Understanding the Masking-Shadowing Function in Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs 2014-09-01 Microfacet-Based BRDFs Eric Heitz Understanding the Masking-Shadowing Function INRIA ; CNRS ; Univ. Grenoble Alpes in Microfacet-Based BRDFs Eric Heitz INRIA ; CNRS ; Univ. Grenoble Alpes
Understanding the Masking-Shadowing Function in Physically Based Shading in Theory and Practice Introduction 2014-09-01 Microfacet-Based BRDFs → Microfacet theory microfacet normals Physically Based Shading in Theory and Practice In this section of the course, I will be reviewing the theoretical aspects of physically based shading, and microfacet theory in particular. → microfacet normals Microfacet theory 1
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs 2
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs Microfacet theory is fundamental to the design of physically based shading models. 3
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs But it is not only limited to that. It is used in other applications, such as fabrication... 4
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs ...or inverse scattering problems. 5
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs Ideally, these applications would build on a perfect descriptor of real-world scattering. 6
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs But this is either too complicated or impossible. 7
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs So instead we use microfacet theory as an approximation of real-world scattering. Of course, as an approximation, it comes with several limitations. 8
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs The first and most obvious limitation is that microfacet theory is, and ever will be, a subset of real-world scattering: there are some materials that cannot be described by microfacet theory. But this is reasonable, as we cannot expect a single theory to describe the entire universe. 9
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs Another, more serious limitation, is that some so-called “microfacet models” are actually mathematically inconsistent. 10
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs A further difficulty is that we now have so many microfacet models in the field of computer graphics that understanding how they are connected together is not always obvious. 11
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs So, microfacet theory is far from perfect, but it is still one of the best tools we have at our disposal for investigating surface scattering. This is why it is important to keep studying and improving it. 12
Understanding the Masking-Shadowing Function in Associated paper Introduction 2014-09-01 Microfacet-Based BRDFs Associated paper Motivation: improving our understanding and validation of microfacet models This JCGT paper serves as the course notes for this talk and we refer the reader to this paper for the derivations of the equations presented in the slides. The main motivation behind the paper is to improve how we choose and validate microfacet models. We will see that this is closely related to the choice of masking function. Motivation: improving our understanding and validation of microfacet models 13
Understanding the Masking-Shadowing Function in Introduction 2014-09-01 Microfacet-Based BRDFs Another related paper Importance Sampling Microfacet-Based BSDFs using the Distribution of Visible Normals Eric Heitz & Eugene d’Eon EGSR 2014 → a practical follow up of the theoretical knowledge presented in this course Another related paper This paper will not be discussed in this talk, but is a practical follow up of its theoretical content. It is a typical example of how theoretical investigations can have practical consequences: by using our Importance Sampling Microfacet-Based BSDFs understanding of the microfacet model, we were able to design a new using the Distribution of Visible Normals importance sampling technique for microfacet BSDFs. Eric Heitz & Eugene d’Eon EGSR 2014 → a practical follow up of the theoretical knowledge presented in this course 14
Understanding the Masking-Shadowing Function in Previous: 512 spp (88.9s) Ours: 408 spp (87.1s) Introduction 2014-09-01 Microfacet-Based BRDFs Previous: 512 spp (88.9s) Ours: 408 spp (87.1s) A dielectric glass plate ( n = 1 . 5) with anisotropic Beckmann roughness ( α x = 0 . 05, α y = 0 . 4). same rendering time Results from the EGSR sampling paper: for the same rendering time, our technique produces images with less variance. A dielectric glass plate ( n = 1 . 5) with anisotropic Beckmann roughness ( α x = 0 . 05, α y = 0 . 4). same rendering time 15
Understanding the Masking-Shadowing Function in 2014-09-01 Microfacet-Based BRDFs Overview of Microfacet Theory and Related Problems Overview of Microfacet Theory and Related Problems 16
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs To get started, I will give you an overview of how microfacet theory is constructed. 17
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs While the geometric surface (or macrosurface) may appear flat, microfacet theory assumes that a very small and rough microsurface is responsible for the scattering occurring at the material interface. The first step is to model the geometry of this microsurface, in other words: what does it look like? 18
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs Once the geometry of the microsurface has been established, we can compute what parts of it will be visible for a given view direction. 19
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs Once we know what parts of the microsurface are visible, we need to model how they will be interacting with the light. Usually, microfacet models assume that the microfacets are perfectly specular and produce mirror-like reflections. Other models, like Oren and Nayar’s, assume that the microfacets are perfect diffusers. 20
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs Once the microsurface geometry, visibility and material are fixed, we can finally derive the complete microsurface BRDF expression. In the case of specular microfacets, this leads to the famous Cook and Torrance equation. 21
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs In common microfacet papers, the first three derivation steps are considered “previous work”, and the Cook and Torrance equation usually serves as the starting point from which to derive new models. By modifying F , G 2 and D , it is possible to create a wide variety of different models. 22
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs Once a new model has been created, it has to be validated. 23
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs We usually consider a microfacet model to be “physically based” if it is positive, reciprocal, and energy conserving. 24
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs However, those criteria are not sufficient to validate a new model, because they are not restrictive enough. Intuitively, one could come up with some random BRDF model that easily satisfies those three conditions, and yet fails to relate to any meaningful physical model. 25
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs What’s missing? The problem is that these intermediate derivation steps have also their own validation criteria. However, since they are almost never mentioned, these associated criteria are almost never checked. 26
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs It turns out that, within the set of what we call “microfacet models” today, there are some that don’t validate those criteria. Such models should not be called “microfacet based”, nor “physically based”. 27
Understanding the Masking-Shadowing Function in Overview of Microfacet Theory and Related Problems 2014-09-01 Microfacet-Based BRDFs This is probably the main message of this talk. 28
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