A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Direct Method <s> This paper presents a new reflectance model for rendering computer synthesized images. The model accounts for the relative brightness of different materials and light sources in the same scene. It describes the directional distribution of the reflected light and a color shift that occurs as the reflectance changes with incidence angle. The paper presents a method for obtaining the spectral energy distribution of the light reflected from an object made of a specific real material and discusses a procedure for accurately reproducing the color associated with the spectral energy distribution. The model is applied to the simulation of a metal and a plastic. <s> BIB001 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Direct Method <s> ``Bump'''' mapping is a variant of texture mapping where the texture information is used to alter the surface normal. Current techniques to pre-filter textures are all relying on the fact that the texture information can be linearly "factored out" of the shading equation, and therefore can be pre-averaged in some way. This is not the case with bump maps, and those techniques fail to filter them correctly. We propose here a technique to pre-filter bump maps by building a pyramid where each level stores distributions of normal vectors reconstructed from the distribution given by the underlying bump map. The distributions are represented as sums of a small number of Phong-like spreads of normal vectors. The technique, besides allowing an effective and smooth transition between a bump map and a single surface description, gives rise to the concept of a multiple surface, where each point of the single surface is characterized by more than one normal vector. This allows the description of visually complex surfaces by a trivial modification of current local illumination models. When a surface has an underlying microstructure, masking and self-shadowing are important factors in its appearance. Along with the filtering of normals we include the filtering of the masking and self-shadowing information. This is accomplished by computing the limiting angles of visibility and their variance along the two texture axes for the reconstructed distribution of normals. These techniques allow the modeling of any surface whose microstructure we can model geometrically. This includes complex but familiar surfaces such as anisotropic surfaces, many woven cloth, and stochastic surfaces. <s> BIB002 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Direct Method <s> Recent advances in GPU technology have produced a shift in focus for real-time rendering applications, whereby improvements in image quality are sought in addition to raw polygon display performance. Rendering effects such as antialiasing, motion blur and shadow casting are becoming commonplace and will likely be considered indispensable in the near future. The last complete and famous survey on shadow algorithms — by Woo et al. 52 in 1990 — has to be updated in particular in view of recent improvements in graphics hardware, which make new algorithms possible. This paper covers all current methods for real-time shadow rendering, without venturing into slower, high quality techniques based on ray casting or radiosity. Shadows are useful for a variety of reasons: first, they help understand relative object placement in a 3D scene by providing visual cues. Second, they dramatically improve image realism and allow the creation of complex lighting ambiances. Depending on the application, the emphasis is placed on a guaranteed framerate, or on the visual quality of the shadows including penumbra effects or “soft shadows”. Obviously no single method can render physically correct soft shadows in real time for any dynamic scene! However our survey aims at providing an exhaustive study allowing a programmer to choose the best compromise for his/her needs. In particular we discuss the advantages, limitations, rendering quality and cost of each algorithm. Recommendations are included based on simple characteristics of the application such as static/moving lights, single or multiple light sources, static/dynamic geometry, geometric complexity, directed or omnidirectional lights, etc. Finally we indicate which methods can efficiently exploit the most recent graphics hardware facilities. <s> BIB003 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Direct Method <s> Physically-based reflectance models typically represent light scattering as a function of surface geometry at the pixel level. With changes in viewing resolution, the geometry imaged within a pixel can undergo significant variations that result in changing reflectance characteristics. To address these transformations, we present a multiresolution reflectance framework based on microfacet normal distributions within a pixel over different scales. Since these distributions must be efficiently determined with respect to resolution, they are recorded at multiple resolution levels in mipmaps. The main contribution of this work is a real-time mipmap filtering technique for these distribution-based parameters that not only provides smooth reflectance transitions in scale, but also minimizes aliasing. With this multiresolution reflectance technique, our system can rapidly and accurately incorporate fine reflectance detail that is customarily disregarded in multiresolution rendering methods. <s> BIB004 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Direct Method <s> The reflectance of a surface depends upon the resolution at which it is imaged. In this work, we propose to represent this resolution-dependent reflectance as a mixture of multiple conventional reflectance models and present a framework for efficiently rendering the reflectance effects of such mixture models over different resolutions. To rapidly determine reflectance at runtime with respect to resolution, we record the mixture model parameters at multiple resolution levels in mipmaps and propose a technique to minimize aliasing in the filtering of these mipmaps. This framework can be applied to several widely used parametric reflectance models and can be implemented in graphics hardware for real-time processing, using a presented hardware-accelerated technique for nonlinear filtering of mixture model parameters. In addition, shadowing and masking effects can be included into this framework to increase the realism of rendering. With this mixture model filtering and rendering framework, our system can efficiently render the fine reflectance detail that is customarily disregarded in conventional rendering methods. <s> BIB005 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Direct Method <s> We present a real-time method for rendering global illumination effects from large area and environmental lights on dynamic height fields. In contrast to previous work, our method handles inter-reflections (indirect lighting) and non-diffuse surfaces. To reduce sampling, we construct one multi-resolution pyramid for height variation to compute direct shadows, and another pyramid for each indirect bounce of incident radiance to compute interreflections. The basic principle is to sample the points blocking direct light, or shedding indirect light, from coarser levels of the pyramid the farther away they are from a given receiver point. We unify the representation of visibility and indirect radiance at discrete azimuthal directions (i.e., as a function of a single elevation angle) using the concept of a "casting set" of visible points along this direction whose contributions are collected in the basis of normalized Legendre polynomials. This analytic representation is compact, requires no precomputation, and allows efficient integration to produce the spherical visibility and indirect radiance signals. Sub-sampling visibility and indirect radiance, while shading with full-resolution surface normals, further increases performance without introducing noticeable artifacts. Our method renders 512x512 height fields (> 500K triangles) at 36Hz. <s> BIB006 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Direct Method <s> We introduce Linear Efficient Antialiased Normal (LEAN) Mapping, a method for real-time filtering of specular highlights in bump and normal maps. The method evaluates bumps as part of a shading computation in the tangent space of the polygonal surface rather than in the tangent space of the individual bumps. By operating in a common tangent space, we are able to store information on the distribution of bump normals in a linearly-filterable form compatible with standard MIP and anisotropic filtering hardware. The necessary textures can be computed in a preprocess or generated in real-time on the GPU for time-varying normal maps. The method effectively captures the bloom in highlight shape as bumps become too small to see, and will even transform bump ridges into anisotropic shading. Unlike even more expensive methods, several layers can be combined cheaply during surface rendering, with per-pixel blending. Though the method is based on a modified Ward shading model, we show how to map between its parameters and those of a standard Blinn-Phong model for compatibility with existing art assets and pipelines, and demonstrate that both models produce equivalent results at the largest MIP levels. <s> BIB007
The direct method uses the moments of the average function f A ðyÞ, which can be linearly MIP-mapped in a map K A . The reformulated function g is then chosen such that gðK A ; yÞ, seen as a function of y, has moments K A . This method has been used for normal maps, with two moments and with g Gaussian  , BIB007 (see  and  in Section 3). In this case, the 0th moment is not needed: it is always 1 because here, f A is a probability distribution. Seeing f as a set of functions ' y ðmÞ indexed by y, the idea is to write each ' y as a linear combination of some functions B k ðmÞ. This gives coefficients a k depending on the index y, and so the average of ff A ðyÞ ¼ R Aŵ ðxÞfðM x ; yÞdx becomes We then get a linear characterization of f A with the parameters k ¼ def ½. . . B k ðmÞ . . . T . The function g is obtained by truncating the above sum to a finite number of terms. Symmetrically, instead of using B k ðmÞ functions, we can also write f as a linear combination of B k ðyÞ functions: We then get a linear characterization of f A with the parameters k ¼ def ½. . . a k ðmÞ . . . T . This method has been used for horizon maps, with Legendre polynomials BIB006 (compare (44) with BIB001 in Section 4). It has also been used for shadow maps, by using a decomposition of f in Fourier series  (compare BIB003 with  in Section 5). The direct method uses this decomposition on the average function f A . This method has been used for normal maps, with B k functions represented with Blinn-Phong lobes BIB002 or with isotropic Gaussian lobes BIB004 , BIB005 (compare (46) with (20) and (21) in Section 3).