SURVEY OF TEXTURE MAPPINGPaul S. HeckbertPIXARABSTRACTTe xture mapping is one of the most successful new techniques in high quality image synthesis. Its use canenhance the visual richness of raster scan images immensely while entailing only a relatively small increasein computation. The technique has been applied to a number of surface attributes: surface color, surfacenormal, specularity, transparency, illumination, and surface displacement, to name a few. Although the listis potentially endless, the techniques of texture mapping are essentially the same in all cases. We will sur-vey the fundamentals of texture mapping, which can be split into two topics: the geometric mapping thatwarps a texture onto a surface, and the filtering that is necessary in order to avoid aliasing. An extensivebibliography is included.INTRODUCTIONWhy Map Texture?In the quest for more realistic imagery, one of the most frequent criticisms of early synthesized rasterimages was the extreme smoothness of surfaces - they showed no texture, bumps, scratches, dirt, or finger-prints. Realism demands complexity, or at least the appearance of complexity. Texture mapping is a rela-tively efficient means to create the appearance of complexity without the tedium of modeling and renderingev ery 3-D detail of a surface.The study of texture mapping is valuable because its methods are applicable throughout computer graphicsand image processing. Geometric mappings are relevant to the modeling of parametric surfaces in CADand to general 2-D image distortions for image restoration and artistic uses. The study of texture filteringleads into the development of space variant filters, which are useful for image processing, artistic effects,depth-of-field simulation, and motion blur.DefinitionsWe define a texture rather loosely: it can be either a texture in the usual sense (e.g. cloth, wood, gravel) - adetailed pattern that is repeated many times to tile the plane, or more generally, a multidimensional imagethat is mapped to a multidimensional space. The latter definition encompasses non-tiling images such asbillboards and paintings.Te xture mapping means the mapping of a function onto a surface in 3-D. The domain of the function canbe one, two, or three-dimensional, and it can be represented by either an array or by a mathematical func-tion. For example, a 1-D texture can simulate rock strata; a 2-D texture can represent wav es, vegetation[Nor82], or surface bumps [Per84]; a 3-D texture can represent clouds [Gar85], wood [Pea85], or marble[Per85a]. For our purposes textures will usually be 2-D arrays.The source image (texture) is mapped onto a surface in 3-D object space, which is then mapped to the des-tination image (screen) by the viewing projection. Te xture space is labeled (u, v), object space is labeled(xo, yo, zo), and screen space is labeled (x, y).We assume the reader is familiar with the terminology of 3-D raster graphics and the issues of antialiasing[Rog85], [Fol82].author’s address: PIXAR, P.O. Box 13719, San Rafael, CA, 94913.This paper appeared in IEEE Computer Graphics and Applications, Nov. 1986, pp. 56-67. An earlier version ofthis paper appeared in Graphics Interface ’86, May 1986, pp. 207-212.-2-Uses for Texture MappingThe possible uses for mapped texture are myriad. Some of the parameters that have been texture mapped todate are, in roughly chronological order:surface color (the most common use) [Cat74],specular reflection [Bli76],normal vector perturbation (‘‘bump mapping’’) [Bli78a],specularity (the glossiness coefficient) [Bli78b],transparency [Gar85],diffuse reflection [Mil84],shadows, surface displacement, and mixing coefficients [Coo84],local coordinate system (‘‘frame mapping’’) [Kaj85].Our focus in this paper is on the computational aspects of texturing: those tasks common to all types of tex-ture mapping. We will not attempt a thorough survey of the optical and semantic implications of texturing,a careful review of which is available [Car85]. One type of texture mapping warrants particular attention,however: illumination mapping.Illumination mapping is the mapping of specular or diffuse reflection. It is also known as reflection map-ping or environment mapping. Mapping illumination is rather different from mapping other parameters,since an illumination map is not associated with a particular object in the scene but with an imaginary infi-nite radius sphere, cylinder, or cube surrounding the scene [Gre86a]. Whereas standard texture maps areindexed by the surface parameters u and v, a specular reflection map is indexed by the reflected ray direc-tion [Bli76] and a diffuse reflection map is indexed by the surface normal direction [Mil84]. The techniquecan be generalized for transparency as well, indexing by the refracted ray direction [Kay79]. In the specialcase that all surfaces have the same reflectance and they are viewed orthographically the total reflectedintensity is a function of surface orientation only, so the diffuse and specular maps can be merged into one[Hor81]. Efficient filtering is especially important for illumination mapping, where high surface curvatureoften necessitates broad areas of the sky to be averaged.Illumination mapping facilitates the simulation of complex lighting environments, since the time requiredto shade a point is independent of the number of light sources. There are other reasons for its recent popu-larity: it is one of the few demonstrated techniques for antialiasing highlights [Wil83], and it is an inexpen-sive approximation to ray tracing for mirror reflection and to radiosity methods [Gor84] for diffuse reflec-tion of objects in the environment.MAPPINGThe mapping from texture space to screen space is split into two phases, as shown in figure 1. First is thesurface parameterization that maps texture space to object space, followed by the standard modeling andviewing transformations that map object space to screen space, typically with a perspective projection[Fol82]. These two mappings are composed to find the overall 2-D texture space to 2-D screen space map-ping, and the intermediate 3-D space is often forgotten. This simplification suggests texture mapping’sclose ties with image warping and geometric distortion.Scanning OrderThere are three general approaches to drawing a texture mapped surface: a scan in screen space, a scan intexture space, and two-pass methods. The three algorithms are outlined below:-3-SCREEN