A Reflectance Graphics ROBERT L. COOK Lucasfilm Ltd. and KENNETH E. TORRANCE Cornell University Model for Computer A new reflectance model for rendering computer synthesized images is presented. 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. A method for obtaining the spectral energy distribution of the light reflected from an object made of a specific real material is presented, and a procedure for accurately reproducing the color associated with the spectral energy distribution is discussed. The model is applied to the simulation of a metal and a plastic. Categories and Subject Descriptors: 1.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism--color, shading, shadowing, and texture General Terms: Algorithms Additional Key Words and Phrases: image synthesis, reflectance INTRODUCTION The rendering of realistic images in computer graphics requires a model of how objects reflect light. The reflectance model must describe both the color and the spatial distribution of the reflected light. The model is independent of the other aspects of image synthesis, such as the surface geometry representation and the hidden surface algorithm. Most real surfaces are neither ideal specular (mirrorlike) reflectors nor ideal diffuse (Lambertian) reflectors. Phong [14, 15] proposed a reflectance model for computer graphics that was a linear combination of specular and diffuse reflection. The specular component was spread out around the specular direction by using a cosine function raised to a power. Subsequently, Blinn [5, 6] used similar ideas together with a specular reflection model from [23], which accounts for the off- specular peaks that occur when the incident light is at a grazing angle relative to This paper is a revision of a paper that appeared in Computer Graphics, vol. 15, no. 3, 1981, ACM. This work was supported in part by the National Science Foundation under Grant MCS-7811984. Authors' addresses: R. L. Cook, Lucasfflm Ltd., P.O. Box 2009, San Rafael, CA 94912; K. E. Torrance, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853 Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. O 1982 ACM 0730-0301/82/0100-0007 $00.75 ACM Transactions on Graphics, Vol. 1, No. 1, January 1982, Pages 7-24.8 R.L. Cook and K. E. Torrance the surface normal. Whitted [24] extended these models by adding a term for ideal specular reflection from perfectly smooth surfaces. All of these models are based on geometrical optics (ray theory). The foregoing models treat reflection as consisting of three components: ambient, diffuse, and specular. The ambient component represents light that is assumed to be uniformly incident from the environment and that is reflected equally in all directions by the surface. The diffuse and specular components are associated with light from specific light sources. The diffuse component represents light that is scattered equally in all directions. The specular component represents highlights, light that is concentrated around the mirror direction. The specular component was assumed to be the color of the light source; the Fresnel equation was used to obtain the angular variation of the intensity, but not the color, of the specular component. The ambient and diffuse components were assumed to be the color of the material. The resulting models produce images that look realistic for certain types of materials. This paper presents a reflectance model for rough surfaces that is more general than previous models. It is based on geometrical optics and is applicable to a broad range of materials, surface conditions, and lighting situations. The basis of this model is a reflectance definition that relates the brightness of an object to the intensity and size of each light source that illuminates it. The model predicts the directional distribution and spectral composition of the reflected light. A procedure is described for calculating red, green, and blue (RGB) values from the spectral energy distribution. The new reflectance model is then applied to the simulation of a metal and a plastic, with an explanation of why images rendered with previous models often look plastic, and how this plastic appearance can be avoided. THE REFLECTANCE MODEL Given a light source, a surface, and an observer, a reflectance model describes the intensity and spectral composition of the reflected light reaching the observer. The intensity of the reflected light is determined by the intensity and size of the light source and by the reflecting ability and surface properties of the material. The spectral composition of the reflected light is determined by the spectral composition of the light source and the wavelength-selective reflection of the surface. In this section the appropriate reflectance definitions are introduced and combined into a general reflectance model. Figure 1 contains a summary of the symbols used in this model. The geometry of reflection is shown in Figure 2. An observer is looking at a point P on a surface. V is the unit vector in the direction of the viewer, N is the unit normal to the surface, and L is the unit vector in the direction of a specific light source. H is a normalized vector in the direction of the angular bisector of V and L, and is defined by V+L H- length(V + L) ' which is the unit normal to a hypothetical surface that would reflect light ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.A Reflectance Model for Computer Graphics 9 {X 0 D d dw~ Ei F f G H Ii Ii. L 17. k L m N n Ra R Rd R, 8 V W Angle between N and H Angle between L and H or V and H Wavelength Facet slope distribution function Fraction of reflectance that is diffuse Solid angle of a beam of incident light Energy of the incident light Reflectance of a perfectly smooth surface Unblocked
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