Publications
Oct
2025
High-Performance Elliptical Cone Tracing
Computer Graphics Forum (Proceedings of Pacific Graphics 2025)
In this work, we discuss elliptical cone traversal in scenes that employ typical triangular meshes. We derive accurate and numerically-stable intersection tests for an elliptical conic frustum with an AABB, plane, edge and a triangle, and analyze the performance of elliptical cone tracing when using different acceleration data structures: SAH-based K-d trees, BVHs as well as a modern 8-wide BVH variant adapted for cone tracing, and compare with ray tracing. In addition, several cone traversal algorithms are analyzed, and we develop novel heuristics and optimizations that give better performance than previous traversal approaches. The results highlight the difference in performance characteristics between rays and cones, and serve to guide the design of acceleration data structures for applications that employ cone tracing.
Aug
2025
Wave Tracing: Generalizing The Path Integral To Wave Optics
Modeling the wave nature of light and the propagation and diffraction of electromagnetic fields is crucial for the accurate simulation of many phenomena, yet wave simulations are significantly more computationally complex than classical ray-based models. In this work, we start by analyzing the classical path integral formulation of light transport and rigorously study which wave-optical phenomena can be reproduced by it. We then introduce a bilinear path integral generalization for wave-optical light transport that models the wave interference between paths. This formulation subsumes many existing methods that rely on shooting-bouncing rays or UTD-based diffractions, and serves to give insight into the challenges of such approaches and the difficulty of sampling good paths in a bilinear setting. With this foundation, we develop a weakly-local path integral based on region-to-region transport using elliptical cones that allows sampling individual paths that still model wave effects accurately. As with the classic path integral form of the light transport equation, our path integral makes it possible to derive a variety of practical transport algorithms. We present a complete system for wave tracing with elliptical cones, with applications in light transport for rendering and efficient simulation of long-wavelength radiation propagation and diffraction in complex environments.
Jul
2024
A Free-Space Diffraction BSDF
ACM Transactions on Graphics (Proceedings of SIGGRAPH 2024)
Free-space diffractions are an optical phenomenon where light appears to “bend” around the geometric edges and corners of scene objects. In this paper we present an efficient method to simulate such effects. We derive an edge-based formulation of Fraunhofer diffraction, which is well suited to the common (triangular) geometric meshes used in computer graphics. Our method dynamically constructs a free-space diffraction BSDF by considering the geometry around the intersection point of a ray of light with an object, and we present an importance sampling strategy for these BSDFs. Our method is unique in requiring only ray tracing to produce free-space diffractions, works with general meshes, requires no geometry preprocessing, and is designed to work with path tracers with a linear rendering equation. We show that we are able to reproduce accurate diffraction lobes, and, in contrast to any existing method, are able to handle complex, real-world geometry. This work serves to connect free-space diffractions to the efficient path tracing tools from computer graphics.
Aug
2023
On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions
Hacettepe Journal of Mathematics and Statistics
The Hermite-Gauss basis functions have been extensively employed in classical and quantum optics due to their convenient analytic properties. A class of multivariate Hermite-Gauss functions—the anisotropic Hermite-Gauss functions—arise by endowing the standard univariate Hermite-Gauss functions with a positive definite quadratic form. These functions admit useful applications in optics, signal analysis and probability theory, however they have received little attention in literature. In this paper, we examine the properties of these functions, with an emphasis on applications in computational optics.
Nov
2024
A Generalized Ray Formulation For Wave-Optics Light Transport
ACM Transactions on Graphics (Proceedings of SIGGRAPH ASIA 2024)
Under ray-optical light transport, the classical ray serves as a linear and local “point query” of light’s behaviour. Linearity and locality are crucial to the formulation of sophisticated path tracing and sampling techniques, that enable efficient solutions to light transport problems in complex, real-world settings and environments. However, such formulations are firmly confined to the realm of ray optics, while many applications of interest—in computer graphics and computational optics—demand a more precise understanding of light: as waves. We rigorously formulate the generalized ray, which enables linear and weakly-local queries of arbitrary wave-optical distributions of light. Generalized rays arise from photodetection states, and therefore allow performing backward (sensor-to-source) wave-optical light transport. Our formulations are accurate and highly general: they facilitate the application of modern path tracing techniques for wave-optical rendering, with light of any state of coherence and any spectral properties. We improve upon the state-of-the-art in terms of the generality and accuracy of the formalism, ease of application, as well as performance. As a consequence, we are able to render large, complex scenes, as in Fig. 1, and even do interactive wave-optical light transport, none of which is possible with any existing method. We numerically validate our formalism, and make connection to partially-coherent light transport.
Jul
2022
Towards Practical Physical-Optics Rendering
ACM Transactions on Graphics (Proceedings of SIGGRAPH 2022)
Physical light transport (PLT) algorithms can represent the wave nature of light globally in a scene, and are consistent with Maxwell’s theory of electromagnetism. As such, they are able to reproduce the wave-interference and diffraction effects of real physical optics. However, the recent works that have proposed PLT are too expensive to apply to real-world scenes with complex geometry and materials. To address this problem, we propose a novel framework for physical light transport based on several key ideas that actually makes PLT practical for complex scenes. First, we restrict the spatial coherence shape of light to an anisotropic Gaussian and justify this restriction with general arguments based on entropy. This restriction serves to simplify the rest of the derivations, without practical loss of generality. To describe partially-coherent light, we present new rendering primitives that generalize the radiometric radiance and irradiance, and are based on the well-known Stokes parameters. We are able to represent light of arbitrary spectral content and states of polarization, and with any coherence volume and anisotropy. We also present the wave BSDF to accurately render diffractions and wave-interference effects. Furthermore, we present an approach to importance sample this wave BSDF to facilitate bi-directional path tracing, which has been previously impossible. We show good agreement with state-of-the-art methods, but unlike them we are able to render complex scenes where all the materials are new, coherence-aware physical optics materials, and with performance approaching that of “classical” rendering methods.
Mar
2022
Two-Mirror Compact System for Ideal Concentration of Diffuse Light
Journal Of The Optical Society Of America A
We introduce a simple, compact two-mirror system for diffuse light concentration. The design principle is based on local conservation of optical brightness. The system design is flexible, and we are able to compute mirror shapes given arbitrary incident beam direction and target cross-sectional shape. As illustration, we showcase our design for flat and cylindrical target geometries, and we also demonstrate that our system is able to concentrate efficiently along one or two dimensions. We perform numeric experiments that confirm our theoretical results and provide diffuse light concentration very close to the thermodynamic limit in all cases we considered.
Feb
2022
Rendering of Subjective Speckle Formed by Rough Statistical Surfaces
ACM Transactions on Graphics
Tremendous effort has been extended by the Computer Graphics community to advance the level of realism of material appearance reproduction by incorporating increasingly more advanced techniques. We are now able to re-enact the complicated interplay between light and microscopic surface features—scratches, bumps and other imperfections—in a visually convincing fashion. However, diffractive patterns arise even when no explicitly defined features are present: Any random surface will act as a diffracting aperture and its statistics heavily influence the statistics of the diffracted wave fields. Nonetheless, the problem of rendering diffractions induced by surfaces that are defined purely statistically remains wholly unexplored. We present a thorough derivation, from core optical principles, of the intensity of the scattered fields that arise when a natural, partially coherent light source illuminates a random surface. We follow with a probability theory analysis of the statistics of those fields and present our rendering algorithm. All of our derivations are formally proven and verified numerically as well. Our method is the first to render diffractions that produced by a surface described statistically only and bridges the theoretical gap between contemporary surface modelling and rendering. Finally, we also present intuitive artistic control parameters that allow rendering of physical and non-physical diffraction patterns using our method.
Nov
2021
Physical Light-Matter Interaction in Hermite-Gauss Space
ACM Transactions on Graphics (Proceedings of SIGGRAPH ASIA 2021)
Our purpose in this paper is two-fold: introduce a computationally-tractable decomposition of the coherence properties of light; and, present a general-purpose light-matter interaction framework for partially-coherent light. In a recent publication, Steinberg and Yan 2021 introduced a framework that generalises the classical radiometry-based light transport to physical optics. This facilitates a qualitative increase in the scope of optical phenomena that can be rendered, however with the additional expressibility comes greater analytic difficulty: This coherence of light, which is the core quantity of physical light transport, depends initially on the characteristics of the light source, and mutates on interaction with matter and propagation. Furthermore, current tools that aim to quantify the interaction of partially-coherent light with matter remain limited to specific materials and are computationally intensive. To practically represent a wide class of coherence functions, we decompose their modal content in Hermite-Gauss space and derive a set of light-matter interaction formulae, which quantify how matter scatters light and affects its coherence properties. Then, we model matter as a locally-stationary random process, generalizing the prevalent deterministic and stationary stochastic descriptions. This gives rise to a framework that is able to formulate the interaction of arbitrary partially-coherent light with a wide class of matter. Indeed, we will show that our presented formalism unifies a few of the state-of-the-art scatter and diffraction formulae into one cohesive theory. This formulae include the sourcing of partially-coherent light, scatter by rough surfaces and microgeometry, diffraction grating and interference by a layered structure.
Jul
2021
A Generic Framework for Physical Light Transport
ACM Transactions on Graphics (Proceedings of SIGGRAPH 2021)
Physically accurate rendering often calls for taking the wave nature of light into consideration. In computer graphics, this is done almost exclusively locally, i.e. on a micrometre scale where the diffractive phenomena arise. However, the statistical properties of light, that dictate its coherence characteristics and its capacity to give rise to wave interference effects evolve globally: these properties change on, e.g., interaction with a surface, diffusion by participating media and simply by propagation. In this paper, we derive the first global light transport framework that is able to account for these properties of light and, therefore, is fully consistent with Maxwell’s electromagnetic theory. We show that our framework is a generalization of the classical, radiometry-based light transport—prominent in computer graphics—and retains some of its attractive properties. Finally, as a proof of concept, we apply the presented framework to a few practical problems in rendering and validate against well-studied methods in optics.
Apr
2020
Accurate Rendering of Liquid-Crystals and Inhomogeneous Optically Anisotropic Media
ACM Transactions on Graphics
We present a novel method for devising a closed-form analytic expression to the light transport through the bulk of inhomogeneous optically anisotropic media. Those optically anisotropic materials, e.g., liquid crystals and elastic fluids, arise in a plethora of established applications and exciting new research, however current state-of-the-art methods of visually deducing their optical properties or rendering their appearance are either lacking or non-existent. We formulate our light transport problem under the context of electromagnetism and derive, from first principles, a differential equation of the transmitted complex wave fields that fully accounts for the complicated interference phenomena that arise. At the core of our proposed rendering framework is a powerful mathematical representation, carefully crafted to enable us to produce highly accurate analytic approximative solutions for the light transport. This approach is previously unused in computer rendering, and our framework is capable of rendering accurately optically anisotropic materials with varying optically properties at orders of magnitude faster than existing methods. We demonstrate a few practical applications of our method and validate it against polarized photos of liquid-crystals as well as numerically against numerical solvers and qualitatively against brute-force renderings.
Jul
2019
Analytic Spectral Integration of Birefringence-Induced Iridescence
Computer Graphics Forum (Proceedings of the Eurographics Symposium on Rendering, 2019)
Optical phenomena that are only observable in optically anisotropic materials are generally ignored in the computer graphics. However, such optical effects are not restricted to exotic materials and can also be observed with common translucent objects when optical anisotropy is induced, e.g. via mechanical stress. Furthermore accurate prediction and reproduction of those optical effects has important practical applications. We provide a short but complete analysis of the relevant electromagnetic theory of light propagation in optically anisotropic media and derive the full set of formulations required to render birefringent materials. We then present a novel method for spectral integration of refraction and reflection in an anisotropic slab. Our approach allows fast and robust rendering of birefringence-induced iridescence in a physically faithful manner and is applicable to both real-time and offline rendering.
Jul
2018
Efficient Distributed Execution of Multi-component Scenario-based Models
Model-Driven Engineering and Software Development
In scenario-based programming (SBP), the semantics, which enables direct execution of these intuitive specifications, calls, among others, for synchronizing concurrent scenarios prior to every event-selection decision. Doing so even when the running scenarios are distributed across multiple physical system components, may degrade system performance or robustness. In this paper we describe a technique for automated distribution of an otherwise-centralized specification, such that much of the synchronization requirement may be relaxed. The technique calls for replicating the entire scenario-based executable specification in each of the components, locally transforming it in a component-specific manner, and reducing the synchronization requirements to very specific and well-defined points during execution. Our evaluation of the technique shows promising results. Given that relaxed synchronization can lead to what appears as different runs in different components we discuss various criteria for what would constitute acceptable differences, or divergence, in the parallel, distributed runs of almost-identical copies of a single specification.
Feb
2017
Distributing Scenario-Based Models: A Replicate-and-Project Approach
MODELSWARD 2017 — Proceedings of the 5th International Conference on Model-Driven Engineering and Software Development
In recent years, scenario-based modeling has been proposed to help mitigate some of the underlying difficulties in modeling complex reactive systems, by allowing modelers to specify system behavior in a way that is intuitive and directly executable. This modeling approach simplifies the specification of systems that include events occurring in distinct system components. However, when these system components are physically distributed, executing the scenario-based model requires inter-component coordination that may negatively affect system performance or robustness. We describe a technique that aims to reduce the amount of joint event-selection decisions that require coordination and synchronization among distributed system components. The technique calls for replicating the entire scenario-based executable specification in each of the components,and then transforming it in a component-specific manner that induces the required differences in execution while reducing synchronization requirements. In addition to advantages in streamlining design and improving performance, our approach captures the fact that in certain “smart” distributed systems it is often required that components know what rules govern the behavior of other components. Our evaluation of the technique shows promising results.
