A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Single Lobe Algorithms <s> A growing number of real-time applications need graphics with photorealistic quality, especially in the field of training (virtual operation, driving and flightsimulation), but also in the areas of design or ergonomic research. We take a closer look at main deficiencies of today's real time graphics hardware and present solutions for several of the identified problems in the areas of antialiasing and texture-, bumpand reflection mapping. In the second part of the paper, a new method for antialiasing bump maps is explained in more detail. CR Categories and Subject Desscriptors: I.3.1 [Computer Graphics]: Hardware Architecture – Graphics Processors, Raster Display Devices; I.3.3 [Computer Graphics]: Picture/Image generation. Additional <s> BIB001 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Single Lobe Algorithms <s> Complex repetitive scenes containing forests, foliage, grass, hair, or fur, are challenging for common modeling and rendering tools. The amount of data, the tediousness of modeling and animation tasks, and the cost of realistic rendering have caused such kind of scene to see only limited use even in high-end productions. The author describes how the use of volumetric textures is well suited to such scenes. These primitives can greatly simplify modeling and animation tasks. More importantly, they can be very efficiently rendered using ray tracing with few aliasing artifacts. The main idea, initially introduced by Kajiya and Kay (1989), is to represent a pattern of 3D geometry in a reference volume, that is tiled over an underlying surface much like a regular 2D texture. In our contribution, the mapping is independent of the mesh subdivision, the pattern can contain any kind of shape, and it is prefiltered at different scales as for MIP-mapping. Although the model encoding is volumetric, the rendering method differs greatly from traditional volume rendering. A volumetric texture only exists in the neighborhood of a surface, and the repeated instances (called texels) of the reference volume are spatially deformed. Furthermore, each voxel of the reference volume contains a key feature which controls the reflectance function that represents aggregate intravoxel geometry. This allows for ray tracing of highly complex scenes with very few aliasing artifacts, using a single ray per pixel (for the part of the scene using the volumetric texture representation). The major technical considerations of our method lie in the ray-path determination and in the specification of the reflectance function. <s> BIB002 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Single Lobe Algorithms <s> Anisotropic filtering has been developed as a way of increasing the quality of texture mapping. However, a real hard-ware implementation of anisotropic filters implies approximations and simplifications that result in lower quality. In this paper we present a new, efficient hardware oriented anisotropic filtering technique. Specifically, the new algorithm we propose is based on the utilisation of a new distance computation method. This distance generation scheme permits simplification of the algorithm without reducing its quality. Additionally, a classification procedure for the identification of the position of each texel inside the footprint is proposed. This simple procedure permits the reduction of the computational requirements associated with the algorithm. We also present a new method for the computation of the coverage of a texel, based on the storage of a reduced set of possible coverage patterns. The new distance scheme obtains the patterns of all texels from a given texel through simple shift operations. The good quality results obtained with the filtering algorithm we propose, together with the low computational and storage requirements of the architecture we present, makes it a good candidate for hardware implementation. <s> BIB003 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Single Lobe Algorithms <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> BIB004
Schilling BIB001 models the NDFf A with a Gaussian. He represents it with the 2 Â 2 covariance matrix of the microscale slopes, expressed in a tangent frame aligned with n, the average microscale normal. Because each NDF is expressed in its own local tangent frame, this representation cannot be linearly MIP-mapped and interpolated. Olano and North  model the NDFf A with a 3D Gaussian defined by its mean and its 3 Â 3 symmetric covariance matrix AE: The advantage of this representation is that the best 3D Gaussian fit of a mixture of 3D Gaussians is obtained by linear interpolation. More precisely, the mean and the second moments AE þ T of the best Gaussian fit are linear interpolations of the means and second moments of the input Gaussians (see Section 7). Hence, usual MIP-mapping, bilinear and trilinear interpolation methods can be used on these nine parameters, before computing lighting with  . This method is thus very efficient. It also supports anisotropic NDFs. The drawback is that a single Gaussian cannot represent accurately NDFs with clearly distinct lobes. Neyret BIB002 models the NDFf A with the distribution of the normals to an ellipsoid (his method is designed for volumes but could be used as well for surfaces). For an ellipsoid defined by the points p such that As with Gaussians, a mixture of such NDFs is not a NDF of the same form, but it can be approximated with such a NDF, with a matrix Q À1 given by the linear interpolation of the Q À1 matrices of the input NDF. Hence, these matrices can be linearly MIP-mapped and interpolated. Since they are symmetric and can be multiplied by a constant without changing f A , this method requires only five parameters per texel. Olano and Baker BIB004 model the NDFf A with a single Gaussian, as Olano and North  . However, here they use a 2D Gaussian in a tangent plane above the surface: where ¼ ½ x y T = z . Since a common plane is used for all the NDFs, their first and second moments and AE þ T can be linearly MIP-mapped and interpolated. Here, this gives only five parameters per texel, because the Gaussians are 2D. Toksvig  uses a convolution method (see Section 3.1.2). He models the macroscopic NDF p A with an isotropic Gaussian of the angular deviation from the average normal. This requires four parameters for the average normal and for the variance 2 . However, Toksvig only stores , computed with a linear MIP-mapping of the normal map. He then uses the norm of this average normal to estimate the variance 2 : if the norm is almost 1, this means that all the normals n are almost aligned, and so that 2 is almost 0. Conversely, if the norm is less than 1, then 2 is not null. In practice, Toksvig uses 2 % ð1 À k kÞ=k k. Then, in order to compute the convolution in BIB003 , he also approximates f, assumed here to be the Blinn-Phong lobe ðnhÞ , with a Gaussian. This gives the convolution of two Gaussians, which is itself a Gaussian. The result is a Blinn-Phong lobe with a scaled down exponent 0 , i.e., a wider lobe  :