1 Computer for Model A Reflectance Graphics ROBERT L. COOK Lucasfilm Ltd. and KENNETH E. TORRANCE University Cornell The model computer synthesized images is presented. rendering model accounts reflectance for new A brightness for different materials and light sources in the same scene. It describes the the relative of of the reflected light and directional color shift that occurs as the reflectance changes distribution a incidence A method for obtaining the spectral energy distribution of the light reflected with angle. presented, an of a specific real material is made and a procedure for accurately reproducing from object color associated with the spectral energy distribution is discussed. The model is the to the applied simulation a metal and a plastic. of and Subject 1.3.7 [Computer Graphics]: Three-Dimensional Graphics and Categories Descriptors: shadowing, texture shading, Realism--color, and General Terms: Algorithms Words and Phrases: image synthesis, reflectance Additional Key INTRODUCTION requires realistic images in computer graphics of a model of how rendering The reflect light. The reflectance model must objects both the color and the describe spatial of the reflected light. The model is independent of the other distribution of surface synthesis, such as the aspects geometry representation and the image surface algorithm. hidden specular real are neither Most surfaces (mirrorlike) reflectors nor ideal ideal diffuse (Lambertian) reflectors. Phong [14, 15] proposed a reflectance model for computer graphics was a linear combination of specular and diffuse reflection. that specular component spread out around the specular direction by using The was [5, function to a power. Subsequently, Blinn cosine 6] used similar ideas a raised with a specular reflection model from [23], which accounts for the off- together peaks the occur when specular incident light is at a grazing angle relative to that 1981, paper a revision of a paper that appeared This Computer Graphics, vol. 15, no. 3, is ACM. in This was supported in part by work National Science Foundation under Grant MCS-7811984. the Authors' addresses: R. L. Cook, Lucasfflm Ltd., P.O. Box 2009, San Rafael, CA 94912; K. E. Torrance, Sibley School Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853 of not to without fee all or part of this material is Permission provided that the copies are copy granted made distributed for direct commercial advantage, the or copyright notice and the title of the ACM publication and its date appear, and notice is given that copying is by permission of the Association republish, for To copy otherwise, or to Machinery. requires a fee and/or specific Computing permission. O 1982 ACM 0730-0301/82/0100-0007 $00.75 No. ACM on Graphics, Vol. 1, Transactions 1, January 1982, Pages 7-24.

2 8 R.L. and K. E. Torrance Cook surface normal. [24] extended these models by adding a term for the Whitted reflection ideal smooth surfaces. All of these models are from specular perfectly optics theory). geometrical (ray based on treat reflection as consisting of three components: The foregoing models light specular. ambient component represents The that is and diffuse, ambient, be uniformly incident from the environment and that is reflected assumed to all equally by the surface. The diffuse and specular components are in directions diffuse light light sources. The specific component represents with from associated is scattered equally in all directions. light specular component represents that The light is concentrated around the that direction. The specular highlights, mirror was assumed to be the color of the light source; the Fresnel equation component used was obtain the angular variation of the intensity, but not the color, of the to component. The and diffuse components were assumed to be specular ambient of realistic material. The resulting models produce images that look color the the types materials. certain for of surfaces presents reflectance model paper rough a that is more general This for previous models. It is based on geometrical optics and is applicable than a to broad of materials, surface conditions, and lighting situations. The basis of range brightness model reflectance definition that relates the a of an object to this is intensity and size of each the source that illuminates it. The model predicts light the distribution and spectral composition directional the reflected light. A of procedure is described for calculating red, green, and blue (RGB) values from the spectral energy The new reflectance model is then applied to the distribution. of a and a plastic, with an explanation of why images rendered simulation metal models appearance look plastic, and how this plastic previous can be with often avoided. REFLECTANCE THE MODEL light source, a surface, and Given observer, a reflectance model describes the a an and spectral composition of the reflected light reaching intensity observer. the The of the reflected light is determined by the intensity and size of the intensity source the by the reflecting ability and surface properties of light material. and spectral light of the reflected The is determined by the spectral composition the of light source and the wavelength-selective reflection of the composition surface. In this section the appropriate reflectance definitions are introduced and combined into general reflectance model. Figure 1 contains a summary of the a used this model. symbols in geometry of reflection is shown in Figure 2. An observer is looking at a The in P a surface. V is the unit vector on the direction of the viewer, N is the point unit normal to the surface, and L is the unit vector in the direction of a specific bisector light is a normalized vector in the direction of the angular H of source. V and L, and is defined by V+L H- length(V + L) ' reflect which the unit normal to a hypothetical surface that would is light ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.

3 A Reflectance for Computer Graphics 9 Model {X H between N Angle and H H L between Angle or V and and 0 Wavelength D function Facet slope distribution of Fraction diffuse is that reflectance d of angle dw~ a beam of incident Solid light light incident the of Energy Ei Reflectance a of F surface smooth perfectly of hemisphere the fraction Unblocked f Geometrical attenuation factor G and V of bisector angular Unit L H Ii incident the light of intensity Average Intensity Ii. of light ambient incident the light reflected the of Intensity L Fig. 1. Summary symbols. of Intensity of the reflected ambient light 17. coefficient k Extinction light a L direction Unit vector in the of facets Root mean square slope of m N Unit surface normal Index of refraction n Ambient reflectance Ra reflectance Total bidirectional R Diffuse bidirectional reflectance Rd bidirectional reflectance Specular R, that reflectance of is Fraction specular 8 the of direction in vector V Unit viewer weight Relative a facet slope of W N / The reflection. of 2. Fig. geometry from and light source to the viewer, a is the angle between H specularly N, the so and the angle between H and V, is that cos(0) = V.H = 0 The energy of the incident light is expressed as energy per unit time and per of unit the reflecting surface. The intensity of the incident light is similar, area but is expressed per unit projected area and, in addition, per unit solid angle [20, the 8]. angle is the projected area of the light source divided by (Solid square of ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.

4 10 R.L. and K. E. Torrance Cook distance to light source and can be treated as a constant for a distant the the The energy an incoming beam of light is light source.) in d~0i. Ii(N.L) = El or near-mirrors, the incoming Except is reflected over a wide for mirrors beam angles. For this reason, the reflected intensity in any given direction range of the on energy, not just on the incident intensity. The ratio of depends incident intensity to a given direction reflected the incident energy from another the in the a solid angle) is called small bidirectional reflectance. This direction (within is fundamental for the study reflectance reflection (for additional discussion, of see 8]). For each light source, the bidirectional reflectance R is thus [20, Ir /~- El" is intensity viewer from each light source the then reaching The reflected REi = Ir = L) d~i. RIi (N. bidirectional may be split into reflectance components, specular and The two The specular component represents light that is diffuse. from the surface reflected of material. The diffuse component originates from internal scattering (in the the surface light penetrates beneath the which of the material) or from incident surface surface (which occur if the reflections is sufficiently rough). The multiple specular and diffuse components can have different colors if the material is not homogeneous. The reflectance is thus bidirectional where s+d--1. R=sRs+dRa, an to by individual light sources, illumination object may be In direct addition background or ambient illumination. All light that is not direct illuminated by from a specific light source is lumped together into ambient illumi- illumination The amount of light reflected toward the viewer from any particular nation. of significant illumination is small, but the effect is direction when ambient is over entire integrated of illuminating angles. Consequently, it the hemisphere convenient to introduce an ambient (or hemispherical-directional) reflectance, R,. This reflectance is an integral of the bidirectional reflectance R and is thus a linear combination Rs and Rd. For simplicity, we assume that R, is independent of viewing that In addition we assume of the ambient illumination is direction. illumination incident. reflected intensity due to ambient uniformly is defined The by La = The term f is the fraction of the illuminating hemisphere that is not blocked by nearby objects as a corner) [25]. It is given by (such = 1 ¢ (N. L) do, i, f qr J is done over the unblocked part of the illuminating where integration the hemisphere. ACM Transactions on 1982. Vol. 1, No. 1, January Graphics,

5 A Reflectance for Computer Graphics 1 1 Model total intensity the light reaching the observer is the sum of the reflected The of all light plus the reflected intensity from any ambient intensities from sources used f 1, the basic reflectance model that in this paper illumination. Assuming = becomes IiaRa + ~ Iit(N.Ll) dwit(sR~ + dRd). /r ---- l formulation for the effect of light sources with different intensities accounts This projected scene. which may illuminate a different For example, an and areas of with same intensity (Ii) and angle beam illumination (N. L) as illuminating the beam, but with twice the solid angle (do, i) of that beam, will make a another appear as surface bright. An illuminating beam with twice the intensity of twice beam, but the same angle of illumination and solid angle, will also another with surface as twice a bright. make appear from does consider paper reflection of light not other objects in the This the This reflection can be calculated as in [24] or [6] if the surface environment. is perfectly but even this pure specular reflection should be wavelength smooth, dependent. on model implicitly depends reflectance several variables. For The above the intensities depend on wavelength, s and example, depend on the material, d and reflectances depend on these the plus the reflection geometry and variables the surface roughness. The next two sections consider the directional and wave- length dependence the reflectance model. of DISTRIBUTION OF REFLECTED LIGHT DIRECTIONAL THE all and reflect light equally in components directions. Thus ambient diffuse The Ro do Ra depend on the location of the observer. On the other hand, the and not component reflects more light in some directions than in others, so that specular does Rs on the location of the observer. depend be angular the specular component can of described by assuming The spread the surface consists of microfacets, each that which reflects specularly [23]. of Only whose normal is in the facets H contribute to the specular direction component of reflection from L to V. The specular component is F DG -- Rs L) (N. V) " 7r (N. reflected term Fresnel how light is F from each smooth microfacet. The describes is a It of incidence angle and wavelength and is discussed in the next function section. geometrical attenuation factor G The for the shadowing and accounts masking of one facet by another and is discussed in detail in [5, 6, 23]. Briefly, it is 2(N.H)(N.V) 2(N.H)(N.L)~ G=min 1, (V.H) ' ~ J" The facet slope distribution function D represents the fraction of the facets that have are in the direction H. Various facet slope distribution functions oriented ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.

6 1 2 Cook and K. E. Torrance R.L. considered by [5, 6]. One of the formulations he described is the been Blinn [23]: Gaussian model -(~/m)2 D ce = an constant. is arbitrary c where the ones mentioned In Blinn, other facet slope distribution addition to by possible. In particular, models for the scattering of radar and infrared models are surfaces are available and from applicable to visible wavelengths. radiation are Davies described the spatial distribution of electromagnetic example, [9] For from a rough surface made of a radiation electrical conductor. reflected perfect and [3] extended these results to Porteus metals, and Torrance and Bennett real [22] showed that they apply to nonmetals as well. Beckmann [2] Sparrow provided a theory that encompasses all of these materials and is comprehensive to a range of surface conditions ranging from smooth to very applicable wide rough the Beckmann distribution function is For surfaces, rough. 1 m2 c0s40~ e -[(tana)/rn]2 D - the function similar in shape to is three functions mentioned by distribution This The advantage of the Beckmann function is Blinn. it gives the absolute that magnitude the reflectance without introducing arbitrary constants; the disad- of is it requires more computation. vantage that all of the facet Slope distribution functions, the spread of In specular the component on the root mean square depends slope m. Small values of m (rms) signify gentle facet slopes and give a distribution that is highly directional around the specular as shown in Figure 3a for the Beckmann distribution direction, and in 3b for the Gaussian model. Large values of m imply steep model Figure and as a distribution that is spread out, slopes shown in Figures 3c and facet give the the and Gaussian models, respectively. Note Beckmann similarity 3d for the two models. between wavelength dependence of the reflectance The not affected by the surface is roughness for surfaces that are almost completely smooth, which are except have by (wave theory) and which optics a distribution function described physical that is wavelength dependent. The D distribution model accounts for Beckmann this dependence and for the wavelength region between physical and transition geometrical optics (i.e., between very smooth surfaces and rough surfaces). For simplicity, we the cases in which D is wavelength dependent. (For a further ignore see and [9].) discussion, [2] surfaces have two or more scales of roughness, or slope m, and Some be can modeled using two or more distribution by [16]. In such cases, D is functions expressed as a weighted sum of the distribution functions, each with a different value m: of D = Y, wjD(mj), J where mj is the rms slope of the jth distribution and wj is the weight of the jth distribution. sum of these weights is 1. The ACM 1982. on Graphics, Vol. 1, No. 1, January Transactions

7 d n ~ A c~ ~° II ~s c~

8 14 R.L. and K. E. Torrance Cook COMPOSITION OF REFLECTED LIGHT SPECTRAL THE diffuse, The reflectances all depend on wavelength. Ra, Ro, and ambient, specular appropriate term may be obtained from the Rs reflectance spectra F of and the A nonhomogeneous material may have for reflectance the material. different each the three reflectances, though Ra is of to being a linear for spectra restricted Rs combination Rd. of and spectra been measured for thousands of materials and col- Reflectance have for [10, reflectance data are usually The illumination at normal in 17-19]. lected values are normally measured for polished incidence. and must be These surfaces by to obtain the bidirectional reflectance 1/qr a rough surface [20]. multiplied for materials are measured at only a few wavelengths in the visible range Most around to (typically 15), so that values for intermediate wavelengths must be 10 (a simple interpolation seems to be sufficient). The reflectance interpolated linear shown a for normal incidence is mirror for visible wavelengths of copper spectrum 4a. In choosing a reflectance in careful consideration must be Figure spectrum, to conditions under which the the were made. For example, given measurements metals develop an oxide layer with time which can some alter the drastically color [1]. spectral energy of the reflected light is found by multiplying The distribution by spectral of the incident light distribution the reflectance spectrum the energy the surface. of example of this is shown in Figure 4b. The spectral energy An distributions the sun and a number of CIE standard illuminants are available of in [7]. The spectral energy distribution of CIE standard illuminant D6500, which approximates sunlight a cloudy day, is the top curve shown in Figure 4b. The on curve shows corresponding spectral energy distribution of light reflected lower the copper at illuminated by CIE standard illuminant D6500 a normal from mirror the is It multiplying the top curve by obtained reflectance spectrum incidence. by Figure 4a. in general, Rd and F vary with the geometry of reflection. For convenience, we In take reflectance to be the bidirectional subsequently for illumination in a Rd reasonable normal reflecting surface. This is the because the reflec- direction to varies only slightly for incidence angles within about 70 ° of the surface tance normal [21]. specifically allow for the directional dependence of F, however, We the this to a color shift when as directions of incidence and reflection are leads near grazing. The reflectance may be obtained theoretically from the Fresnel equation F a This the reflectance of expresses perfectly smooth, mirrorlike [21]. equation in terms of the index of refraction (n) and the extinction coefficient (k) of surface with surface the angle of illumination (0). In general, both n and k vary the and wavelength, their values are frequently but known. On the other hand, not experimentally measured values of the reflectance at normal incidence are fre- quently known. F, obtain spectral and angular variation To the we have adopted a practical of compromise. If n and k are known, we use the Fresnel equation. If not, but the measured normal is known, we fit the Fresnel equation to the reflectance normal ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.

9 A Reflectance for Computer Graphics 1 5 Model 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 J I i 1 i 0.6 0.5 0.7 0.4 0.8 (a) Energy 0.5 0.6 0.7 0.8 0.4 (b) Fig. 4. (a) Reflectance of a copper mirror for normal incidence. Wavelength is in micrometers. CIE (b) Spectral energy distribution of curve: standard illuminant D6500. Bottom curve: Top Spectral energy distribution of light reflected from a copper mirror illuminated by D6500. ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.

10 16 R.L. and K. E. Torrance Cook for a surface. For nonmetals, for which k = 0, this immedi- reflectance polished For us of the index of refraction n. estimate metals, for which k is gives ately an 0, we set k equal to 0 and get an effective value for n from the generally not The F dependence of reflectance. is then available from the normal angular The normal procedure yields the correct value of F for equation. Fresnel foregoing only a estimate and its angular dependence, which is good weakly incidence of on the extinction coefficient k. dependent illustrate this procedure, the Fresnel equation for unpolarized incident light To k 0 and is = (g- c) [c(g + c) - 1] 1 f - 2 2 ~ 1 + [c(g c) c) --+--~112j ' F - (g--+ where cos(0) = V.H c = 2_ c g2=n2+ 1. the a expression in [5] that missing similar i factor.) At normal incidence, (Note is = 0; so 0 = 1, g= n, and c 2 = (n lJ " F0 + n the for equation Solving gives 1+ 0 - -- n 1-~0" of n determined in this Values are then substituted into the original Fresnel way equation obtain the reflectance F at to angles of incidence. The procedure other may be repeated at other wavelengths to obtain the spectral and directional dependence of reflectance. the dependence of reflectance on wavelength and the angle of incidence The the the with of the reflected light changes that the incidence angle. implies color 5a. spectra are shown in Figure copper As the incidence angle Reflectance for approaches ~r/2, the color of the reflected light approaches (0) color of the the light (since the reflectance F approaches unity). The colors corresponding source the from of white light (CIE standard illuminant D6500) to copper are reflection is as shown of 0 in Figure 5b. It a evident that the color shift from the function Fresnel equations only becomes important as 8 approaches ~/2 (i.e., as the angle between V L approaches ~r). and It of shift is computationally expensive. color can be simplified Calculation the one of two ways: by creating lookup tables or in using the following approxi- by mation. of F are first calculated for Values value of n corresponding to the a average normal reflectance. These values are then used to interpolate between color the the material at 0 =- 0 and the of at 0 = 7r/2, which is the color of color the light source because F,~/2 is 1.0 at every wavelength. For example, let the red ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.

11 A Reflectance Model for Computer Graphics 1 7 0 (a) 0=0 0 = ¢r/2 (b) 0=0 0 = z'/2 (c) 5. Fig. Reflectance of a copper mirror as a function of wavelength and (a) incidence angle. (b) The color of copper as a function of incidence angle. discussed (c) color of copper as approximated by the method The in this paper. ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.

12 18 R.L. and K. E. Torrance Cook of the at normal incidence be Redo and let the red component component color color of incident light be Red./2. Then the red component of the color of the the is at other angles Fo) max(0, Fo - + Redo - Redo) = Redo (Red~/2 F,,/2 - Fo and blue components are interpolated similarly. Figure 5c shows the The green using the approximate procedure to estimate the color of copper as a effect of results incidence approximate procedure yields The that are of angle. function those from the complete (but more similar procedure (Figure 5b). to expensive) foregoing must always be used approximation the spectral energy distri- The if of the reflected light is not known, in which case all of the RGB values bution are estimates. THE RGB DETERMINING VALUES color computer to be realistic, the scene sensation of an a For synthesized the synthesized scene on a color television monitor must be observer watching to equivalent color sensation of an observer watching a approximately the this scene real world. To produce the equivalent color sensation, corresponding in laws of trichromatic color reproduction are used to the the spectral convert energy of the reflected light to the appropriate RGB values for the distribution monitor used. particular being color sensation can be uniquely described by its location in a three- Every color space One such color dimensional is called the XYZ space. A point space. coordinates, this is specified by three space the color's XYZ tristimulus values. in Each spectral energy distribution is associated with a point in the XYZ color space and with tristimulus values. If two spectral energy distributions are thus with the tristimulus values, they produce the same color sensa- associated same are blue metamers. The red, green, and and phosphors of a monitor tion called set illuminated proportions to produce a in of spectral energy distributions can be define a:, region of XYZ space called the gamut of the monitor. The which goal, then, to find fhe proportions of phosphor illumination that produce a spectral is spectral distribution a metamer of the is energy distribution of the energy that light. reflected proportions calculating determined by These the XYZ tristimulus values are distribution are with the spectral energy that of the reflected light and associated then calculating the RGB values that produce a spectral energy distribution with these tristimulus To do this, the spectral energy distribution of the values. functions light by the XYZ matching multiplied (obtained from [7]) reflected is every wavelength. The resulting spectra are at integrated to obtain the XYZ then tristimulus These XYZ values, which values. be precomputed for each can combination of light source type and surface material, are converted by a matrix multiplication to linear luminance values for a particular set of phosphors RGB are and point. The linear luminances white then converted to RGB monitor voltages, taking into account the nonlinearities of the monitor and the effects of [13]. viewing For a more complete description of this procedure, see conditions. ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.

13 A Reflectance for Computer Graphics 19 Model monitor has maximum luminance at which it can reproduce a given The a XYZ chromaticity. represent luminances greater than this values Any that the XYZ of the monitor. To avoid this problem, all outside maximum are gamut lie scene scaled equally so that they all the inside the monitor gamut in values are so that the color with and greatest luminance is reproduced on the usually the at maximum luminance possible for its chromaticity. But even with monitor the spectral with distributions are associated some tristimulus values scaling, energy such outside lie of the monitor. Because the a color cannot be that gamut on the monitor at any luminance, it must be approximated by a reproduced similar color lies inside the monitor gamut. This color may be chosen in that different ways; this paper, we have decided it is appropriate to maintain many for hue, To the color as necessary. same do this, the tristimulus the desaturating which values to a color space in converted locations are specified by XYZ are wavelength and purity. The purity is then reduced while the dominant dominant wavelength thus roughly the hue) is held constant until the color lies inside (and monitor XYZ The resulting color is then converted back to the space. gamut. a and of dominant wavelength {For purity, see [12].) discussion APPLICATIONS the discusses the application of This reflectance model to two particular section classes of materials, metals and plastics. The main consideration is the homoge- neity of material. Substances that are composed of different materials, such the there is material at the surface and another beneath the surface, are that one may components specular and diffuse and that differ in nonhomogeneous have color. transparent has a substrate that is A or white, with embedded typical plastic particles [11]. Thus the light reflected directly from pigment surface is only the slightly in color from the light source. Any color alterations are a result of altered reflectance that the surface material. Light the penetrates into the material of to with interacts Internal reflections thus give rise the a colored, pigments. uniformly distributed diffuse reflection. A plastic may thus be simulated by using a colored diffuse component and a white specular This is just the model used by Phong and Blinn, and component. that is many computer graphics images so have a significant specular it why look like plastic. Figure 6a shows a component copper-colored plastic simulated vase. figure was generated with the following parameters. This lights: Ii = CIE standard illuminant D6500 2 dwi = 0.0001 and 0.0002 Specular: s 0.1 = = reflectance of a vinyl mirror F the = Beckmann D with m = 0.15 function Diffuse: d = 0.9 Rd = the bidirectional reflectance of for normal incidence copper Ambient: /ia = 0.01 Ii Ra = ~Rd ACM Transactions on Graphics, Vol. l, No. 1, January 1982.

14 20 R.L. and K. E. Torrance Cook I ̧ ̧ ~ ~i i (a) (b) Fig. 6. (a) A copper-colored plastic vase. (b) A copper vase. ACM Transactions on GraphiCs, Vol. 1, No. 1, January 1982.

15 A Reflectance for Computer Graphics 21 Model I TABLE d m Material s 0.7 Carbon 0.40 0.3 0.30 0.6 0.4 Rubber 0.8 0.15 Obsidian 0.2 Lunar dust 0.0 Not used 1.0 0.7 0.50 Olive drab 0.3 0.35 Rust 0.2 0.8 An impinging Metals wave can stimulate electricity. conduct electromagnetic of the near the surface, which in turn leads to reemission motion electrons of wave. There is little depth penetration, and the depth penetration (reflection) a k. increasing of the extinction coefficient values As a result, decreases with from a metal occurs essentially reflection the surface [17]. Thus internal at reflections not present to contribute to a diffuse component, which can be are for a When the rms roughness slope m is small, multiple important nonmetal. entire may be ignored and the also diffuse component disap- surface reflections Figure 6b shows a simulated copper vase. This pears. was generated with figure the parameters. following lights: = CIE standard illuminant D6500 2 Ii -- 0.0001 and 0.0002 du~i s Specular: 1.0 = = the F of a copper mirror reflectance D = Beckmann function with ml = 0.4 = 0.4 wl 0.2 m2 = = 0.6 w2 Diffuse: d = 0.0 the bidirectional reflectance Rd = for copper incidence of normal = Iia Ii Ambient: 0.01 Ra = 7rRd that two values for the rms slope are employed to generate a realistic Note rough surface The specular reflectance component has a copper color. The copper finish. in appearance 6b does not display the plastic vase of the vase in Figure 6a, Figure of that correct treatment of the color a the specular component is needed showing to obtain a realistic nonplastic appearance. Figure 7 vases made of a variety of materials. In every case, the specular shows diffuse (i.e., have the same color and Rd = Fo/Tr). The lighting components to conditions of the vases are identical all the lighting conditions for Figures for 6a and 6b. The six metals were generated with the same parameters used for The Figure for the reflectance spectra. except six nonmetals were generated 6b, with the parameters shown in Table I. ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.

16 22 R.L. and K. E. Torrance Cook 7. A of vases. Fig. variety Fig. 8. A watch. 8 shows a watch made with a variety of materials and surface Figure conditions. It illuminated by a single light source. The is band of the watch is made of outer gold, and the inner band is made of stainless steel. The pattern on the links of the surface outer made by using a rougher was for the interior than for the band border. The light-emitting diodes (LEDs) are standard red 640 nanometer LEDs, same and their was approximated by using a color with the color dominant wavelength. ACM Transactions on Graphics, Vol. 1, No. 1, January 1982.

17 A Reflectance for Computer Graphics 23 Model CONCLUSIONS The can be stated. following conclusions specular 1. usually the color of the material, not the color of component The is may The and specular components diffuse, have source. ambient, the light the material is not different colors if homogeneous. concept bidirectional reflectance is necessary of simulate different light The 2. to materials in the same scene. sources and facet 3. distribution models used by Blinn are easy to calculate and The slope similar slope others in the optics literature. More than one facet very are to can represent combined to function a surface. distribution be of Fresnel The a color shift equation the specular component at 4. predicts angles. Calculating this color shift grazing computationally expensive unless is an procedure or a lookup table is used. approximation The spectral distribution of light reflected from a specific material can 5. energy by together the reflectance model obtained with the spectral energy be using spectrum of source and the reflectance light of the material. distribution the laws of trichromatic color reproduction can be used to convert this The energy distribution to the appropriate RGB values for the particular spectral being used. monitor objects types materials, notably 6. painted of and plastics, have Certain some and diffuse components that do specular have the same color. Metals have not a component with a color determined specular the light source and the by reflectance of the metal. The diffuse component is often negligible for metals. ACKNOWLEDGMENTS The was performed at the Program of Computer Graphics of Cornell work The authors Gary Meyer for the invaluable contributions he University. thank this photometric His color software and to measurements of the made paper. spectral it to accurately convert possible energy distributions into monitors made values. The authors also thank Dr. Donald Greenberg for his helpful RGB and suggestions discussions at every stage of the research. The watch valuable effort 8) result of a joint the with Stuart Sechrest. (Figure was REFERENCES BARKMAN, E. F. Specular and diffuse 1. measurements of aluminum surfaces. In reflectance Appearance Metallic Surfaces, ASTM Special Tech. of 478, American Society for Testing Publ. and Materials, Philadelphia, 1970, pp. 46-58. 2. BECKMANN, AND SPIZZICHINO, A. The Scattering of Electromagnetic Waves from Rough P. MacMillan, York, 1963, pp. 1-33, 70-98. Surfaces. New BENNETT, H. n., AND PORTEUS, J.O. Relation between surface 3. and specular reflec- roughness tance normal incidence. J. Opt. at Am., 51, 2 (1961), 123-129. Soe. 4. BLINN, Z. F., AND NEWELL, M. E. Texture and reflection in computer generated images. Commun. ACM 10 (Oct. 1976), 542-547. 19, synthesized BLINN, Models of light 5. for computer J.F. pictures. Computer Gr. 11, 2 reflection (1977), 192-198. 6. BLINN, J.F. "Coniputer Display of Curved Surfaces." Ph.D. dissertation, Univ. of Utah, Salt Lake 1978. City, ACM Transactions on 1982. Vol. 1, No. 1, January Graphics,

18 24 R.L. and K. E. Torrance Cook CIE INTERNATIONAL ON ILLUMINATION Official recommendations of the interna- 7. COMMISSION on illumination. (E-1.3.1), Publ. CIE 15, Bureau Central de la CIE, tional commission Colorimetry 1970. Paris, Synthesis." Reflection Model for Realistic Image 8. Master's thesis, Cornell Univ., COOK, "A R.L. Ithaca, 1981. H. reflection DAVIES, of electromagnetic waves from a rough surface. Proceedings of the 9. The Electrical (1954), 101 of 209-214. Institution Engineers R.H. G. JANSSEN, GUBAREFF, E., AND TORBORG, G., Thermal Radiation Properties Survey: 10. J. Review of the Literature. Honeywell Research Center, A 1960. Minneapolis, 11. R.S. The Measurement of Appearance. Wiley, New York, 1975, pp. 26-30. HUNTER, and JUDD, AND WYSZECKI, G. Color in Business, Science, B. Industry. Wiley, New York, 12. D. pp. 170-172. 1975, MEYER, G. W. AND GREENBERG, D.P. Perceptual color spaces for computer graphics. Computer 13. 14, (1980), Gr. 254-261. 3 Ph.D. PHONG, for Computer Generated Images." "Illumination dissertation, Univ. of Utah, 14. B.T. Lake City, 1973. Salt Commun. PHONG, Illumination for computer generated pictures. B.T. ACM 18, 6 (June 1975), 15. 311-317. 16. PORTEUS, J.O. Relation between the height distribution of a rough surface and the reflectance at normal J. Opt. Soc. Am. 53, 12 (1963), 1394-1402. incidence. Purdue University, Properties of Matter, vol. 7: Thermal Radiative Properties 17. Thermophysical Plenum, 1970. York, Metals, of New $: University, Properties Purdue Matter, vol. Thermophysical Thermal Radiative Properties 18. of Nonmetallic Solids, Plenum, New York, of 1970. 19. University, Thermophysical Properties of Matter, vol. 9: Thermal Radiative Properties Purdue Coatings, 1970. New York, of Plenum, Transfer. SIEGEL, AND HOWELL, J.R. 20. Radiation Heat R. McGraw-Hill, New York, Thermal 1980, pp. 64-73. 21. SPARROW, E. M. AND CESS, R.D. Radiation Heat Transfer. McGraw-Hill, New York, 1978, pp. 64-68. 22. K. E. AND SPARROW, E.M. Biangular reflectance of an electric nonconductor as a TORRANCE, of Heat and surface roughness. Journal of function Transfer 87, series C (1965), 283- wavelength 292. 23. K. E. AND SPARROW, E. TORRANCE, Theory for off-specular reflection from roughened M. surfaces. J. Opt. Soc. Am. 57, (Sept. 1967), 1105-1114. display. 24. An improved illumination model for shaded T. Commun. ACM 23, 6 (June WHITTED, 1980), 343-349. 25. WHITTED, T. Private communication. Received 1981; revised October 1981; accepted October 1981 August 1982. Transactions on Graphics, Vol. 1, No. 1, January ACM

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