A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Interreflections and Subsurface Scattering <s> We describe a physically-based Monte Carlo technique for approximating bidirectional reflectance distribution functions (BRDFs) for a large class of geometries by directly simulating optical scattering. The technique is more general than previous analytical models: it removes most restrictions on surface microgeometry. Three main points are described: a new representation of the BRDF, a Monte Carlo technique to estimate the coefficients of the representation, and the means of creating a milliscale BRDF from microscale scattering events. These allowthe prediction of scattering from essentially arbitrary roughness geometries. The BRDF is concisely represented by a matrix of spherical harmonic coefficients; the matrix is directly estimated from a geometric optics simulation, enforcing exact reciprocity. The method applies to roughness scales that are large with respect to the wavelength of light and small with respect to the spatial density at which the BRDF is sampled across the surface; examples include brushed metal and textiles. The method is validated by comparing with an existing scattering model and sample images are generated with a physically-based global illumination algorithm. CR Categories and Subject Descriptors: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism. <s> BIB001 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Interreflections and Subsurface Scattering <s> Lambert's model for body reflection is widely used in computer graphics. It is used extensively by rendering techniques such as radiosity and ray tracing. For several real-world objects, however, Lambert's model can prove to be a very inaccurate approximation to the body reflectance. While the brightness of a Lambertian surface is independent of viewing direction, that of a rough surface increases as the viewing direction approaches the light source direction. In this paper, a comprehensive model is developed that predicts body reflectance from rough surfaces. The surface is modeled as a collection of Lambertian facets. It is shown that such a surface is inherently non-Lambertian due to the foreshortening of the surface facets. Further, the model accounts for complex geometric and radiometric phenomena such as masking, shadowing, and interreflections between facets. Several experiments have been conducted on samples of rough diffuse surfaces, such as, plaster, sand, clay, and cloth. All these surface demonstrate significant deviation from Lambertian behavior. The reflectance measurements obtained are in strong agreement with the reflectance predicted by the model. <s> BIB002 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Interreflections and Subsurface Scattering <s> Many researchers have been arguing that geometry, bump maps, and BRDFs present a hierarchy of detail that should be exploited for efficient rendering purposes. In practice however, this is often not possible due to inconsistencies in the illumination for these different levels of detail. For example, while bump map rendering often only considers direct illumination and no shadows, geometry-based rendering and BRDFs will mostly also respect shadowing effects, and in many cases even indirect illumination caused by scattered light. In this paper, we present an approach for overcoming these inconsistencies. We introduce an inexpensive method for consistently illuminating height fields and bump maps, as well as simulating BRDFs based on precomputed visibility information. With this information we can achieve a consistent illumination across the levels of detail. The method we propose offers significant performance benefits over existing algorithms for computing the light scattering in height fields and for computing a sampled BRDF representation using a virtual gonioreflectometer. The performance can be further improved by utilizing graphics hardware, which then also allows for interactive display. Finally, our method also approximates the changes in illumination when the height field, bump map, or BRDF is applied to a surface with a different curvature. <s> BIB003 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Interreflections and Subsurface Scattering <s> This paper introduces a simple model for subsurface light transport in translucent materials. The model enables efficient simulation of effects that BRDF models cannot capture, such as color bleeding within materials and diffusion of light across shadow boundaries. The technique is efficient even for anisotropic, highly scattering media that are expensive to simulate using existing methods. The model combines an exact solution for single scattering with a dipole point source diffusion approximation for multiple scattering. We also have designed a new, rapid image-based measurement technique for determining the optical properties of translucent materials. We validate the model by comparing predicted and measured values and show how the technique can be used to recover the optical properties of a variety of materials, including milk, marble, and skin. Finally, we describe sampling techniques that allow the model to be used within a conventional ray tracer. <s> BIB004 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Interreflections and Subsurface Scattering <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> BIB005
The methods in Sections 3, 4, and 5 ignored the interreflections of the incident light between the surface bumps inside the footprint area A. However, these interreflections can have an important effect for surfaces with a high albedo, or with^-shaped bumps. Without them, the surface appears darker than in reality. We also ignored subsurface scattering that could occur inside this footprint. This effect is important for translucent materials: it makes bumps appear smoother by reducing the contrast between parts that are directly lit or not. We are not aware of any nonlinear prefiltering method taking these effects into account. There are several methods to simulate interreflections in height fields, such as in BIB005 , BIB003 , and  . However, these methods compute the interreflections at each frame, they do not prefilter them. Interreflections are sometimes explicitly taken into account in analytical and numerical BRDF models, as in BIB002 or BIB001 . Here, the interreflections are prefiltered, but only for the scales where the individual bumps are no longer visible. The smaller scales, for which maps used nonlinearly for rendering would be needed (such as a bump map), and which are in the scope of our survey, are not addressed. Subsurface scattering has also been represented with an extended BRDF, called a BSSRDF BIB004 . But here again, the fine scales for which maps used nonlinearly for rendering would be needed are not addressed.