence properties of the scattered radiation. (c) Thin coating over the wings of a silver scarab induces interference. The distinct colours on the left and right wings arise solely due to the difference in the spectral composition and coherence of the incident light. The surface is smooth and the scattered light retains the coherence shape of the incident light. (d,e) On the other hand, scatter by rough surfaces induces coherence properties and anisotropies that are dictated by the surface parameters. (f) Diffraction grating by (unrecorded) DVD disks. Note that the secondary diffraction lobes diminish due to the limited spatial coherence of light. One of the primary theoretical conclusions of this paper is that it is the ensemble-averaged reflectivity of the matter that drives the coherence shape of the scattered light. This can be seen in (c) and (f), where the induced interference does not influence the scattered radiation’s coherence properties.

A Generic Framework for Physical Light Transport

Mon, 26 Apr 2021 12:00:00 +0000

The ability of a light beam to produce observable wave interference phenomena evolves globally: A small but powerful white LED source (marked by a yellow circle) illuminates a scene. The light falls upon the head of a desk lamp made of brushed aluminum, however (a) no diffractive effects are visible because the lamp is close to the source. The light beam is then incident upon a Venus de Milo statue made of scratched bronze. The illumination of the upper part of the statue is dominated by direct incident light, and (b) visible interference patterns arise. On the other hand, light reaching the lower parts of the statue is diffused by a large decorative vase filled with water, altering the coherence properties of the light and (c) diminishing the observable diffraction effects. Rendering is done using a bi-directional path tracer that propagates coherence information, under our formalism, from the light sources.

Accurate Rendering of Liquid-Crystals and Inhomogeneous Optically Anisotropic Media

Mon, 03 Feb 2020 12:00:00 +0000

Liquid-crystal shells rendered using our method. The shells are formed when a spherical liquid-crystal droplet suspended in liquid is injected with an optically isotropic liquid (see figure 9 in the paper for an illustration of the geometry). The imaging is performed by passing linearly polarized light, emitted from a source at −𝑦, through the shell and then through a polarizer oriented perpendicular to the source polarization (“cross polarized” light) and finally captured by a camera located at +𝑦. The orientation of the polarizers is depicted in the bottom left corner of the figures. The shells were illuminated using blue (480 nm), green (580 nm), red (630 nm) and white (illuminant E) light. The artefacts around the left and right edges of the rendered shells are numerical errors. See the paper for a comparison with captured micrograph photos of the same liquid-crystal shells.

Fast Complex Error Function and Faddeeva Function

Mon, 29 Jul 2019 04:08:11 +0000

While the real error function is easy to approximate and is available in C++ standard library, the imaginary and complex valued error functions are neither.

Analytic Spectral Integration of Birefringence-Induced Iridescence

Mon, 08 Jul 2019 13:19:31 +0000

(Left) Photo captured through the window of a train using a common handheld device and viewed through the polarising lens of a pair of sunglasses. The window exhibits stress-induced birefringence which gives rise to the visible iridescence. Notice that the visual effect is most powerful when the incident light is reflected off the road as light reflected around the Brewster’s angle is strongly polarized. (Right) An optically anisotropic slab rendered using our method and exhibiting iridescence induced by birefringence as well. Incident light was assumed to be partially polarized.

Efficient Distributed Execution of Multi-component Scenario-based Models

Mon, 30 Jul 2018 20:56:01 +0000

Fast, Shared, Upgradeable Mutex

Sun, 24 Jun 2018 04:25:42 +0000

Mutex operations are generally expensive on modern architectures and impose harsh limits on the concurrent throughput and scalability of an algorithm or system. Nonetheless mutual exclusion is easy to understand, widely applicable and is a prevailing method of solving resource sharing in concurrent systems.

Distributing Scenario-Based Models: A Replicate-and-Project Approach

Wed, 22 Feb 2017 11:02:41 +0000

Designing a Lock-Free, Wait-Free Hash Map

Mon, 28 Sep 2015 19:25:37 +0000

Wait-free algorithms attract vast interest and are an area of intense research, the motivation being that true lock-free algorithms and data structures provide great benefits in terms of performance and scalability over lock-based variants. However designing lock-free systems isn’t a simple matter.

Graduate Students

Mon, 01 Jan 0001 00:00:00 +0000

Currently I am not recruiting additional graduate students.

Students

Ruomai Yang (PhD)
Yiwei Zhang (PhD)
Minha Armada Ju (MMath)
Matthew Avolio (MMath)

FAQ

(To be occasionally updated)

[PhD] Graduate studies at UWaterloo.

Information about the admissions process can be found here. All (full-time) graduate students receive funding. See funding information, tuition and fees, and rough estimates of living costs. If you wish to apply, please get in touch close to the application deadline.
[PhD] Should I pursue PhD studies?

Publications

Mon, 01 Jan 0001 00:00:00 +0000

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Mon, 01 Jan 0001 00:00:00 +0000