Unity Publications

At Unity, we do research for Graphics, AI, Performance and much more. We share that research with you and the community through talks, conferences and journals. See below for the latest publications.

Sampling the GGX Distribution of Visible Normals

Eric Heitz - JCGT 2018

Importance sampling microfacet BSDFs using their Distribution of Visible Normals (VNDF) yields significant variance reduction in Monte Carlo rendering. In this article, we describe an efficient and exact sampling routine for the VNDF of the GGX microfacet distribution. This routine leverages the property that GGX is the distribution of normals of a truncated ellipsoid and sampling the GGX VNDF is equivalent to sampling the 2D projection of this truncated ellipsoid. To do that, we simplify the problem by using the linear transformation that maps the truncated ellipsoid to a hemisphere. Since linear transformations preserve the uniformity of projected areas, sampling in the hemisphere configuration and transforming the samples back to the ellipsoid configuration yields valid samples from the GGX VNDF.

Paper
Bib
Sample Code

Analytische Berechnung eines Raumwinkels, der von einem beliebig gesetzten Ellipsoid bei einer Punktquelle geschnitten wird

Eric Heitz –  Kerntechnische Messgeräte und -methoden in der Physikforschung 2018

Wir präsentieren ein geometrisches Verfahren für die Berechnung einer Ellipse, die denselben Raumwinkelbereich wie ein beliebig gesetztes Ellipsoid schneidet. Damit wird es möglich, existierende analytische Raumwinkelberechnungen von Ellipsen auf Ellipsoide anzuwenden. Unser Ansatz besteht in der Anwendung linearer Transformation am Ellipsoid, sodass dieses zu einer Kugel umgeformt wird, von welcher eine Scheibe berechnet werden kann, die denselben Raumwinkel einnimmt. Wir demonstrieren, wie die Anwendung einer invertierten linearen Transformation auf diese Scheibe eine Ellipse erzeugt, die denselben Raumwinkelbereich wie das Ellipsoid schneidet. Wie stellen eine MATLAB-Implementierung unseres Algorithmus bereit und können ihn mathematisch validieren.

Verlegerversion
Kostenlose Autorendruckversion

Eine Beobachtung zum Streckenlängen-Sampling mit nicht-exponentiellen Verteilungen

Eric Heitz, Laurent Belcour - Tech Report 2018

Beim Streckenlängen-Sampling handelt es sich um den Vorgang des Samplings zufälliger Intervalle gemäß einer bestimmten Entfernungsverteilung. Das bedeutet, dass keine punktuelle Entfernung von der Entfernungsverteilung bestimmt wird, sondern ein Intervall möglicher Entfernungen. Der Streckenlängen-Sampling-Prozess ist korrekt, wenn die erwarteten Intervalle der Zielentfernungsverteilung entsprechen. Anders ausgedrückt: Der Durchschnittswert der Sample-Intervalle sollte zum Wert der Entfernungsverteilung tendieren, je mehr Sample-Intervalle bestimmt werden. Hier muss deutlich angemerkt werden, dass die Entfernungsverteilung, die für die Bestimmung von punktuellen Entfernungs-Samples verwendet wird, und die Streckenlängenverteilung, die für die Bestimmung von Sample-Intervallen verwendet wird, nicht dasselbe sind. Der Unterschied kann überraschend sein. Unseres Wissens nach wurde das Streckenlängen-Sampling hauptsächlich im Transportwesen studiert, wo die Entfernungsverteilung exponentiell ist: In diesem Fall ist sowohl die Entfernungsverteilung als auch die Streckenlängenverteilung dieselbe exponentielle Verteilung. Im Allgemeinen sind sie jedoch nicht gleich, wenn die Verteilung nicht exponentiell ist.

Veröffentlichung

Kombination analytischer Direktbeleuchtung und stochastischer Schatten

Eric Heitz, Stephen Hill (Lucasfilm), Morgan McGuire (NVIDIA) - I3D 2018 (Short Paper) (Preis für beste Paper-Präsentation)

In diesem Paper schlagen wir einen Verhältniskalkulator für die Direktbeleuchtungsgleichung vor, mit dem wir analytische Beleuchtungstechniken mit stochastischen Raytracing-Schatten kombinieren und deren Korrektheit aufrechterhalten können. Unser Hauptbeitrag dazu besteht darin, zu zeigen, dass die Schattenbeleuchtung in das Produkt der unbeschatteten Beleuchtung und beleuchtungsgewichteten Schatten aufgeteilt werden kann. Diese Terme können separat berechnet werden, möglicherweise sogar mit unterschiedlichen Verfahren, ohne die Genauigkeit des finalen Ergebnisses, das aus deren Produkt entsteht, zu beeinträchtigen. Die Formulierung erweitert den Einsatzbereich analytischer Beleuchtungstechniken auf Raytracing-Anwendungen, wo deren Einsatz bisher vermieden wurde, da sie keine Schatten umfassten. Wir nutzen solche Methoden, die zu scharfen und rauschfreien Schatten im Bild mit unbeschatteter Beleuchtung führen, und wir berechnen das Bild mit gewichteten Schatten durch stochastisches Raytracing. Der Vorteil der Beschränkung der stochastischen Berechnung auf das Bild mit gewichteten Schatten liegt darin, dass im finalen Ergebnis ein Rauschen nur im Schattenbereich sichtbar ist. Weiterhin entfernen wir Rauschen in einem separaten Prozess von beleuchteten Bereichen, sodass auch aggressive Rauschentfernung nur die Schatten übermäßig weichzeichnet, hochfrequente Schattendetails (Texturen, Normal-Maps, usw.) aber unangetastet lässt.

Veröffentlichung
Zusätzliche
Folien
Code + Demo

Tiling of Procedural Noise

Aleksandr Kirillov

Procedural noise functions have many applications in computer graphics, ranging from texture synthesis to atmospheric effect simulation or to landscape geometry specification. Noise can either be precomputed and stored into a texture, or evaluated directly at application runtime. This choice offers a trade-off between image variance, memory consumption and performance.

Advanced tiling algorithms can be used to decrease visual repetition. Wang tiles allow a plane to be tiled in a non-periodic way, using a relatively small set of textures. Tiles can be arranged in a single texture map to enable the GPU to use hardware filtering.

Paper

High-Performance By-Example Noise using a Histogram-Preserving Blending Operator

Eric Heitz, Fabrice Neyret (Inria) - HPG 2018 (Best Paper Award)

We propose a new by-example noise algorithm that takes as input a small example of a stochastic texture and synthesizes an infinite output with the same appearance. It works on any kind of random-phase inputs as well as on many non-random-phase inputs that are stochastic and non-periodic, typically natural textures such as moss, granite, sand, bark, etc. Our algorithm achieves high-quality results comparable to state-of-the-art procedural-noise techniques but is more than 20 times faster

Paper
Supplemental
Slides
Video

Unsupervised Deep Single-Image Intrinsic Decomposition using Illumination-Varying Image Sequences

Louis Lettry (ETH Zürich), Kenneth Vanhoey, Luc Van Gool (ETH Zürich) - Pacific Graphics 2018 / Computer Graphics Forum

Intrinsic Decomposition decomposes a photographed scene into albedo and shading. Removing shading  allows to "delight" images, which can then be reused in virtually relit scenes. We propose an unsupervised learning method to solve this problem.

Recent techniques use supervised learning: it requires a large set of known decompositions, which are hard to obtain. Instead, we train on unannotated images by using time lapse imagery gained from static webcams. We exploit the assumption that albedo is static by definition, and shading varies with lighting. We transcribe this into a siamese training for deep learning.

Paper
Supplemental
Supplemental code

Bib
Slides
 

Efficient Rendering of Layered Materials using an Atomic Decomposition with Statistical Operators

Laurent Belcour - ACM SIGGRAPH 2018

We derive a novel framework for the efficient analysis and computation of light transport within layered materials. Our derivation consists of two steps. First, we decompose light transport into a set of atomic operators that act on its directional statistics. Speci€cally, our operators consist of reflƒection, refraction, scaŠttering, and absorption, whose combinations are sufficient to describe the statistics of light scattŠering multiple times within layered structures. We show that the €first three directional moments (energy, mean and variance) already provide an accurate summary. Second, we extend the adding-doubling method to support arbitrary combinations of such operators eciently. During shading, we map the directional moments to BSDF lobes. We validate that the resulting BSDF closely matches the ground truth in a lightweight and efficient form. Unlike previous methods, we support an arbitrary number of textured layers, and demonstrate a practical and accurate rendering of layered materials with both an offl„ine and real-time implementation that are free from per-material precomputation.

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Supplemental code
Bib
Video
Slides

An Adaptive Parameterization for Material Acquisition and Rendering

Jonathan Dupuy and Wenzel Jakob (EPFL) - ACM SIGGRAPH Asia 2018

One of the key ingredients of any physically based rendering system is a detailed specification characterizing the interaction of light and matter of all materials present in a scene, typically via the Bidirectional Reflectance Distribution Function (BRDF). Despite their utility, access to real-world BRDF datasets remains limited: this is because measurements involve scanning a four-dimensional domain at sufficient resolution, a tedious and often infeasible time-consuming process. We propose a new parameterization that automatically adapts to the behavior of a material, warping the underlying 4D domain so that most of the volume maps to regions where the BRDF takes on non-negligible values, while irrelevant regions are strongly compressed. This adaptation only requires a brief 1D or 2D measurement of the material’s retro-reflective properties. Our parameterization is unified in the sense that it combines several steps that previously required intermediate data conversions: the same mapping can simultaneously be used for BRDF acquisition, storage, and it supports efficient Monte Carlo sample generation.

Paper
Video
Isotropic BRDF Dataset
Anisotropic BRDF Dataset
MERL Database Validation
C++ & Python code
Material Database

Stochastic Shadows

Eric Heitz, Stephen Hill (Lucasfilm), Morgan McGuire (NVIDIA) 

In this paper, we propose a ratio estimator of the direct-illumination equation that allows us to combine analytic illumination techniques with stochastic raytraced shadows while maintaining correctness. Our main contribution is to show that the shadowed illumination can be split into the product of the unshadowed illumination and the illumination-weighted shadow. These terms can be computed separately — possibly using different techniques — without affect- ing the exactness of the final result given by their product.

This formulation broadens the utility of analytic illumination tech- niques to raytracing applications, where they were hitherto avoided because they did not incorporate shadows. We use such methods to obtain sharp and noise-free shading in the unshadowed-illumination image and we compute the weighted-shadow image with stochastic raytracing. The advantage of restricting stochastic evaluation to the weighted-shadow image is that the final result exhibits noise only in the shadows. Furthermore, we denoise shadows separately from illumination so that even aggressive denoising only overblurs shad- ows, while high-frequency shading details (textures, normal maps, etc.) are preserved.

Paper

Adaptive GPU Tessellation with Compute Shaders

Jad Khoury, Jonathan Dupuy, and Christophe Riccio - GPU Zen 2 (to appear)

GPU rasterizers are most efficient when primitives project into more than a few pixels. Below this limit, the Z-buffer starts aliasing, and shading rate decreases dramatically [Riccio 12]; this makes the rendering of geometrically-complex scenes challenging, as any moderately distant polygon will project to sub-pixel size. In order to minimize such sub-pixel projections, a simple solution consists in procedurally refining coarse meshes as they get closer to the camera. In this chapter, we are interested in deriving such a procedural refinement technique for arbitrary polygon meshes.

Paper
Code

Linien- und Scheiben-Licht-Schatten-Effekte in Echtzeit mit linear transformiertem Cosinus

Eric Heitz (Unity Technologies) and Stephen Hill (Lucasfilm) - ACM SIGGRAPH Courses 2017

We recently introduced a new real-time area-light shading technique dedicated to lights with polygonal shapes. In this talk, we extend this area-lighting framework to support lights shaped as lines, spheres and disks in addition to polygons.

Slides
Demo code
WebGL demo for quad, line and disk lights

Mikrofacetten-Normal-Mapping für robustes Monte Carlo Path Tracing

Vincent Schüssler (KIT), Eric Heitz (Unity Technologies), Johannes Hanika (KIT) and Carsten Dachsbacher (KIT) - ACM SIGGRAPH ASIA 2017

Normal mapping imitates visual details on surfaces by using fake shading normals. However, the resulting surface model is geometrically impossible and normal mapping is thus often considered a fundamentally flawed approach with unavoidable problems for Monte Carlo path tracing: it breaks either the appearance (black fringes, energy loss) or the integrator (different forward and backward light transport). In this paper, we present microfacet-based normal mapping, an alternative way of faking geometric details without corrupting the robustness of Monte Carlo path tracing such that these problems do not arise.

Paper

Ein sphärisches, cap-erhaltendes Parametrisierungsverfahren für sphärische Verteilung

Jonathan Dupuy, Eric Heitz and Laurent Belcour - ACM SIGGRAPH 2017

We introduce a novel parameterization for spherical distributions that is based on a point located inside the sphere, which we call a pivot. The pivot serves as the center of a straight-line projection that maps solid angles onto the opposite side of the sphere. By transforming spherical distributions in this way, we derive novel parametric spherical distributions that can be evaluated and importance-sampled from the original distributions using simple, closed-form expressions. Moreover, we prove that if the original distribution can be sampled and/or integrated over a spherical cap, then so can the transformed distribution. We exploit the properties of our parameterization to derive efficient spherical lighting techniques for both real-time and offline rendering. Our techniques are robust, fast, easy to implement, and achieve quality that is superior to previous work.

Paper
Video

Eine praktische Erweiterung der Mikrofacetten-Theorie für die Modellierung variierender Schillereffekte

Laurent Belcour (Unity), Pascal Barla (Inria) - ACM SIGGRAPH 2017

Thin film iridescence permits to reproduce the appearance of leather. However, this theory requires spectral rendering engines (such as Maxwell Render) to correctly integrate the change of appearance with respect to viewpoint (known as goniochromatism). This is due to aliasing in the spectral domain as real-time renderers only work with three components (RGB) for the entire range of visible light. In this work, we show how to anti-alias a thin-film model, how to incorporate it in microfacet theory, and how to integrate it in a real-time rendering engine. This widens the range of reproducible appearances with microfacet models.

Paper
Supplemental
Bib
Video
Code
Slides

Linear-Light Shading with Linearly Transformed Cosines

Eric Heitz, Stephen Hill (Lucasfilm) - GPU Zen (book)

In this book chapter, we extend our area-light framework based on Linearly Transformed Cosines to support linear (or line) lights. Linear lights are a good approximation for cylindrical lights with a small but non-zero radius. We describe how to approximate these lights with linear lights that have similar power and shading, and discuss the validity of this approximation.

Paper

Eine praktische Einführung in die Frequenzanalyse des Lichtteilchentransports

Laurent Belcour - ACM SIGGRAPH Courses 2016

Frequency Analysis of Light Transport expresses Physically Based Rendering (PBR) using signal processing tools. It is thus tailored to predict sampling rate, perform denoising, perform anti-aliasing, etc. Many method have been proposed to deal with specific cases of light transport (motion, lenses, etc). This course aims to introduce concepts and present practical application scenario of frequency analysis of light transport in a unified context. To ease the understanding of theoretical elements, frequency analysis will be introduced in pair with an implementation.

Course

Polygonale Licht-Schatten-Effekte in Echtzeit mit linear transformiertem Cosinus

Eric Heitz, Jonathan Dupuy, Stephen Hill (Ubisoft), David Neubelt (Ready at Dawn Studios) - ACM SIGGRAPH 2016

Shading with area lights adds a great deal of realism to CG renders. However, it requires solving spherical equations that make it challenging for real-time rendering. In this project, we develop a new spherical distribution that allows us to shade physically based materials with polygonal lights in real-time.

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Slides
MATLAB
Plots and Validation
Comparison against Technicolor's Technique
Demo
WebGL Demo
BRDF fitting code
Video

Weiterer Fortschritt hin zur Vereinigung der Mikrofacetten- und Mikroschuppen-Theorien

Jonathan Dupuy and Eric Heitz - EGSR 2016 (E&I)

We study the links between microfacet and microflake theories from the perspective of linear transport theory. In doing so, we gain additional insights, find several simplifications and touch upon important open questions as well as possible paths forward in extending the unification of surface and volume scattering models. First, we introduce a semi-infinite homogeneous exponential-free-path medium that (a) produces exactly the same light transport as the Smith microsurface scattering model and the inhomogeneous Smith medium that was recently introduced by Heitz et al, and (b) allows us to rederive all the Smith masking and shadowing functions in a simple way. Second, we investigate in detail what new aspects of linear transport theory enable a volume to act like a rough surface. We show that this is mostly due to the use of non-symmetric distributions of normals and explore how the violation of this symmetry impacts light transport within the microflake volume without breaking global reciprocity. Finally, we argue that the surface profiles that would be consistent with very rough Smith microsurfaces have geometrically implausible shapes. To overcome this, we discuss an extension of Smith theory in the volume setting that includes NDFs on the entire sphere in order to produce a single unified reflectance model capable of describing everything from a smooth flat mirror all the way to a semi-infinite isotropically scattering medium with both low and high roughness regimes in between.

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Slides

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