A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Parallax Offset <s> We present an extension to texture mapping that supports the representation of 3-D surface details and view motion parallax. The results are correct for viewpoints that are static or moving, far away or nearby. Our approach is very simple: a relief texture (texture extended with an orthogonal displacement per texel) is mapped onto a polygon using a two-step process: First, it is converted into an ordinary texture using a surprisingly simple 1-D forward transform. The resulting texture is then mapped onto the polygon using standard texture mapping. The 1-D warping functions work in texture coordinates to handle the parallax and visibility changes that result from the 3-D shape of the displacement surface. The subsequent texture-mapping operation handles the transformation from texture to screen coordinates. <s> BIB001 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Parallax Offset <s> We present a technique for mapping relief textures onto arbitrary polygonal models in real time, producing correct self-occlusions, interpenetrations, shadows and per-pixel lighting. The technique uses a pixel-driven formulation based on an efficient ray-height-field intersection implemented on the GPU. It has very low memory requirements, supports extreme close-up views of the surfaces and can be applicable to surfaces undergoing deformation. <s> BIB002 </s> A Survey of Nonlinear Prefiltering Methods for Efficient and Accurate Surface Shading <s> Parallax Offset <s> This paper presents a per-pixel ray tracing algorithm with dynamic lighting of surfaces in real-time on the GPU. First, we propose a method for increased precision of the critical ray-height field intersection and adaptive height field sampling. We achieve higher quality results than the existing inverse displacement mapping algorithms. Second, soft shadows are computed by estimating light visibility for the displaced surfaces. Third, we describe an adaptive level-of-detail system which uses the information supplied by the graphics hardware during rendering to automatically manage shader complexity. This LOD scheme maintains smooth transitions between the full displacement computation and a simplified representation at a lower level of detail without visual artifacts. The algorithm performs well for animated objects and supports dynamic rendering of height fields for a variety of interesting displacement effects. The presented method is scalable for a range of consumer grade GPU products. It exhibits a low memory footprint and can be easily integrated into existing art pipelines for games and effects rendering. <s> BIB003
We argue here that the parallax offset can be handled separately from the prefiltering problem. Indeed, prefiltering a map to quickly compute its average value on arbitrary footprints A is independent of the method used to compute A. More precisely, surface bumps whose apparent size is much larger than a pixel can be represented by the underlying coarse mesh on which the maps are defined. The parallax offset is then automatically taken into account during the projection of this mesh on screen. Conversely, surface bumps whose size is much smaller than the footprint area A do not give any visible offset. This leaves the case of surface bumps whose size is of the order of A. In this case, the pixel footprint A 0 on the coarse mesh may not correspond to the correct footprint that must be used, i.e., the orthogonal projection A on the coarse mesh of the pixel footprint S on the complex surface (see Fig. 7 ). However, computing A is independent of evaluating prefiltered maps in A. Hence, the parallax offset can be ignored when prefiltering complex surface maps, and treated separately during rendering. In fact, several methods have been proposed to evaluate this parallax offset, such as Displacement Mapping  , Relief Mapping BIB001 , BIB002 , and Parallax Occlusion Mapping BIB003 . However, these methods only consider "punctual" footprints (they cast rays and not cones), and they do not consider the correct prefiltering of the height maps used for tracing these rays. Still, they could be used as a first approximation to estimate S from the parallax offset and from its partial derivatives, evaluated at the center of A.