acquired material models have a high memory footprint which limits applicability;
• it is not easy to assess the accuracy of a material model or a measurement setup.
1.2 SCOPE OF THE BOOK
This book provides an overview of reflection functions, the state-of-the-art material models and reflection acquisition setups, and could be seen as a beginner’s guide providing existing techniques for material representation and acquisition in computer graphics, aimed to help in selecting the most appropriate reflectance models and measurement technique for a specific problem. The focus is mainly on current Bidirectional Reflectance Distribution Function (BRDF) representations and acquisition setups, although different reflectance functions will be described where appropriate. For better understanding of the reflectance topic, we begin with a brief overview of the existing reflectance functions, provided in Chapter 2.
Selecting a suitable reflectance model to render a virtual material is not a straightforward task since each reflectance model often aims to represent a specific (subset of) properties, with the result that a given model can describe plastic very well but not metals and so on; BRDF models are described in Chapter 3, where we also describe some tools for BRDF visualization and fitting. In this book we also present different acquisition setups, ranging from low to high cost, each with a varying degree of accuracy. Reflectance acquisition setups are described in Chapter 4, where we guide the reader through available techniques, providing pros and cons of each setup.
For relevant background in mathematics we suggest some additional readings, such as Ström et al. [SAA15]; as for the physics background the reader can find more details in [Gla94].
CHAPTER 2
Reflectance Functions
Human perception of a material depends on how the light that reflected, transmitted, absorbed by an object and reaches the viewer [DR05]. Hence, the appearance of materials may vary significantly depending on a wide range of properties such as color, smoothness, geometry, roughness, reflectance and angle from which the material is viewed and lighting directions.
Clearly not all materials interact with light in the same way: some let part of the light go through the surface, even to the extent of being transparent or semi-transparent; some scatter the light back, toward the light source itself; others show a mirror-like behavior. A ray of light can hit a surface at particular point of an object surface and possibly “travel” under its surface in different directions before leaving the surface in a different spot, after some time, with a totally different direction than initially. The most general reflectance function hence would need to take into account a number of variables (namely 16), which includes the wavelength of the incident ray of light (1 variable) and its direction (2 variables), the time when the ray of light hits the surface (1 variable) and the location on the surface (3 variables), the wavelength (1 variable) and direction (2 variables) of the ray of light leaving the surface at a (possibly) different location on the surface (3 variables) after some time (1 variable), and it must also account for the transmittance direction though the surface (2 variables). These parameters and the parametrization of such a general reflectance function RF are summarized in the following Table 2.1 and Equation 2.1:
The reflectance function RF needs to be measured for each wavelength in the visible spectrum or, at the very least, for the color channels of the RGB color space. Such a reflectance function, schematized in Figure 2.1, can fully describe a material appearance; however, due to its high dimensionality it is currently unfeasible to measure and would produce a vast amount of data, which cannot be handled by current computer graphics and virtual reality applications, considering also that the most general definition of a RF includes the dependence on the polarization state of the incident and reflected light.
For these reasons, in computer graphics and related fields it is customary to rely on several classes of simplified reflectance functions, obtained by discarding some dimensions, more suited for a practical use; in Figure 2.2 we report the taxonomy of the reflectance functions introduced in this section, along with their parameterizations.
The aforementioned simplifications are obtained by assuming the radiance to be constant along the rays of light, which allows discarding the z coordinate of the points on the surface under consideration. By dropping the dependency on the time (ti and t0, hence assuming that the light transport does not take a measurable time), on the wavelength (λi and λ0), thus assuming that the interaction with the surface does not change the wavelength of the light and restricting our attention to the RGB color bands) and assuming no transmittance (θt = ϕt = 0), we obtain the Bidirectional Surface Scattering Reflectance Distribution Function (BSSRDF), the most complex reported in Figure 2.2, which has 8 dimensions. The BSSRDF is able to represent a ray of light incident at a point on the surface, traveling under the surface where it gets scattered in different directions before leaving the surface from a different point and in a different direction. Many common translucent materials like milk, skin and alabaster are characterized by their subsurface scattering behavior that smooth the appearance of surface details, with the light shining through them. Thanks to its properties the BSSRDF is able to describe phenomena like translucency, self shadowing, self occlusions and inter-reflections. Unfortunately, it is still a very complex function to measure and often simpler representations are preferred over it.
Table 2.1: Parameters of a general reflectance function
Figure 2.1: Schematic representation of the general reflectance function RF.
Figure 2.2: Reflectance functions.
If we assume that the ray o light leaves the surface at the same location where it was incident (hence xi = xr = x, yi = yr = y), we obtain the Bidirectional Texture Function (BTF), a 6-dimensional representation able to describe not only the local variations in reflectance but also the mesoscopic effects due to small-scale geometry, like self-shadowing, self-occlusions and inter-reflections: BTF(x, y, θi, ϕi, θr, ϕr). The term BTF was first introduced by Dana et al. [DVGNK99] as an image-based representation that can describe the fine-scale appearance of a rough surface. The mesoscopic effects are difficult to quantify and separate from the measured data, hence BTF acquisition generally needs a large number of samples of the surface as well as high-end hardware support due to lengthy acquisition times and storage demands [HF13]. Nevertheless, there exist low cost acquisition setups, like the kaleidoscopic device by Han and Perlin [HP03] or the more recent mechanical gantry with rotating arms by Filip et al. [FVK14], built using a toy construction set. BTFs generally result in very realistic material appearance. The first BTF database, described in [DVGNK99], contains
